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\u7684\u60c5\u51b5\uff09\u3002<\/p>\n\n\n\n<p>\u4e3a\u7f13\u89e3\u8fd9\u4e9b\u95ee\u9898\uff0c\u8bb8\u591a\u7814\u7a76\u660e\u786e\u5bf9\u4eba\u7c7b\u884c\u4e3a\u8fdb\u884c\u5efa\u6a21 \u2014\u2014 \u8981\u4e48\u901a\u8fc7\u8f68\u8ff9\u9884\u6d4b [17]\uff0c\u8981\u4e48\u5c06\u5176\u8868\u793a\u4e3a\u9a6c\u5c14\u53ef\u592b\u51b3\u7b56\u8fc7\u7a0b [18]\u2014\u2014 \u5e76\u5c06\u8fd9\u4e9b\u6a21\u578b\u878d\u5165\u7efc\u5408\u6846\u67b6\u3002\u6b64\u5916\uff0c\u4eba\u673a\u65f6\u5e8f\u4ea4\u4e92\uff08HR\u03c9I\uff09\u4e5f\u53ef\u76f4\u63a5\u5efa\u6a21\u4e3a\u968f\u673a\u53cc\u4eba\u535a\u5f08 [19]\u3002\u8fd9\u79cd\u65b9\u5f0f\u867d\u80fd\u901a\u8fc7\u968f\u673a\u6027\u4f53\u73b0\u4eba\u7c7b\u7b56\u7565\u7684\u5c40\u90e8\u53ef\u884c\u6027\uff0c\u4f46\u65e0\u6cd5\u6ee1\u8db3\u4eba\u7c7b\u7b56\u7565\u81ea\u4e3b\u6027\u7684\u9700\u6c42\u3002<\/p>\n\n\n\n<p>\u4e3a\u8fdb\u4e00\u6b65\u63d0\u5347\u4eba\u7c7b\u81ea\u4e3b\u6027\uff0c\u53ef\u91c7\u7528\u57fa\u4e8e \u201c\u53ef\u63a5\u53d7\u6027\u201d \u7684\u65b9\u6cd5 [20][21]\uff1a\u8fd9\u7c7b\u65b9\u6cd5\u80fd\u8ba9\u673a\u5668\u4eba\u5728\u786e\u4fdd\u4efb\u52a1\u5b8c\u6210\u7684\u540c\u65f6\uff0c\u91c7\u7528\u5bf9\u591a\u79cd\u4eba\u7c7b\u884c\u4e3a\u90fd\u5177\u5907\u9c81\u68d2\u6027\u7684\u884c\u4e3a\u3002\u4e0e\u4e4b\u4e0d\u540c\uff0cSchuppe \u7b49\u4eba [22] \u805a\u7126\u4e8e \u201c\u4ea4\u4e92\u5f0f\u5efa\u8bae\u201d\uff1a\u673a\u5668\u4eba\u901a\u8fc7 \u201c\u5047\u8bbe &#8211; \u4fdd\u8bc1\u201d \u5f0f\u6307\u5bfc\u5411\u4eba\u7c7b\u63d0\u4f9b\u5efa\u8bae\uff0c\u4ee5\u6700\u5c11\u7684\u4eba\u7c7b\u534f\u4f5c\u652f\u6301\u5171\u540c\u76ee\u6807\u7684\u8fbe\u6210\u3002\u4f46\u8fd9\u4e9b\u65b9\u6cd5\u5b58\u5728\u5c40\u9650\uff1a\u673a\u5668\u4eba\u9700\u7ed1\u5b9a\u9884\u8ba1\u7b97\u7684\u56fa\u5b9a\u7b56\u7565\uff0c\u4e14\u8981\u4e48\u5bf9\u4eba\u7c7b\u884c\u4e3a\u6709\u4e25\u683c\u5047\u8bbe\uff0c\u8981\u4e48\u4f9d\u8d56\u9759\u6001\u3001\u9884\u5b9a\u4e49\u7684\u5efa\u8bae\u5f62\u5f0f\u3002<\/p>\n\n\n\n<p>\u53e6\u4e00\u7c7b\u76f8\u5173\u7814\u7a76\u4ec5\u4e3a\u673a\u5668\u4eba\u8bbe\u5b9a\uff08\u975e\u53cd\u5e94\u578b\uff09\u903b\u8f91\u89c4\u5212\u76ee\u6807\uff0c\u5e76\u901a\u8fc7 \u201c\u63a7\u5236\u5c4f\u969c\u51fd\u6570\uff08CBF\uff09\u201d \u5728\u673a\u5668\u4eba\u5de5\u4f5c\u7a7a\u95f4\u4e2d\u4fdd\u969c\u4eba\u7c7b\u5b89\u5168 \u2014\u2014 \u63a7\u5236\u5c4f\u969c\u51fd\u6570\u53ef\u4f5c\u4e3a\u5e95\u5c42\u8fde\u7eed\u673a\u5668\u4eba\u52a8\u529b\u5b66\u7684\u5b89\u5168\u8fc7\u6ee4\u5668 [23]\u3002\u8fd1\u5e74\u6765\uff0c\u8be5\u65b9\u6cd5\u88ab\u6574\u5408\u5230\u534f\u4f5c\u5f0f HR\u03c9I \u6846\u67b6\u4e2d [24]-[26]\uff1a\u5728\u8fd9\u4e9b\u6846\u67b6\u4e2d\uff0c\u4eba\u673a\u53cc\u65b9\u7684\uff08\u53cd\u5e94\u578b\uff09\u903b\u8f91\u76ee\u6807\u5747\u4e3a\u5df2\u77e5\uff0c\u56e0\u6b64\u53ef\u901a\u8fc7\u79bb\u7ebf\u96c6\u4e2d\u5f0f\u535a\u5f08\u6c42\u89e3\u3002\u4f46\u4eba\u673a\u5728\u7ebf\u9002\u5e94\u4ec5\u5728\u7269\u7406\u5e95\u5c42\u901a\u8fc7\u63a7\u5236\u5c4f\u969c\u51fd\u6570\u5b9e\u73b0\uff0c\u4e0d\u5b58\u5728\u7b56\u7565\u5c42\u9762\u7684\u81ea\u4e3b\u6027\u3002\u7c7b\u4f3c\u5730\uff0c\u8fd1\u671f\u9488\u5bf9\u4eba\u673a\u4ea4\u4e92\u7684\u52a8\u6001\u535a\u5f08\u7814\u7a76 [27][28] \u4e5f\u805a\u7126\u4e8e\u5373\u65f6\u7269\u7406\u4ea4\u4e92\uff0c\u800c\u975e\u4eba\u673a\u957f\u671f\u7684\u7b56\u7565\u6027\u9002\u5e94\u4e0e\u4ea4\u4e92\u3002<\/p>\n\n\n\n<p>\u4e0e\u4e0a\u8ff0\u65b9\u6cd5\u4e0d\u540c\uff0c\u672c\u6587\u63d0\u51fa\u7684 HR\u03c9I \u65b9\u6cd5\u4ee5 \u201c\u81ea\u4e3b\u6027\u201d \u4e3a\u6838\u5fc3\uff0c\u805a\u7126\u9ad8\u5c42\u7b56\u7565\u6027\u4ea4\u4e92\u3002\u6b64\u524d\u7684\u76f8\u5173\u7814\u7a76 [20]-[22][29][30] \u867d\u4e5f\u5173\u6ce8\u8fd9\u4e00\u65b9\u5411\uff0c\u4f46\u6700\u7ec8\u4f1a\u751f\u6210\u9884\u8ba1\u7b97\u7684\u534f\u4f5c\u6216\u53cd\u9988\u5f62\u5f0f\uff0c\u4e14\u4ec5\u8003\u8651\u6709\u9650\u65f6\u95f4\u8303\u56f4\u7684\u76ee\u6807\uff1b\u800c\u672c\u6587\u6846\u67b6\u901a\u8fc7 \u201c\u5728\u7ebf\u9002\u5e94\u201d \u4e0e \u201c\u53ef\u8c03\u53cd\u9988\u201d \u7684\u534f\u540c\uff0c\u4e3a\u6709\u9650\u548c\u65e0\u9650\u65f6\u95f4\u8303\u56f4\u7684 LTL \u4efb\u52a1\u751f\u6210\u590d\u6742\u7684\u65b0\u5174\u534f\u4f5c\u884c\u4e3a\u3002\u4ece\u5f62\u5f0f\u5316\u89d2\u5ea6\u800c\u8a00\uff0c\u8be5\u65b0\u9896\u6846\u67b6\u7684\u5b9e\u73b0\u4f9d\u8d56\u4e8e \u201c\u03c9- \u6b63\u5219\u535a\u5f08\u201d \u7684\u5bbd\u5bb9\u5f0f\u7b56\u7565\u6a21\u677f [31]\uff08\u7531 LTL \u76ee\u6807\u63a8\u5bfc\u800c\u6765\uff09\uff0c\u8fd9\u79cd\u6a21\u677f\u53ef\u7b80\u6d01\u5730\u8868\u793a\u65e0\u9650\u591a\u79cd\u7b56\u7565\u3002\u7b56\u7565\u6a21\u677f\u5df2\u5728\u591a\u4e2a\u9886\u57df\u5f97\u5230\u5e94\u7528 [32]-[39]\uff0c\u4f46\u636e\u6211\u4eec\u6240\u77e5\uff0c\u672c\u6587\u9996\u6b21\u5c06\u5176\u5e94\u7528\u4e8e HR\u03c9I \u573a\u666f\u3002\u5177\u4f53\u800c\u8a00\uff0c\u6211\u4eec\u501f\u9274\u4e86 [33] \u4e2d\u7684\u6700\u65b0\u6210\u679c \u2014\u2014 \u8be5\u6210\u679c\u53ef\u6355\u6349\u6240\u6709\u80fd\u5728 \u201c\u6700\u5c0f\u534f\u4f5c\u201d \u4e0b\u4fdd\u8bc1 \u03c6\uff08\u4efb\u52a1\u76ee\u6807\uff09\u6ee1\u8db3\u7684\u4eba\u673a\u7b56\u7565\uff0c\u4e3a\u672c\u6587\u63d0\u51fa\u7684 \u201c\u5177\u5907\u5f3a\u5f62\u5f0f\u5316\u4fdd\u969c\u7684\u5728\u7ebf\u9002\u5e94\u201d \u63d0\u4f9b\u4e86\u7406\u8bba\u57fa\u7840\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.2 \u7814\u7a76\u8d21\u732e<\/h3>\n\n\n\n<p>\u672c\u6587\u7684\u6838\u5fc3\u8d21\u732e\u662f\u4e00\u4e2a\u901a\u7528\u7684 HR\u03c9I \u6846\u67b6\uff0c\u8be5\u6846\u67b6\u9002\u7528\u4e8e\u6240\u6709\u7c7b\u578b\u7684 LTL \u4efb\u52a1\uff0c\u4e14\u4e0d\u5047\u8bbe\u4eba\u7c7b\u4f1a\u8fdb\u884c\u7279\u5b9a\u7684\u7b56\u7565\u6027\u534f\u4f5c\u3002\u4ece\u6982\u5ff5\u4e0a\u8bb2\uff0c\u8be5\u6846\u67b6\u8ba9\u673a\u5668\u4eba\u4e0d\u518d\u5c06\u4eba\u673a\u4ea4\u4e92\u4ec5\u89c6\u4e3a \u201c\u9700\u9650\u5236\u7684\u4e0d\u786e\u5b9a\u6027\u6765\u6e90\u201d\uff0c\u800c\u662f\u66f4\u591a\u5730\u5c06\u5176\u89c6\u4e3a \u201c\u53ef\u5229\u7528\u7684\u8d44\u6e90\u201d\u3002\u5728\u6267\u884c\u9ad8\u5c42 LTL \u4efb\u52a1 \u03c6 \u65f6\uff0c\u673a\u5668\u4eba\u7b56\u7565\u5177\u5907\u4e24\u5927\u7279\u70b9\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8fd0\u884c\u65f6\u9002\u5e94\u4eba\u7c7b\u884c\u4e3a\uff1a\u4f8b\u5982\uff0c\u82e5\u4eba\u7c7b\u5e0c\u671b\u5f62\u6210 \u201c\u897f\u5357 &#8211; \u4e1c\u5317\u201d \u65b9\u5411\u7684\u5bf9\u89d2\u7ebf\uff0c\u673a\u5668\u4eba\u4f1a\u987a\u5e94\u8fd9\u4e00\u884c\u4e3a\uff0c\u800c\u975e\u575a\u6301\u5f62\u6210\u53e6\u4e00\u65b9\u5411\u7684\u5bf9\u89d2\u7ebf\uff0c\u4ee5\u5728\u4efb\u4f55\u53ef\u80fd\u7684\u60c5\u51b5\u4e0b\u6700\u5927\u5316\u534f\u4f5c\uff1b<\/li>\n\n\n\n<li>\u4ec5\u5728\u5fc5\u8981\u65f6\u63d0\u4f9b\u7b56\u7565\u6027\u53cd\u9988\uff1a\u5f53\u4ec5\u9760\u673a\u5668\u4eba\u81ea\u8eab\u9002\u5e94\u65e0\u6cd5\u786e\u4fdd \u03c6 \u7684\u63a8\u8fdb\u65f6\uff08\u4f8b\u5982\uff0c\u4eba\u7c7b\u6301\u7eed\u79fb\u9664\u4e2d\u95f4\u79ef\u6728\uff0c\u963b\u788d\u5bf9\u89d2\u7ebf\u5f62\u6210\uff09\uff0c\u673a\u5668\u4eba\u624d\u4f1a\u8bf7\u6c42\u4eba\u7c7b\u505c\u6b62\u8be5\u884c\u4e3a\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u8fd9\u79cd\u8bbe\u8ba1\u80fd\u6700\u5927\u7a0b\u5ea6\u51cf\u5c11\u4eba\u673a\u5e72\u6270\u3001\u63d0\u5347\u534f\u4f5c\u6548\u7387\u3001\u4fdd\u969c\u4eba\u7c7b\u81ea\u4e3b\u6027\uff0c\u540c\u65f6\u82e5\u4eba\u7c7b\u6700\u7ec8\u542c\u4ece\u53cd\u9988\uff0c\u8fd8\u80fd\u786e\u4fdd\u673a\u5668\u4eba\u4efb\u52a1\u7684\u6700\u7ec8\u5b8c\u6210\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u901a\u8fc7\u4eff\u771f\u548c\u673a\u5668\u4eba\u786c\u4ef6\u5b9e\u9a8c\u9a8c\u8bc1\u4e86\u8be5\u65b9\u6cd5\uff1a\u9664\u56fe 1 \u6240\u793a\u7684\u673a\u5668\u4eba\u79ef\u6728\u64cd\u4f5c\u573a\u666f\u5916\uff0c\u8fd8\u5728 Overcooked-AI \u4eff\u771f\u73af\u5883 [40]\uff08\u591a\u667a\u80fd\u4f53\u534f\u4f5c\u89c4\u5212\u7684\u5e38\u7528\u57fa\u51c6\u6d4b\u8bd5\u5e73\u53f0\uff09\u4e2d\u5bf9\u6846\u67b6\u8fdb\u884c\u4e86\u8bc4\u4f30\u3002\u5728\u8be5\u73af\u5883\u4e2d\uff0c\u4eba\u673a\u9700\u53cd\u590d\u6267\u884c\u70f9\u996a\u4efb\u52a1\uff0c\u76ee\u6807\u662f\u6301\u7eed\u5236\u4f5c\u6c64\u54c1\u3002\u53cc\u65b9\u5404\u6709\u72ec\u7acb\u7684 LTL \u4efb\u52a1\uff08\u7f16\u7801\u4e3a\u98df\u8c31\u89c4\u8303\uff09\uff0c\u4e14\u4efb\u52a1\u5f7c\u6b64\u4fdd\u5bc6\u3002\u4eba\u7c7b\u884c\u4e3a\u901a\u8fc7\u6982\u7387\u7b56\u7565\u6a21\u62df\u3002<\/p>\n\n\n\n<p>\u5728\u8fd9\u4e00\u5e94\u7528\u573a\u666f\u4e2d\uff0c\u201c\u03c9- \u6b63\u5219\u89c4\u8303\u201d \u76f8\u6bd4\u5e38\u7528\u7684 \u201c\u53ef\u8fbe\u6027\u4efb\u52a1\u201d \u7684\u4f18\u52bf\u6108\u53d1\u660e\u663e\uff1a\u7531\u4e8e\u53cc\u65b9\u90fd\u9700\u5c3d\u53ef\u80fd\u5236\u4f5c\u7b26\u5408\u81ea\u8eab\u89c4\u8303\u7684\u6c64\u54c1\uff0c\u5373\u4fbf\u89c4\u8303\u51b2\u7a81\uff0c\u4e5f\u53ef\u901a\u8fc7 \u201c\u8f6e\u6d41\u5236\u4f5c\u7b26\u5408\u5404\u81ea\u89c4\u8303\u7684\u6c64\u54c1\u201d \u5b9e\u73b0\u534f\u4f5c\u3002\u5b9e\u9a8c\u8868\u660e\uff0c\u901a\u8fc7\u672c\u6587\u6846\u67b6\u7684\u5728\u7ebf\u9002\u5e94\u4e0e\u53cd\u9988\u673a\u5236\uff0c\u8fd9\u79cd\u76f4\u89c2\u7684\u534f\u4f5c\u884c\u4e3a\u80fd\u81ea\u4e3b\u6d8c\u73b0\u3002\u636e\u6211\u4eec\u6240\u77e5\uff0c\u8be5\u6846\u67b6\u4ea7\u751f\u7684 HR\u03c9I \u65b0\u5174\u884c\u4e3a\u7684\u590d\u6742\u6027\u8fdc\u8d85\u73b0\u6709\u6240\u6709\u65b9\u6cd5\uff0c\u540c\u65f6\u8fd8\u80fd\u63d0\u4f9b\u5f62\u5f0f\u5316\u4fdd\u969c\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2 \u95ee\u9898\u8bbe\u5b9a<\/h2>\n\n\n\n<p>\u672c\u6587\u805a\u7126\u4e8e \u201c\u8f6e\u6d41\u884c\u52a8\u201d \u7684\u4eba\u673a\u4ea4\u4e92\u573a\u666f\uff1a\u673a\u5668\u4eba\u4e0e\u4eba\u7c7b\u5728\u5171\u4eab\u73af\u5883\u4e2d\u4ea4\u66ff\u884c\u52a8\u3002\u7ed9\u5b9a\u673a\u5668\u4eba\u7684\u9ad8\u5c42\u65f6\u5e8f\u4efb\u52a1\uff0c\u672c\u6587\u7684\u76ee\u6807\u662f\u5f00\u53d1\u4e00\u4e2a\u6846\u67b6\uff0c\u8ba9\u673a\u5668\u4eba\u80fd\u57fa\u4e8e\u89c2\u5bdf\u5230\u7684\u4eba\u7c7b\u884c\u4e3a\u5728\u7ebf\u8c03\u6574\u7b56\u7565\uff0c\u5e76\u4ee5\u89c4\u8303\u3001\u53ef\u8c03\u7684\u65b9\u5f0f\u63d0\u4f9b\u53cd\u9988 \u2014\u2014 \u5373\u4fbf\u4eba\u7c7b\u6267\u884c\u72ec\u7acb\u76ee\u6807\u4e14\u5176\u7b56\u7565\u53ef\u80fd\u963b\u788d\u673a\u5668\u4eba\u4efb\u52a1\u63a8\u8fdb\uff0c\u4e5f\u80fd\u786e\u4fdd\u673a\u5668\u4eba\u53ef\u9760\u5b8c\u6210\u4efb\u52a1\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.1 \u53cd\u5e94\u578b\u89c4\u5212\u57df<\/h3>\n\n\n\n<p>\u6211\u4eec\u5c06\u4eba\u673a\u4ea4\u4e92\u5efa\u6a21\u4e3a\u53cd\u5e94\u578b\u89c4\u5212\u57df\\(D=&lt;S, s_0, A, AP, L&gt;\\)\uff0c\u5404\u5143\u7d20\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\(S = S_r \\cup S_h\\)\uff1a\u72b6\u6001\u96c6\u5408\uff0c\u5206\u4e3a\u673a\u5668\u4eba\u72b6\u6001\\(S_r\\)\u548c\u4eba\u7c7b\u72b6\u6001\\(S_h\\)\uff1b<\/li>\n\n\n\n<li>\\(s_0 \\in S\\)\uff1a\u521d\u59cb\u72b6\u6001\uff1b<\/li>\n\n\n\n<li>\\(A = A_r \\cup A_h\\)\uff1a\u52a8\u4f5c\u96c6\u5408\uff08\u5efa\u6a21\u4e3a\u6709\u5411\u8fb9\uff09\uff0c\u5206\u4e3a\u673a\u5668\u4eba\u52a8\u4f5c\\(A_r \\subseteq S_r \\times S_h\\)\u548c\u4eba\u7c7b\u52a8\u4f5c\\(A_h \\subseteq S_h \\times S_r\\)\uff1b<\/li>\n\n\n\n<li>AP\uff1a\u4e0e\u4efb\u52a1\u76f8\u5173\u7684\u547d\u9898\u96c6\u5408\uff0c\u6bcf\u4e2a\u547d\u9898\u5728\u7279\u5b9a\u72b6\u6001\u4e0b\u8981\u4e48\u4e3a \u201c\u771f\u201d\uff0c\u8981\u4e48\u4e3a \u201c\u5047\u201d\uff1b<\/li>\n\n\n\n<li>\\(L: S \\to 2^{AP}\\)\uff1a\u6807\u7b7e\u51fd\u6570\uff0c\u4e3a\u6bcf\u4e2a\u72b6\u6001\u5206\u914d\u4e00\u7ec4 \u201c\u4e3a\u771f\u7684\u547d\u9898\u201d\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u89c4\u5212\u57df\u53ef\u901a\u8fc7 \u201c\u89c4\u5212\u57df\u5b9a\u4e49\u8bed\u8a00\uff08PDDL\uff09\u201d[41] \u63cf\u8ff0 \u2014\u2014 \u8fd9\u662f AI \u89c4\u5212\u9886\u57df\u7684\u6807\u51c6\u8bed\u8a00\u3002\u5728 PDDL \u63cf\u8ff0\u4e2d\uff0c\u201c\u72b6\u6001\u201d \u6355\u6349\u76f8\u5173\u5bf9\u8c61\u53ca\u5176\u4f4d\u7f6e\uff0c\u201c\u52a8\u4f5c\u201d \u901a\u8fc7 \u201c\u524d\u7f6e\u6761\u4ef6\u201d \u548c \u201c\u6548\u679c\u201d \u5b9a\u4e49\u3002<\/p>\n\n\n\n<p>\u89c4\u5212\u57df\u7684 \u201c\u8fd0\u884c\u8f68\u8ff9\u201d\\(\\rho = s_0 s_1 s_2 \\dots\\)\u662f\u65e0\u9650\u72b6\u6001\u5e8f\u5217\uff0c\u6ee1\u8db3\\(s_0\\)\u4e3a\u521d\u59cb\u72b6\u6001\uff0c\u4e14\u5bf9\u6240\u6709\\(i \\geq 0\\)\uff0c\u5b58\u5728\u52a8\u4f5c\u4f7f\u7cfb\u7edf\u4ece\\(s_i\\)\u8f6c\u79fb\u5230\\(s_{i+1}\\)\uff08\u5373\\((s_i, s_{i+1}) \\in A\\)\uff09\u3002\u8fd0\u884c\u8f68\u8ff9\\(\\rho\\)\u4f1a\u751f\u6210 \u201c\u8ff9\u201d\\(L(\\rho) = L(s_0) L(s_1) L(s_2) \\dots\\)\u2014\u2014 \u8fd9\u662f\u4e00\u4e2a\u57fa\u4e8e\\(2^{AP}\\)\u7684\u65e0\u9650\u5b57\u7b26\u4e32\uff0c\u5bf9\u5e94\u8f68\u8ff9\u4e2d\u5404\u72b6\u6001\u7684\u6807\u7b7e\u5e8f\u5217\u3002\u672c\u6587\u5047\u8bbe\u4eba\u673a\u8f6e\u6d41\u884c\u52a8\uff1a\u82e5\\(s_i \\in S_r\\)\uff08\u5f53\u524d\u4e3a\u673a\u5668\u4eba\u72b6\u6001\uff09\uff0c\u5219\\(s_{i+1} \\in S_h\\)\uff08\u4e0b\u4e00\u72b6\u6001\u4e3a\u4eba\u7c7b\u72b6\u6001\uff09\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002<\/p>\n\n\n\n<p>\u673a\u5668\u4eba\u7b56\u7565\\(\\pi_r: S^* S_r \\to A_r\\)\u662f\u4e00\u4e2a\u51fd\u6570\uff1a\u5c06 \u201c\u4ee5\u673a\u5668\u4eba\u72b6\u6001\u7ed3\u5c3e\u7684\u4ea4\u4e92\u5386\u53f2\uff08\u72b6\u6001\u5e8f\u5217\uff09\u201d \u6620\u5c04\u4e3a\u673a\u5668\u4eba\u5e94\u6267\u884c\u7684\u52a8\u4f5c\u3002\u82e5\u5bf9\u6240\u6709\\(i \\geq 0\\)\uff0c\u5f53\\(s_i \\in S_r\\)\u65f6\uff0c\\(s_{i+1} = \\pi_r(s_0 s_1 \\dots s_i)\\)\uff0c\u5219\u8fd0\u884c\u8f68\u8ff9\\(\\rho = s_0 s_1 s_2 \\dots\\)\u79f0\u4e3a \u201c\\(\\pi_r\\)- \u8f68\u8ff9\u201d\u3002\u4eba\u7c7b\u7b56\u7565\\(\\pi_h\\)\u548c \u201c\\(\\pi_h\\)- \u8f68\u8ff9\u201d \u7684\u5b9a\u4e49\u4e0e\u6b64\u7c7b\u4f3c\u3002<\/p>\n\n\n\n<p><strong>\u793a\u4f8b 1<\/strong>\uff1a\u56fe 2 \u5c55\u793a\u4e86 \u201c\u8f6e\u6d41\u4eba\u673a\u4ea4\u4e92\u201d \u53cd\u5e94\u578b\u89c4\u5212\u57df\u7684\u90e8\u5206\u89c6\u56fe\u3002\u6bcf\u4e2a\u5706\u5f62\u8282\u70b9\uff08\u5982 r0\u3001r1\u2026\uff09\u5bf9\u5e94\\(S_r\\)\u4e2d\u7684\u673a\u5668\u4eba\u72b6\u6001\uff0c\u6bcf\u4e2a\u77e9\u5f62\u8282\u70b9\uff08\u5982 h0\u3001h1\u2026\uff09\u5bf9\u5e94\\(S_h\\)\u4e2d\u7684\u4eba\u7c7b\u72b6\u6001\u3002\u8282\u70b9\u5185\u90e8\u7684 3\u00d73 \u7f51\u683c\u4ee3\u8868\u73af\u5883\uff1a\u7ea2\u8272\u65b9\u5757\u4e3a\u4eba\u7c7b\u653e\u7f6e\u7684\u7269\u4f53\uff0c\u84dd\u8272\u5706\u5f62\u4e3a\u673a\u5668\u4eba\u653e\u7f6e\u7684\u7269\u4f53\u3002\u8fb9\u4ee3\u8868\u52a8\u4f5c\u96c6\u5408A\u4e2d\u7684\u52a8\u4f5c\uff0c\u6839\u636e\u8f6e\u6d41\u4ea4\u4e92\u89c4\u5219\u5728\u4eba\u673a\u52a8\u4f5c\u95f4\u4ea4\u66ff\u3002\u4f8b\u5982\uff0c\u4ece\u72b6\u6001 r2 \u5230 h2 \u7684\u8fb9\u4ee3\u8868 \u201c\u673a\u5668\u4eba\u79fb\u9664\uff081,1\uff09\u683c\u5b50\uff08\u5373\u7b2c 1 \u884c\u7b2c 1 \u5217\uff09\u4e2d\u84dd\u8272\u5706\u5f62\u7269\u4f53\u201d \u7684\u52a8\u4f5c\u3002\u56fe 1 \u5c55\u793a\u4e86 Franka \u673a\u68b0\u81c2\u5728\u771f\u5b9e\u573a\u666f\u4e2d\u6267\u884c\u8be5\u52a8\u4f5c\u7684\u753b\u9762\u3002<\/p>\n\n\n\n<p>\u6807\u7b7e\u51fd\u6570L\u53ef\u7528\u4e8e\u6355\u6349AP\u4e2d\u4e0e\u4efb\u52a1\u76f8\u5173\u7684\u547d\u9898\u3002\u4f8b\u5982\uff0c\u8bbe\\(AP = \\{adj, diag, major\\}\\)\uff0c\u5404\u547d\u9898\u542b\u4e49\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>adj\uff1a\u65e0\u4e24\u4e2a\u7269\u4f53\u76f8\u90bb\uff08\u6c34\u5e73\u6216\u5782\u76f4\u65b9\u5411\uff09\uff1b<\/li>\n\n\n\n<li>diag\uff1a\u4e00\u6761\u5bf9\u89d2\u7ebf\u88ab\u5b8c\u5168\u5360\u636e\uff1b<\/li>\n\n\n\n<li>major\uff1a9 \u4e2a\u683c\u5b50\u4e2d\u81f3\u5c11 4 \u4e2a\u88ab\u5360\u636e\uff08\u591a\u6570\u5360\u636e\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5728\u8fd9\u79cd\u5b9a\u4e49\u4e0b\uff0c\u4ec5\u72b6\u6001 r0\u3001t1\u3001t2 \u6ee1\u8db3\\(adj = \u771f\\)\uff1b\u72b6\u6001 r5\u3001t2 \u6ee1\u8db3\\(diag = \u771f\\)\uff1b\u9664 h0 \u548c r0 \u5916\uff0c\u6240\u6709\u72b6\u6001\u5747\u6ee1\u8db3\\(major = \u771f\\)\u3002\u4ece\u521d\u59cb\u72b6\u6001 h0 \u51fa\u53d1\uff0c\u4e00\u4e2a\u53ef\u80fd\u7684\u8fd0\u884c\u8f68\u8ff9\u4e3a\\(\\rho = h0 (r1 h1 r2 h2)^\\omega\\)\uff08\u201c\\(\\omega\\)\u201d \u8868\u793a\u5faa\u73af\uff09\uff0c\u5176\u751f\u6210\u7684\u8ff9\u4e3a\\(L(\\rho) = \\{major\\}^\\omega\\)\uff08\u5373\u6240\u6709\u72b6\u6001\u5747\u6ee1\u8db3 \u201c\u591a\u6570\u5360\u636e\u201d\uff09\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.2 \u4f5c\u4e3a LTL \u516c\u5f0f\u7684\u65f6\u5e8f\u4efb\u52a1<\/h3>\n\n\n\n<p>\u4e3a\u8868\u8fbe\u4eba\u673a\u4efb\u52a1\uff0c\u6211\u4eec\u91c7\u7528 \u201c\u7ebf\u6027\u65f6\u5e8f\u903b\u8f91\uff08LTL\uff09\u201d\u2014\u2014 \u8fd9\u662f\u4e00\u79cd\u5728\u547d\u9898\u903b\u8f91\u57fa\u7840\u4e0a\u6269\u5c55\u4e86\u65f6\u5e8f\u7b97\u5b50\u7684\u89c4\u8303\u8bed\u8a00 [42]\u3002\u7ed9\u5b9a\u539f\u5b50\u547d\u9898\u96c6\u5408AP\uff0cLTL \u516c\u5f0f\u901a\u8fc7\u4ee5\u4e0b\u89c4\u5219\u9012\u5f52\u5b9a\u4e49\uff1a<\/p>\n\n\n\n<p>\\(\\varphi ::= \\top | p | \\neg \\varphi | \\varphi_1 \\land \\varphi_2 | \\bigcirc \\varphi | \\varphi_1 \\mathcal{U} \\varphi_2\\)<\/p>\n\n\n\n<p>\u5176\u4e2d\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\(p \\in AP\\)\uff1a\u539f\u5b50\u547d\u9898\uff1b<\/li>\n\n\n\n<li>\\(\\neg\\)\u3001\\(\\land\\)\uff1a\u5e03\u5c14\u7b97\u5b50\uff08\u5426\u5b9a\u3001\u5408\u53d6\uff09\uff1b<\/li>\n\n\n\n<li>\\(\\bigcirc\\)\u3001\\(\\mathcal{U}\\)\uff1a\u65f6\u5e8f\u7b97\u5b50\uff08\u201c\u4e0b\u4e00\u4e2a\u201d\u3001\u201c\u76f4\u5230\u201d\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5176\u4ed6\u6807\u51c6\u7b97\u5b50\uff08\u5982\u6790\u53d6\\(\\lor\\)\u3001\u8574\u542b\\(\\rightarrow\\)\u3001\u201c\u6700\u7ec8\u201d\\(\\diamond\\)\u3001\u201c\u5168\u5c40\u201d\\(\\square\\)\uff09\u53ef\u7531\u4e0a\u8ff0\u7b97\u5b50\u63a8\u5bfc\u5f97\u51fa\u3002LTL \u516c\u5f0f\u7684\u8bed\u4e49\u57fa\u4e8e\\((2^{AP})^\\omega\\)\u4e2d\u7684\u65e0\u9650\u539f\u5b50\u547d\u9898\u96c6\u5408\u5e8f\u5217\uff0c\u8be6\u7ec6\u5b9a\u4e49\u53ef\u53c2\u8003\u76f8\u5173\u6807\u51c6\u6587\u732e [43, \u7b2c 5.1.2 \u7ae0]\u3002\u82e5\u8fd0\u884c\u8f68\u8ff9\\(\\rho\\)\u751f\u6210\u7684\u8ff9\u6ee1\u8db3 LTL \u516c\u5f0f\\(\\varphi\\)\uff0c\u5219\u79f0\\(\\rho\\)\u6ee1\u8db3\\(\\varphi\\)\uff0c\u8bb0\u4e3a\\(\\rho \\vDash \\varphi\\)\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"362\" src=\"https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/\u622a\u5c4f2025-10-15-21.40.37-1024x362.png\" alt=\"\" class=\"wp-image-274\" srcset=\"https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/\u622a\u5c4f2025-10-15-21.40.37-1024x362.png 1024w, https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/\u622a\u5c4f2025-10-15-21.40.37-300x106.png 300w, https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/\u622a\u5c4f2025-10-15-21.40.37-768x272.png 768w, https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/\u622a\u5c4f2025-10-15-21.40.37.png 1278w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><strong>\u793a\u4f8b 2<\/strong>\uff1a\u518d\u6b21\u8003\u8651\u793a\u4f8b 1 \u4e2d\u7684\u53cd\u5e94\u578b\u89c4\u5212\u57df\uff0c\u539f\u5b50\u547d\u9898\u96c6\u5408\\(AP = \\{adj, diag, major\\}\\)\u3002\u5047\u8bbe\u673a\u5668\u4eba\u4efb\u52a1\u662f \u201c\u53cd\u590d\u5230\u8fbe\u2018\u65e0\u7269\u4f53\u76f8\u90bb\u4e14\u591a\u6570\u683c\u5b50\u88ab\u5360\u636e\u2019\u7684\u72b6\u6001\u201d\uff0c\u8be5\u4efb\u52a1\u53ef\u8868\u793a\u4e3a LTL \u516c\u5f0f\\(\\varphi_r = \\square \\diamond (adj \\land major)\\)\uff08\u201c\\(\\square\\)\u201d \u8868\u793a \u201c\u59cb\u7ec8\u201d\uff0c\u201c\\(\\diamond\\)\u201d \u8868\u793a \u201c\u6700\u7ec8\u201d\uff09\u3002\u4eba\u7c7b\u4efb\u52a1\u53ef\u80fd\u662f \u201c\u53cd\u590d\u5230\u8fbe\u2018\u5bf9\u89d2\u7ebf\u88ab\u5b8c\u5168\u5360\u636e\u2019\u7684\u72b6\u6001\u201d\uff0c\u53ef\u8868\u793a\u4e3a\\(\\varphi_h = \\square \\diamond diag\\)\u3002\u82e5\u8fd0\u884c\u8f68\u8ff9\u53cd\u590d\u7ecf\u8fc7\u72b6\u6001 t1\uff0c\u5219\u8be5\u8f68\u8ff9\u540c\u65f6\u6ee1\u8db3\\(\\varphi_r\\)\u548c\\(\\varphi_h\\)\uff1b\u82e5\u8f68\u8ff9\u6700\u7ec8\u4ec5\u5728\u72b6\u6001 t2 \u5faa\u73af\uff0c\u5219\u4ec5\u6ee1\u8db3\\(\\varphi_r\\)\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2.3 \u95ee\u9898\u63cf\u8ff0<\/h3>\n\n\n\n<p>\u672c\u6587\u7814\u7a76\u7684\u4eba\u673a\u4ea4\u4e92\u573a\u666f\u4e2d\uff0c\u53cc\u65b9\u5404\u6709\u72ec\u7acb\u4efb\u52a1\u4e14\u5f7c\u6b64\u672a\u77e5\u3002\u5728\u8fd9\u7c7b\u573a\u666f\u4e2d\uff0c\u5373\u4fbf\u5e76\u975e\u6545\u610f\uff0c\u4e00\u65b9\u7684\u7b56\u7565\u4e5f\u53ef\u80fd\u963b\u788d\u53e6\u4e00\u65b9\u7684\u4efb\u52a1\u63a8\u8fdb\u3002\u672c\u6587\u7684\u76ee\u6807\u662f\u5f00\u53d1\u4e00\u4e2a\u6846\u67b6\uff0c\u8ba9\u673a\u5668\u4eba\u80fd\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u57fa\u4e8e\u5c40\u90e8\u89c2\u5bdf\u8c03\u6574\u7b56\u7565\uff1b<\/li>\n\n\n\n<li>\u5728\u5fc5\u8981\u65f6\u5411\u4eba\u7c7b\u63d0\u4f9b\u53cd\u9988\uff1b<\/li>\n\n\n\n<li>\u6700\u7ec8\u6301\u7eed\u5b8c\u6210\u81ea\u8eab\u4efb\u52a1\u3002<\/li>\n<\/ol>\n\n\n\n<p><strong>\u95ee\u9898 1<\/strong>\uff1a\u7ed9\u5b9a \u201c\u4eba\u673a\u4ea4\u4e92\u53cd\u5e94\u578b\u89c4\u5212\u57dfD\u201d \u53ca \u201c\u673a\u5668\u4eba\u7684 LTL \u4efb\u52a1\\(\\varphi\\)\u201d\uff0c\u4e14\u4eba\u7c7b\u6267\u884c\u672a\u77e5\u7684\u6f5c\u5728\u4efb\u52a1\uff0c\u9700\u5f00\u53d1\u4e00\u4e2a\u6846\u67b6\u6ee1\u8db3\u4ee5\u4e0b\u8981\u6c42\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6355\u6349\u6240\u6709\u80fd\u8ba9\u673a\u5668\u4eba\u5b8c\u6210\\(\\varphi\\)\u7684\u4eba\u7c7b\u534f\u4f5c\u884c\u4e3a\uff1b<\/li>\n\n\n\n<li>\u57fa\u4e8e\u4ea4\u4e92\u8fc7\u7a0b\u4e2d\u89c2\u5bdf\u5230\u7684\u4eba\u7c7b\u7b56\u7565\u884c\u4e3a\uff0c\u8c03\u6574\u673a\u5668\u4eba\u7b56\u7565\uff1b<\/li>\n\n\n\n<li>\u6574\u5408\u53ef\u8c03\u53cd\u9988\u673a\u5236\uff0c\u5728\u9700\u8981\u65f6\u5411\u4eba\u7c7b\u63d0\u4f9b\u53cd\u9988\uff0c\u4ee5\u63a8\u8fdb\u673a\u5668\u4eba\u4efb\u52a1\u5b8c\u6210\u3002<\/li>\n<\/ol>\n\n\n\n<p><strong>\u793a\u4f8b 3<\/strong>\uff1a\u518d\u6b21\u8003\u8651\u793a\u4f8b 1 \u4e2d\u7684\u4ea4\u4e92\u573a\u666f\uff0c\u673a\u5668\u4eba\u4efb\u52a1\u4e3a\u793a\u4f8b 2 \u4e2d\u7684\\(\\varphi_r = \\square \\diamond (adj \\land major)\\)\u3002\u5047\u8bbe\u4eba\u7c7b\u4e3a\u5b9e\u73b0\u81ea\u8eab\u6f5c\u5728\u4efb\u52a1\uff0c\u53cd\u590d\u6cbf\u5bf9\u89d2\u7ebf\u653e\u7f6e\u7269\u4f53\u3002\u4ece\u673a\u5668\u4eba\u89c6\u89d2\u770b\uff0c\u8fd9\u79cd\u4eba\u7c7b\u884c\u4e3a\u53ef\u80fd\u4f7f\u8fd0\u884c\u8f68\u8ff9\u6ee1\u8db3\\(\\varphi_r\\)\uff0c\u56e0\u6b64\u673a\u5668\u4eba\u5e94\u5229\u7528\u8fd9\u79cd\uff08\u975e\u6545\u610f\u7684\uff09\u4eba\u7c7b\u534f\u4f5c\u6765\u5b8c\u6210\u4efb\u52a1\u3002<\/p>\n\n\n\n<p>\u4f46\u673a\u5668\u4eba\u65e0\u6cd5\u901a\u8fc7 \u201c\u9884\u5148\u7ed1\u5b9a\u5355\u4e00\u7b56\u7565\u201d \u6765\u786e\u4fdd\\(\\varphi_r\\)\u7684\u6ee1\u8db3\uff08\u65e0\u8bba\u4eba\u7c7b\u884c\u4e3a\u5982\u4f55\uff09\u3002\u4f8b\u5982\uff0c\u82e5\u673a\u5668\u4eba\u9884\u5148\u9009\u62e9 \u201c\u901a\u8fc7 t1 \u72b6\u6001\u7684\u914d\u7f6e\u6ee1\u8db3\\(\\varphi_r\\)\u201d \u7684\u56fa\u5b9a\u7b56\u7565\uff0c\u800c\u4eba\u7c7b\u4ecd\u575a\u6301\u6cbf\u5bf9\u89d2\u7ebf\u653e\u7f6e\u7269\u4f53\uff0c\u53cc\u65b9\u4ea4\u4e92\u4f1a\u9677\u5165\u5faa\u73af\uff0c\\(\\varphi_r\\)\u6c38\u8fdc\u65e0\u6cd5\u6ee1\u8db3\u3002\u76f8\u53cd\uff0c\u673a\u5668\u4eba\u9700\u901a\u8fc7\u5c40\u90e8\u89c2\u5bdf\u8bc6\u522b \u201c\u4eba\u7c7b\u7cfb\u7edf\u6027\u6cbf\u5bf9\u89d2\u7ebf\u653e\u7f6e\u7269\u4f53\u201d \u8fd9\u4e00\u884c\u4e3a\uff0c\u5e76\u81ea\u4e3b\u9009\u62e9\u80fd\u5bfc\u5411 t2 \u72b6\u6001\u7684\u52a8\u4f5c \u2014\u2014t2 \u72b6\u6001\u7684\u914d\u7f6e\u65e2\u80fd\u5bb9\u7eb3\u4eba\u7c7b\u7684\u5bf9\u89d2\u7ebf\u653e\u7f6e\u884c\u4e3a\uff0c\u53c8\u80fd\u6ee1\u8db3\\(\\varphi_r\\)\u3002\u5f53\u7136\uff0c\u8fd9\u4e00\u8fc7\u7a0b\u7684\u524d\u63d0\u662f\\(\\varphi_r\\)\u4e0e\u4eba\u7c7b\u6f5c\u5728\u4efb\u52a1\u53ef\u540c\u65f6\u6ee1\u8db3\u3002<\/p>\n\n\n\n<p>\u82e5\u53cc\u65b9\u76ee\u6807\u51b2\u7a81\uff0c\u4ec5\u9760\u673a\u5668\u4eba\u9002\u5e94\u4eba\u7c7b\u884c\u4e3a\u4e0d\u8db3\u4ee5\u89e3\u51b3\u95ee\u9898\u3002\u4f8b\u5982\uff0c\u5047\u8bbe\u4eba\u7c7b\u6301\u7eed\u6267\u884c \u201ch2\u2192r3\u201d \u548c \u201ch3\u2192r4\u201d \u7684\u52a8\u4f5c\uff0c\u6b64\u65f6\u673a\u5668\u4eba\u9700\u8bc6\u522b\u51fa \u201c\u4eba\u7c7b\u884c\u4e3a\u5df2\u65e0\u6cd5\u7528\u4e8e\uff08\u975e\u6545\u610f\u7684\uff09\u534f\u4f5c\u201d\uff0c\u5e76\u5411\u4eba\u7c7b\u63d0\u4f9b\u53cd\u9988 \u2014\u2014 \u4f8b\u5982\uff0c\u8bf7\u6c42\u4eba\u7c7b\u79fb\u9664\uff082,2\uff09\u683c\u5b50\u4e2d\u7684\u7269\u4f53\uff08\u901a\u8fc7\u6267\u884c \u201ch3\u2192t1\u201d \u52a8\u4f5c\uff09\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3 \u57fa\u4e8e\u5bbd\u5bb9\u5f0f\u7b56\u7565\u6a21\u677f\u7684\u9002\u5e94\u4e0e\u53cd\u9988\u673a\u5236<\/h2>\n\n\n\n<p>\u4e3a\u5206\u6790\u673a\u5668\u4eba\u9488\u5bf9 LTL \u4efb\u52a1\u7684\u7b56\u7565\u884c\u4e3a\uff0c\u6211\u4eec\u9996\u5148\u5c06 \u201c\u89c4\u5212\u57df + LTL \u4efb\u52a1\u201d \u8f6c\u5316\u4e3a \u201c\u4eba\u673a\u53cc\u4eba\u535a\u5f08\u201d\uff08\u8fd9\u662f\u8be5\u9886\u57df\u7684\u5e38\u7528\u65b9\u6cd5 [43]\uff09\uff0c\u968f\u540e\u5229\u7528\u56fe\u535a\u5f08\u4e2d\u6700\u65b0\u63d0\u51fa\u7684 \u201c\u5bbd\u5bb9\u5f0f\u7b56\u7565\u6a21\u677f\u201d[31][32] \u89e3\u51b3\u4e0a\u8ff0\u95ee\u9898 1\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.1 \u03c9- \u6b63\u5219\u535a\u5f08<\/h3>\n\n\n\n<p>\u4f5c\u4e3a\u7b2c\u4e00\u6b65\uff0c\u6211\u4eec\u5f15\u5165 \u201c\u53cc\u4eba\uff08\u8f6e\u6d41\u884c\u52a8\uff09\u03c9- \u6b63\u5219\u535a\u5f08\u201d \u7684\u6982\u5ff5\uff0c\u8be5\u6982\u5ff5\u662f\u672c\u6587\u6846\u67b6\u7684\u57fa\u7840\u3002<\/p>\n\n\n\n<p><strong>\u5b9a\u4e49 1<\/strong>\uff1a\u53cc\u4eba\uff08\u8f6e\u6d41\u884c\u52a8\uff09\u03c9- \u6b63\u5219\u535a\u5f08\u662f\u4e00\u4e2a\u4e8c\u5143\u7ec4\\(G = &lt;D, \\Omega&gt;\\)\uff0c\u5176\u4e2d\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\(D = &lt;S, s_0, A, AP, L>\\)\uff1a\u53cd\u5e94\u578b\u89c4\u5212\u57df\uff08\u5b9a\u4e49\u89c1 2.1 \u8282\uff09\uff1b<\/li>\n\n\n\n<li>\\(\\Omega \\subseteq S^\\omega\\)\uff1a\u65e0\u9650\u72b6\u6001\u5e8f\u5217\u7684 \u03c9- \u6b63\u5219\u96c6\u5408\uff0c\u5b9a\u4e49\u4e86\u535a\u5f08\u7684 \u201c\u83b7\u80dc\u6761\u4ef6\u201d\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u7c7b \u03c9- \u6b63\u5219\u535a\u5f08\u53ef\u6807\u51c6\u5730\u8868\u793a\u4e3a \u201cparity \u535a\u5f08\u201d[43]\u3002Parity \u535a\u5f08\u662f \u03c9- \u6b63\u5219\u535a\u5f08\u7684\u4e00\u79cd\u7279\u6b8a\u5f62\u5f0f\uff0c\u5176\u83b7\u80dc\u6761\u4ef6\\(\\Omega = Parity[c]\\)\u7531 \u201c\u7740\u8272\u51fd\u6570\u201d\\(c: S \\to \\mathbb{N}\\)\u5b9a\u4e49 \u2014\u2014 \u8be5\u51fd\u6570\u4e3a\u6bcf\u4e2a\u72b6\u6001\u5206\u914d\u4e00\u4e2a\u81ea\u7136\u6570\uff08\u989c\u8272\uff09\u3002\u82e5\u8fd0\u884c\u8f68\u8ff9\\(\\rho\\)\u4e2d \u201c\u65e0\u9650\u6b21\u51fa\u73b0\u7684\u6700\u5927\u989c\u8272\u4e3a\u5076\u6570\u201d\uff0c\u5219\\(\\rho \\in Parity[c]\\)\u3002\u901a\u8fc7\u6807\u51c6\u6280\u672f [43]\uff0c\u53ef\u5c06 \u201c\u89c4\u5212\u57df + LTL \u4efb\u52a1\u201d \u8f6c\u5316\u4e3a parity \u535a\u5f08\uff0c\u5177\u4f53\u5f62\u5f0f\u5316\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p><strong>\u547d\u9898 1<\/strong>\uff1a\u7ed9\u5b9a\u53cd\u5e94\u578b\u89c4\u5212\u57dfD\u548c\u57fa\u4e8eAP\u7684 LTL \u516c\u5f0f\\(\\varphi\\)\uff0c\u53ef\u6784\u9020 parity \u535a\u5f08\\(G = &lt;D&#8217;, \\Omega&gt;\\)\uff0c\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>D\u7684\u8fd0\u884c\u8f68\u8ff9\u4e0e\\(D&#8217;\\)\u7684\u8fd0\u884c\u8f68\u8ff9\u5b58\u5728\u4e00\u4e00\u5bf9\u5e94\u5173\u7cfb\uff1b<\/li>\n\n\n\n<li>D\u7684\u8fd0\u884c\u8f68\u8ff9\\(\\rho\\)\u6ee1\u8db3\\(\\varphi\\)\uff0c\u5f53\u4e14\u4ec5\u5f53\\(D&#8217;\\)\u4e2d\u5bf9\u5e94\u7684\u8fd0\u884c\u8f68\u8ff9\\(\\rho&#8217;\\)\u5c5e\u4e8e\\(\\Omega\\)\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">3.2 \u5bbd\u5bb9\u5f0f\u7b56\u7565\u6a21\u677f<\/h3>\n\n\n\n<p>\u5728\u53cc\u4eba\u535a\u5f08\u4e2d\uff0c\u201c\u7b56\u7565\u6a21\u677f\u201d \u901a\u8fc7\u5bf9\u667a\u80fd\u4f53\u52a8\u4f5c\u7684\u5c40\u90e8\u7ea6\u675f\uff0c\u7b80\u6d01\u5730\u8868\u793a\u65e0\u9650\u591a\u4e2a\u7b56\u7565\uff0c\u662f\u5bf9 \u201c\u7b56\u7565\u201d \u6982\u5ff5\u7684\u6269\u5c55\u3002\u5f62\u5f0f\u5316\u800c\u8a00\uff0c\u667a\u80fd\u4f53i\u7684\u7b56\u7565\u6a21\u677f\\(\\Pi_i\\)\u5305\u542b\u4ee5\u4e0b\u4e09\u7c7b\u7ea6\u675f\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e0d\u5b89\u5168\u52a8\u4f5c\\(U \\subseteq A_i\\)\uff1a\u667a\u80fd\u4f53\u7981\u6b62\u6267\u884c\u7684\u52a8\u4f5c\uff1b<\/li>\n\n\n\n<li>\u5171\u6d3b\u52a8\u4f5c\\(Co \\subseteq A_i\\)\uff1a\u5728\u4efb\u4f55\u8fd0\u884c\u8f68\u8ff9\u4e2d\uff0c\u667a\u80fd\u4f53\u6700\u591a\u6267\u884c\u6709\u9650\u6b21\u7684\u52a8\u4f5c\uff1b<\/li>\n\n\n\n<li>\u6d3b\u7ec4\\(H \\subseteq 2^{A_i}\\)\uff1a\u52a8\u4f5c\u96c6\u5408\uff0c\u82e5\u67d0\u6d3b\u7ec4\\(H \\in H\\)\u7684\u6e90\u72b6\u6001\u88ab\u65e0\u9650\u6b21\u8bbf\u95ee\uff0c\u5219\u667a\u80fd\u4f53\u5fc5\u987b\u65e0\u9650\u6b21\u6267\u884c\u8be5\u6d3b\u7ec4\u4e2d\u7684\u81f3\u5c11\u4e00\u4e2a\u52a8\u4f5c\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u82e5\u8fd0\u884c\u8f68\u8ff9\\(\\rho\\)\u6ee1\u8db3\u7b56\u7565\u6a21\u677f\\(\\Pi_i\\)\u7684\u6240\u6709\u7ea6\u675f\uff0c\u5219\u79f0\\(\\rho\\)\u201c\u7b26\u5408\u201d\\(\\Pi_i\\)\u3002\u82e5\u6240\u6709\\(\\pi_i\\)- \u8f68\u8ff9\u5747\u7b26\u5408\\(\\Pi_i\\)\uff0c\u5219\u79f0\u7b56\u7565\\(\\pi_i\\)\u201c\u9075\u5faa\u201d\\(\\Pi_i\\)\uff0c\u8bb0\u4e3a\\(\\pi_i \\vDash \\Pi_i\\)\u3002\u5173\u4e8e\u7b56\u7565\u6a21\u677f\u7684\u8be6\u7ec6\u5f62\u5f0f\u5316\u5b9a\u4e49\u53ca\u66f4\u591a\u89e3\u91ca\uff0c\u53ef\u53c2\u8003 [31]\u3002<\/p>\n\n\n\n<p>\u6700\u65b0\u7814\u7a76 [33] \u8868\u660e\uff1a\u5728\u4eba\u673a parity \u535a\u5f08\u4e2d\uff0c\u53ef\u5408\u6210\u4e00\u5bf9\u7b56\u7565\u6a21\u677f\\((\\Pi_r, \\Pi_h)\\)\uff08\u5206\u522b\u5bf9\u5e94\u673a\u5668\u4eba\u548c\u4eba\u7c7b\uff09\uff0c\u5176\u4e2d\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\(\\Pi_h\\)\u6355\u6349\u6240\u6709\u80fd\u5b9e\u73b0\u534f\u4f5c\u7684\u4eba\u7c7b\u884c\u4e3a\uff1b<\/li>\n\n\n\n<li>\\(\\Pi_r\\)\u5305\u542b\u6240\u6709 \u201c\u80fd\u5bf9\u6297\u534f\u4f5c\u4eba\u7c7b\u884c\u4e3a\u3001\u786e\u4fdd\u83b7\u80dc\u6761\u4ef6\u6ee1\u8db3\u201d \u7684\u673a\u5668\u4eba\u7b56\u7565\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong>\u547d\u9898 2<\/strong>\uff1a\u7ed9\u5b9a parity \u535a\u5f08\\(G = (D, \\Omega)\\)\uff0c\u53ef\u5408\u6210\u673a\u5668\u4eba\u4e0e\u4eba\u7c7b\u7684\u7b56\u7565\u6a21\u677f\u5bf9\\((\\Pi_r, \\Pi_h)\\)\uff0c\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6240\u6709\u5c5e\u4e8e\\(\\Omega\\)\u7684\u8fd0\u884c\u8f68\u8ff9\\(\\rho\\)\u5747\u7b26\u5408\\(\\Pi_h\\)\uff1b<\/li>\n\n\n\n<li>\u6240\u6709\u9075\u5faa\\(\\Pi_r\\)\u7684\u7b56\u7565\\(\\pi_r\\)\uff08\u5373\\(\\pi_r \\vDash \\Pi_r\\)\uff09\u5747\u80fd\u786e\u4fdd\uff1a\u6240\u6709\u7b26\u5408\\(\\Pi_h\\)\u7684\\(\\pi_r\\)- \u8f68\u8ff9\u5747\u5c5e\u4e8e\\(\\Omega\\)\u3002<\/li>\n<\/ol>\n\n\n\n<p><strong>\u793a\u4f8b 4<\/strong>\uff1a\u9488\u5bf9\u56fe 2 \u4e2d \u201c\u673a\u5668\u4eba\u4efb\u52a1\u4e3a\\(\\varphi_r = \\square \\diamond (adj \\land major)\\)\u201d \u7684\u7f51\u683c\u4e16\u754c\u573a\u666f\uff0c\u53ef\u6839\u636e\u547d\u9898 1 \u6784\u9020 parity \u535a\u5f08 \u2014\u2014 \u8be5\u535a\u5f08\u4e0e\u56fe 2 \u4e2d\u7684\u89c4\u5212\u57df\u7ed3\u6784\u76f8\u540c\uff0c\u4f46\u9700\u4e3a\u5404\u72b6\u6001\u5206\u914d\u9002\u5f53\u7684\u989c\u8272\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6ee1\u8db3 \u201c\\(adj \\land major\\)\u201d \u7684\u72b6\u6001\uff08\u5373\u65e0\u7269\u4f53\u76f8\u90bb\u4e14\u591a\u6570\u683c\u5b50\u88ab\u5360\u636e\uff09\u5206\u914d\u989c\u8272 2\uff08\u5076\u6570\uff09\uff1b<\/li>\n\n\n\n<li>\u5176\u4ed6\u72b6\u6001\u5206\u914d\u989c\u8272 1\uff08\u5947\u6570\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u79cd\u7740\u8272\u65b9\u5f0f\u6355\u6349\u4e86\u673a\u5668\u4eba\u7684\u76ee\u6807 \u2014\u2014 \u53cd\u590d\u5230\u8fbe \u201c\u65e0\u7269\u4f53\u76f8\u90bb\u4e14\u591a\u6570\u683c\u5b50\u88ab\u5360\u636e\u201d \u7684\u72b6\u6001\u3002\u901a\u8fc7\u547d\u9898 2 \u4e2d\u7684\u5408\u6210\u8fc7\u7a0b\uff0c\u53ef\u8ba1\u7b97\u5f97\u5230\u4eba\u673a\u7b56\u7565\u6a21\u677f\u5bf9\\((\\Pi_r, \\Pi_h)\\)\uff0c\u4ee5\u6355\u6349\u534f\u4f5c\u884c\u4e3a\u3002\u4f8b\u5982\uff0c\u4eba\u7c7b\u7b56\u7565\u6a21\u677f\\(\\Pi_h\\)\u5305\u542b\u6d3b\u7ec4\\(\\{h3 \\to t1\\}\\)\uff08\u56fe 2 \u4e2d\u7eff\u8272\u865a\u7ebf\u6240\u793a\u7684\u5176\u4ed6\u6d3b\u7ec4\u4e5f\u5305\u542b\u5728\u5185\uff09\uff0c\u8fd9\u4e00\u7ea6\u675f\u786e\u4fdd\u4eba\u7c7b\u4e0d\u4f1a\u6301\u7eed\u963b\u788d\u673a\u5668\u4eba\u4efb\u52a1\u63a8\u8fdb\uff08\u5982\u793a\u4f8b 3 \u4e2d\u6240\u8ff0\uff09\u3002\u7c7b\u4f3c\u5730\uff0c\u673a\u5668\u4eba\u7b56\u7565\u6a21\u677f\\(\\Pi_r\\)\u5305\u542b\u7684\u6d3b\u7ec4\u53ef\u786e\u4fdd\uff1a\u53ea\u8981\u4eba\u7c7b\u9075\u5faa\\(\\Pi_h\\)\uff0c\u673a\u5668\u4eba\u5c31\u80fd\u59cb\u7ec8\u5230\u8fbe\u6ee1\u8db3 \u201c\\(adj \\land major\\)\u201d \u7684\u72b6\u6001\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.3 \u9002\u5e94\u4e0e\u53cd\u9988\u673a\u5236<\/h3>\n\n\n\n<p>\u547d\u9898 2 \u7684\u7ed3\u679c\u4e3a \u201c\u6355\u6349\u534f\u4f5c\u884c\u4e3a\u201d\uff08\u5373\u95ee\u9898 1 \u7684\u8981\u6c42 1\uff09\u63d0\u4f9b\u4e86\u57fa\u7840\uff0c\u4f46\u5e76\u672a\u76f4\u63a5\u89e3\u51b3 \u201c\u9002\u5e94\u201d \u548c \u201c\u53cd\u9988\u201d \u95ee\u9898\uff08\u5373\u95ee\u9898 1 \u7684\u8981\u6c42 2 \u548c 3\uff09\u3002\u4e3a\u6b64\uff0c\u672c\u6587\u63d0\u51fa\u4ee5\u4e0b\u6846\u67b6\uff1a\u5229\u7528\u7b56\u7565\u6a21\u677f\\((\\Pi_r, \\Pi_h)\\)\u7684\u5bbd\u5bb9\u6027\uff0c\u8ba9\u673a\u5668\u4eba\u57fa\u4e8e\\(\\Pi_r\\)\u8c03\u6574\u7b56\u7565\uff0c\u5e76\u57fa\u4e8e\\(\\Pi_h\\)\u5411\u4eba\u7c7b\u63d0\u4f9b\u53cd\u9988\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">3.3.1 \u9002\u5e94\u673a\u5236<\/h4>\n\n\n\n<p>\u7531\u4e8e\\(\\Pi_r\\)\u4e3a\u6bcf\u4e2a\u72b6\u6001\u63d0\u4f9b\u4e86\u4e00\u7ec4\u53ef\u9009\u52a8\u4f5c\uff0c\u673a\u5668\u4eba\u65e0\u9700\u9884\u5148\u7ed1\u5b9a\u5355\u4e00\u7b56\u7565\u3002\u76f8\u53cd\uff0c\u5728\u8fd0\u884c\u65f6\uff0c\u673a\u5668\u4eba\u4f1a\u4ece\u5f53\u524d\u72b6\u6001\u7684\\(\\Pi_r\\)\u5141\u8bb8\u52a8\u4f5c\u96c6\u4e2d\u968f\u673a\u9009\u62e9\u52a8\u4f5c\u3002\u8fd9\u79cd\u65b9\u5f0f\u8ba9\u673a\u5668\u4eba\u5728\u518d\u6b21\u8bbf\u95ee\u540c\u4e00\u72b6\u6001\u65f6\uff0c\u80fd\u8c03\u6574\u52a8\u4f5c\u9009\u62e9\u3002\u5177\u4f53\u800c\u8a00\uff0c\u82e5\u673a\u5668\u4eba\u67d0\u6b21\u9009\u62e9\u7684\u52a8\u4f5c\u672a\u5e26\u6765\u7406\u60f3\u7ed3\u679c\uff08\u5982\u4eba\u7c7b\u8868\u73b0\u51fa\u4e0d\u534f\u4f5c\u884c\u4e3a\uff09\uff0c\u8fd0\u884c\u8f68\u8ff9\u6700\u7ec8\u4f1a\u56de\u5230\u540c\u4e00\u72b6\u6001\uff0c\u6b64\u65f6\u673a\u5668\u4eba\u53ef\u901a\u8fc7\u968f\u673a\u6027\u4ece\\(\\Pi_r\\)\u7684\u5141\u8bb8\u52a8\u4f5c\u96c6\u4e2d\u9009\u62e9\u5176\u4ed6\u52a8\u4f5c\u3002\u8be5\u9002\u5e94\u673a\u5236\u53ef\u6709\u6548\u6ee1\u8db3\u95ee\u9898 1 \u7684\u8981\u6c42 2\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">3.3.2 \u53cd\u9988\u673a\u5236<\/h4>\n\n\n\n<p>\u4e3a\u5b9e\u73b0\u95ee\u9898 1 \u8981\u6c42 3 \u4e2d\u7684 \u201c\u53ef\u8c03\u53cd\u9988\u673a\u5236\u201d\uff0c\u672c\u6587\u5f15\u5165\u53cd\u9988\u9608\u503c\\(\\alpha \\in [0,1]\\)\u2014\u2014 \u8be5\u9608\u503c\u51b3\u5b9a\u673a\u5668\u4eba\u5411\u4eba\u7c7b\u63d0\u4f9b\u53cd\u9988\u7684\u9891\u7387\u3002\u9700\u6ce8\u610f\u4ee5\u4e0b\u89c4\u5219\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e8e\\(\\Pi_h\\)\u4e2d\u7684 \u201c\u4e0d\u5b89\u5168\u52a8\u4f5c\u201d\uff1a\u8fd9\u7c7b\u52a8\u4f5c\u662f\u4eba\u7c7b\u4e3a\u786e\u4fdd\u673a\u5668\u4eba\u4efb\u52a1\u5b8c\u6210\u5fc5\u987b\u907f\u514d\u7684\u52a8\u4f5c\uff0c\u56e0\u6b64\u53ea\u8981\u5f53\u524d\u72b6\u6001\u5b58\u5728\u4e0d\u5b89\u5168\u52a8\u4f5c\uff0c\u673a\u5668\u4eba\u4f1a\u7acb\u5373\u544a\u77e5\u4eba\u7c7b\uff1b<\/li>\n\n\n\n<li>\u5bf9\u4e8e\\(\\Pi_h\\)\u4e2d\u7684 \u201c\u5171\u6d3b\u52a8\u4f5c\u201d \u548c \u201c\u6d3b\u7ec4\u201d\uff1a\u673a\u5668\u4eba\u4f1a\u89c2\u5bdf\u4eba\u7c7b\u52a8\u4f5c\uff0c\u7edf\u8ba1\u4eba\u7c7b\u8fdd\u53cd\u8fd9\u4e9b\u7ea6\u675f\u7684\u9891\u7387\uff08\u5373\u6267\u884c\u5171\u6d3b\u52a8\u4f5c\u3001\u6216\u907f\u514d\u6267\u884c\u6d3b\u7ec4\u4e2d\u52a8\u4f5c\u7684\u6b21\u6570\u5360\u6bd4\uff09\u3002\u5f53\u8fdd\u53cd\u9891\u7387\u8d85\u8fc7\\(\\alpha\\)\u65f6\uff0c\u673a\u5668\u4eba\u4ece\u4e0b\u4e00\u65f6\u523b\u5f00\u59cb\u63d0\u4f9b\u53cd\u9988\uff0c\u76f4\u81f3\u8fdd\u53cd\u9891\u7387\u4f4e\u4e8e\\(\\alpha\\)\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u6839\u636e\u547d\u9898 2\uff0c\u53ea\u8981\u4eba\u7c7b\u9075\u5faa\\(\\Pi_h\\)\uff0c\u673a\u5668\u4eba\u7b56\u7565\u5c31\u80fd\u786e\u4fdd\u4efb\u52a1\u5b8c\u6210\u3002\u8fd9\u79cd\u53cd\u9988\u673a\u5236\u8ba9\u673a\u5668\u4eba\u4ec5\u5728\u4eba\u7c7b\u884c\u4e3a\u663e\u8457\u504f\u79bb\\(\\Pi_h\\)\u6355\u6349\u7684\u534f\u4f5c\u884c\u4e3a\u65f6\uff0c\u624d\u63d0\u4f9b\u53cd\u9988\uff0c\u53ef\u6709\u6548\u6ee1\u8db3\u95ee\u9898 1 \u7684\u8981\u6c42 3\u3002<\/p>\n\n\n\n<p><strong>\u793a\u4f8b 5<\/strong>\uff1a\u5ef6\u7eed\u793a\u4f8b 4 \u7684\u573a\u666f\uff0c\u673a\u5668\u4eba\u53ef\u5728\u8fd0\u884c\u65f6\u901a\u8fc7 \u201c\u4ece\\(\\Pi_r\\)\u5141\u8bb8\u52a8\u4f5c\u96c6\u4e2d\u968f\u673a\u9009\u62e9\u52a8\u4f5c\u201d \u8c03\u6574\u7b56\u7565\u3002\u4f8b\u5982\uff0c\u82e5\u4eba\u7c7b\u5982\u793a\u4f8b 3 \u6240\u8ff0\u6301\u7eed\u6cbf\u5bf9\u89d2\u7ebf\u653e\u7f6e\u7269\u4f53\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5047\u8bbe\u673a\u5668\u4eba\u5f53\u524d\u5904\u4e8e\u72b6\u6001 h0\uff0c\u4e14\u539f\u672c\u8ba1\u5212\u901a\u8fc7 t1 \u72b6\u6001\u7684\u914d\u7f6e\u63a8\u8fdb\u4efb\u52a1\uff1b<\/li>\n\n\n\n<li>\u82e5\u4eba\u7c7b\u7ee7\u7eed\u6cbf\u5bf9\u89d2\u7ebf\u653e\u7f6e\u7269\u4f53\uff08\u5373\u6267\u884c \u201ch0\u2192r1\u201d \u52a8\u4f5c\uff0c\u8be5\u52a8\u4f5c\u8fdd\u53cd\\(\\Pi_h\\)\u4e2d\u7684\u6d3b\u7ec4\\(\\{h0\u2192r0\\}\\)\uff09\uff0c\u673a\u5668\u4eba\u4f1a\u8c03\u6574\u7b56\u7565\uff0c\u9009\u62e9\u5bfc\u5411 t2 \u72b6\u6001\u7684\u52a8\u4f5c \u2014\u2014t2 \u72b6\u6001\u7684\u914d\u7f6e\u65e2\u80fd\u5bb9\u7eb3\u4eba\u7c7b\u7684\u5bf9\u89d2\u7ebf\u653e\u7f6e\u884c\u4e3a\uff0c\u53c8\u80fd\u6ee1\u8db3\\(\\varphi_r\\)\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u518d\u8003\u8651\u53e6\u4e00\u79cd\u573a\u666f\uff1a\u82e5\u4eba\u7c7b\u4e3a\u5b9e\u73b0\u81ea\u8eab\u6f5c\u5728\u4efb\u52a1\uff0c\u6301\u7eed\u6267\u884c \u201ch2\u2192r3\u201d \u548c \u201ch3\u2192r4\u201d \u52a8\u4f5c\uff08\u5982\u793a\u4f8b 3 \u6240\u8ff0\uff0c\u8be5\u884c\u4e3a\u4f1a\u963b\u788d\u673a\u5668\u4eba\u4efb\u52a1\uff09\u3002\u5f53\u4eba\u7c7b\u8fdd\u53cd\u6d3b\u7ec4\u7ea6\u675f\u7684\u9891\u7387\u8d85\u8fc7\u53cd\u9988\u9608\u503c\\(\\alpha\\)\u65f6\uff0c\u673a\u5668\u4eba\u4f1a\u5411\u4eba\u7c7b\u63d0\u4f9b\u53cd\u9988\uff0c\u8bf7\u6c42\u5176\u6267\u884c\u6d3b\u7ec4\u52a8\u4f5c \u201ch3\u2192t1\u201d\u2014\u2014 \u8be5\u52a8\u4f5c\u80fd\u5e2e\u52a9\u673a\u5668\u4eba\u63a8\u8fdb\\(\\varphi_r\\)\u7684\u5b8c\u6210\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">4 \u5b9e\u9a8c<\/h2>\n\n\n\n<p>\u6211\u4eec\u5728\u4e24\u4e2a\u5b9e\u9a8c\u573a\u666f\u4e2d\u8bc4\u4f30\u4e86\u6240\u63d0\u6846\u67b6\uff0c\u4ee5\u4f53\u73b0\u8be5\u65b0\u9896 HR\u03c9I \u6846\u67b6\u7684\u4e0d\u540c\u4f18\u52bf\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u79ef\u6728\u64cd\u4f5c\u573a\u666f<\/strong>\uff1a\u5728\u7269\u7406\u673a\u5668\u4eba\u5e73\u53f0\u4e0a\u9a8c\u8bc1\u65b9\u6cd5\uff0c\u573a\u666f\u5982\u56fe 1 \u6240\u793a\uff08\u5bf9\u5e94\u793a\u4f8b 1-5\uff09\u3002\u8be5\u573a\u666f\u4e3a \u201c\u89c2\u5bdf\u673a\u5668\u4eba\u5982\u4f55\u57fa\u4e8e\u4eba\u7c7b\u52a8\u4f5c\u5728\u7ebf\u8c03\u6574\u7b56\u7565\u3001\u5e76\u5728\u4eba\u7c7b\u963b\u788d\u4efb\u52a1\u8d85\u8fc7\u9608\u503c\u65f6\u63d0\u4f9b\u53ef\u8c03\u53cd\u9988\u201d \u63d0\u4f9b\u4e86\u53ef\u89e3\u91ca\u7684\u6d4b\u8bd5\u5e73\u53f0\uff1b<\/li>\n\n\n\n<li><strong>Overcooked-AI \u73af\u5883<\/strong>\uff1a\u8fd9\u662f\u534f\u4f5c\u89c4\u5212\u7684\u6807\u51c6\u57fa\u51c6\u6d4b\u8bd5\u5e73\u53f0 [40]\uff0c\u53ef\u4f53\u73b0 \u201c\u6307\u5bfc\u4e0e\u9002\u5e94\u80fd\u529b\u201d \u5728 \u201c\u81ea\u4e3b\u6d8c\u73b0\u590d\u6742\u4eba\u673a\u7b56\u7565\u6027\u4ea4\u4e92\u201d \u4e2d\u7684\u4f5c\u7528\u3002\u5c24\u5176\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u03c9- \u6b63\u5219\u89c4\u8303\u7684\u5929\u7136\u7ed3\u6784\u8ba9\u6211\u4eec\u80fd\u7814\u7a76 \u201c\u4eba\u673a\u4efb\u52a1\u4ece\u5b8c\u5168\u4e00\u81f4\u5230\u90e8\u5206 \/ \u5b8c\u5168\u51b2\u7a81\u201d \u7b49\u4e0d\u540c\u96be\u5ea6\u4e0b\u7684\u65b0\u5174\u4ea4\u4e92\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u8fd9\u4e24\u4e2a\u5b9e\u9a8c\u5171\u540c\u8868\u660e\uff1a\u8be5\u65b9\u6cd5\u5728\u7b26\u53f7\u57df\u4e2d\u5177\u5907\u900f\u660e\u5ea6\uff0c\u4e14\u80fd\u5728\u8fd0\u884c\u65f6\u81ea\u4e3b\u751f\u6210\u8fdc\u8d85\u73b0\u6709\u65b9\u6cd5\u80fd\u529b\u7684\u590d\u6742\u4eba\u673a\u7b56\u7565\u6027\u4ea4\u4e92\u3002<\/p>\n\n\n\n<p><strong>\u6ce8 1<\/strong>\uff1aSchuppe \u7b49\u4eba [22] \u4e5f\u7814\u7a76\u4e86 \u201c\u673a\u5668\u4eba\u5411\u4eba\u7c7b\u63d0\u4f9b\u5efa\u8bae\u201d \u7684\u4eba\u673a\u4ea4\u4e92\u573a\u666f\uff08\u201cFollow My Advice\u201d\uff0cFMA\uff09\uff0c\u4f46\u5176\u65b9\u6cd5\u805a\u7126\u4e8e \u201c\u4e3a\u4eba\u7c7b\u8ba1\u7b97\u5145\u5206\u5047\u8bbe\u201d\uff0c\u5e76\u57fa\u4e8e\u9884\u8ba1\u7b97\u7684\u673a\u5668\u4eba\u7b56\u7565\u8bbe\u8ba1\u9759\u6001\u53cd\u9988\u673a\u5236\uff0c\u4ee5\u5b9e\u73b0\u6709\u9650\u65f6\u95f4\u8303\u56f4\u7684\u76ee\u6807\u3002\u4e0e\u4e4b\u4e0d\u540c\uff0c\u672c\u6587\u6846\u67b6\u5f3a\u8c03 \u201c\u673a\u5668\u4eba\u7b56\u7565\u57fa\u4e8e\u4eba\u7c7b\u884c\u4e3a\u7684\u5728\u7ebf\u9002\u5e94\u201d\uff0c\u5e76\u91c7\u7528\u53ef\u8c03\u53cd\u9988\u673a\u5236\u5904\u7406\u6301\u7eed\u7684 \u03c9- \u6b63\u5219\u76ee\u6807 \u2014\u2014 \u8fd9\u4e00\u70b9\u5df2\u5728\u4e0b\u6587\u5b9e\u9a8c\u4e2d\u5f97\u5230\u9a8c\u8bc1\u3002\u82e5\u8981\u5c06\u4e24\u79cd\u65b9\u6cd5\u76f4\u63a5\u5bf9\u6bd4\uff0c\u9700\u5c06\u672c\u6587\u573a\u666f\u91cd\u6784\u4e3a\u6709\u9650\u65f6\u95f4\u8303\u56f4\u4efb\u52a1\uff0c\u4f46\u8fd9\u4f1a\u524a\u5f31\u672c\u6587\u6846\u67b6 \u201c\u805a\u7126\u9002\u5e94\u4e0e\u53cd\u9988\u534f\u540c\u4ee5\u5b9e\u73b0\u6301\u7eed\u76ee\u6807\u201d \u7684\u6838\u5fc3\u4ef7\u503c\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.1 \u7f51\u683c\u4e16\u754c\u79ef\u6728\u64cd\u4f5c<\/h3>\n\n\n\n<p>\u5728\u8be5\u5b9e\u9a8c\u4e2d\uff0c\u6211\u4eec\u5728 Franka Emika Panda \u673a\u68b0\u81c2\uff08\u8fd0\u884c ROS Jazzy \u7cfb\u7edf\uff09\u4e0a\u5b9e\u73b0\u4e86\u7b80\u5316\u7684\u7f51\u683c\u4e16\u754c\u79ef\u6728\u64cd\u4f5c\u573a\u666f\uff0c\u4ee5\u9a8c\u8bc1\u6846\u67b6\u5728\u62bd\u8c61\u6a21\u578b\u4e4b\u5916\u7684\u53ef\u884c\u6027\u3002\u5b9e\u9a8c\u8bbe\u7f6e\u5982\u4e0b\uff1a\u673a\u68b0\u81c2\u5728 3\u00d73 \u5de5\u4f5c\u7a7a\u95f4\u5185\u64cd\u4f5c\u5b9e\u4f53\u79ef\u6728\uff08\u53ef\u653e\u7f6e\u6216\u79fb\u9664\uff09\uff0c\u4e0e\u793a\u4f8b 1 \u4e2d\u63cf\u8ff0\u7684\u72b6\u6001\u5b8c\u5168\u5bf9\u5e94\u3002\u4eba\u7c7b\u901a\u8fc7\u653e\u7f6e\u7ea2\u8272\u79ef\u6728\u4e0e\u5de5\u4f5c\u7a7a\u95f4\u4ea4\u4e92\uff0c\u673a\u5668\u4eba\u5219\u653e\u7f6e\u84dd\u8272\u79ef\u6728\u3002\u7cfb\u7edf\u4f1a\u5b9e\u65f6\u76d1\u6d4b\u79ef\u6728\u914d\u7f6e\uff0c\u5e76\u8bc4\u4f30\u673a\u5668\u4eba\u4efb\u52a1\u89c4\u8303\uff08\u5982 \u201c\u4fdd\u6301\u79ef\u6728\u4e0d\u76f8\u90bb\u201d\uff09\u662f\u5426\u5f53\u524d\u6ee1\u8db3\u3002<\/p>\n\n\n\n<p>\u8be5\u6f14\u793a\u80cc\u540e\u7684\u53cd\u5e94\u578b\u89c4\u5212\u57df\u5305\u542b\u7ea6 7000 \u4e2a\u72b6\u6001\u548c 18 \u4e2a\u547d\u9898\uff0c\u7f16\u7801\u4e86 \u201c\u4eba\u673a\u7269\u4f53\u7684\u6240\u6709\u53ef\u80fd\u653e\u7f6e\u65b9\u5f0f\u201d \u53ca \u201c\u5408\u6cd5\u7684\u8f6e\u6d41\u52a8\u4f5c\u201d\u3002\u6211\u4eec\u7684\u5b9e\u73b0\u9700\u7ea6 6 \u79d2\u5b8c\u6210 parity \u535a\u5f08\u7684\u6784\u9020\u548c\u7b56\u7565\u6a21\u677f\u7684\u5408\u6210\uff08\u8be5\u8fc7\u7a0b\u5728\u6267\u884c\u524d\u79bb\u7ebf\u5b8c\u6210\uff09\u3002\u5728\u6267\u884c\u9636\u6bb5\uff0c\u673a\u5668\u4eba\u9075\u5faa\u81ea\u9002\u5e94\u7b56\u7565\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u57fa\u4e8e\u89c2\u5bdf\u5230\u7684\u4eba\u7c7b\u52a8\u4f5c\u66f4\u65b0\u81ea\u8eab\u52a8\u4f5c\uff1b<\/li>\n\n\n\n<li>\u5f53\u4eba\u7c7b\u884c\u4e3a\u53ef\u80fd\u963b\u788d\u4efb\u52a1\u5b8c\u6210\u65f6\uff08\u5982\u793a\u4f8b 3 \u6240\u8ff0\uff09\uff0c\u901a\u8fc7\u663e\u793a\u5c4f\u751f\u6210\u53cd\u9988\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u56fe 1 \u5c55\u793a\u4e86\u8be5\u5b9e\u9a8c\u8bbe\u7f6e\u7684\u5b9e\u7269\u56fe\uff0c\u4f53\u73b0\u4e86\u62bd\u8c61\u57df\u5728\u771f\u5b9e\u4e16\u754c\u4e2d\u7684\u5b9e\u73b0\u65b9\u5f0f\u3002\u8be5\u5b9e\u9a8c\u8868\u660e\uff0c\u6211\u4eec\u7684\u6846\u67b6\u80fd\u4ece\u5f62\u5f0f\u5316\u6a21\u578b\u6269\u5c55\u5230\u771f\u5b9e\u573a\u666f\uff0c\u4e3a\u8bc4\u4f30 \u201c\u9002\u5e94\u80fd\u529b\u201d \u548c \u201c\u4eba\u7c7b\u53cd\u9988\u201d \u63d0\u4f9b\u4e86\u53ef\u89e3\u91ca\u7684\u6d4b\u8bd5\u5e73\u53f0\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.2 Overcooked-AI<\/h3>\n\n\n\n<p>\u6211\u4eec\u5728 Overcooked-AI \u73af\u5883 [40]\uff08\u591a\u667a\u80fd\u4f53\u534f\u4f5c\u89c4\u5212\u7684\u5e38\u7528\u57fa\u51c6\u6d4b\u8bd5\u5e73\u53f0\uff09\u4e2d\u8fdb\u4e00\u6b65\u8bc4\u4f30\u4e86\u6846\u67b6\u3002\u5728\u8be5\u73af\u5883\u4e2d\uff0c\u4eba\u673a\u9700\u53cd\u590d\u6267\u884c\u70f9\u996a\u4efb\u52a1\uff0c\u76ee\u6807\u662f\u6301\u7eed\u5236\u4f5c\u6c64\u54c1\u3002\u53cc\u65b9\u5404\u6709\u72ec\u7acb\u7684 LTL \u4efb\u52a1\uff08\u7f16\u7801\u4e3a\u98df\u8c31\u89c4\u8303\uff09\uff0c\u4e14\u4efb\u52a1\u5f7c\u6b64\u4fdd\u5bc6\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">4.2.1 \u5b9e\u9a8c\u573a\u666f\u8bbe\u8ba1<\/h4>\n\n\n\n<p>\u6211\u4eec\u8bbe\u8ba1\u4e86\u4e09\u7c7b\u5b9e\u9a8c\u573a\u666f\uff0c\u4ee5 \u201c\u4eba\u673a\u98df\u8c31\u7684\u5173\u7cfb\u201d \u4e3a\u533a\u5206\u6807\u51c6\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5b8c\u5168\u4e00\u81f4<\/strong>\uff1a\u4eba\u673a\u98df\u8c31\u76f8\u540c\uff0c\u53cc\u65b9\u5728\u4e0d\u77e5\u60c5\u7684\u60c5\u51b5\u4e0b\u6267\u884c\u540c\u4e00\u4efb\u52a1\uff1b<\/li>\n\n\n\n<li><strong>\u517c\u5bb9<\/strong>\uff1a\u4eba\u673a\u98df\u8c31\u4e0d\u540c\uff0c\u4f46\u5b58\u5728\u81f3\u5c11\u4e00\u79cd\u6c64\u54c1\u80fd\u540c\u65f6\u6ee1\u8db3\u53cc\u65b9\u89c4\u8303\uff1b<\/li>\n\n\n\n<li><strong>\u51b2\u7a81<\/strong>\uff1a\u4eba\u673a\u98df\u8c31\u4e0d\u540c\uff0c\u4e14\u4e0d\u5b58\u5728\u4efb\u4f55\u80fd\u540c\u65f6\u6ee1\u8db3\u53cc\u65b9\u89c4\u8303\u7684\u6c64\u54c1\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u8fd9\u4e09\u7c7b\u573a\u666f\u6db5\u76d6\u4e86 \u201c\u4eba\u673a\u4efb\u52a1\u4ece\u5b8c\u5168\u4e00\u81f4\u5230\u5b8c\u5168\u51b2\u7a81\u201d \u7684\u4e0d\u540c\u9519\u4f4d\u7a0b\u5ea6\u3002\u8868 1 \u603b\u7ed3\u4e86\u5b9e\u9a8c\u4e2d\u4f7f\u7528\u7684\u98df\u8c31\u914d\u7f6e\u3002<\/p>\n\n\n\n<p><strong>\u8868 1 Overcooked-AI \u5b9e\u9a8c\u4e2d\u7684\u98df\u8c31\u914d\u7f6e<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u573a\u666f<\/th><th>\u673a\u5668\u4eba\u98df\u8c31<\/th><th>\u4eba\u7c7b\u98df\u8c31<\/th><\/tr><\/thead><tbody><tr><td>\u5b8c\u5168\u4e00\u81f4<\/td><td>\u9700 3 \u4e2a\u6d0b\u8471<\/td><td>\u9700 3 \u4e2a\u6d0b\u8471<\/td><\/tr><tr><td>\u51b2\u7a81<\/td><td>\u9700 3 \u4e2a\u6d0b\u8471<\/td><td>\u9700 2 \u4e2a\u6d0b\u8471<\/td><\/tr><tr><td>\u517c\u5bb9<\/td><td>\u9700 2 \u4e2a\u6d0b\u8471\uff08\u5207\u534a\uff09<\/td><td>\u9700 2 \u4e2a\u6d0b\u8471\uff08\u6574\u4e2a\uff09<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">4.2.2 \u73af\u5883\u5efa\u6a21\u4e0e\u5b9e\u9a8c\u6d41\u7a0b<\/h4>\n\n\n\n<p>Overcooked-AI \u73af\u5883\u5929\u7136\u9002\u5408 \u201c\u6301\u7eed\u4efb\u52a1\u201d \u7684\u5b9e\u73b0 \u2014\u2014 \u4eba\u673a\u9700\u53cd\u590d\u5b8c\u6210\u98df\u8c31\u3002\u6bcf\u4e2a\u98df\u8c31\u89c4\u8303\u5bf9\u5e94\u4e00\u4e2a \u03c9- \u6b63\u5219\u76ee\u6807\uff1a\u82e5\u8fd0\u884c\u8f68\u8ff9\u4e2d \u201c\u7b26\u5408\u8981\u6c42\u7684\u98df\u8c31\u88ab\u65e0\u9650\u6b21\u6267\u884c\u201d\uff0c\u5219\u8be5\u8f68\u8ff9\u6ee1\u8db3\u4efb\u52a1\u3002\u8fd9\u4e00\u7279\u6027\u8ba9\u6211\u4eec\u4e0d\u4ec5\u80fd\u8bc4\u4f30 \u201c\u5355\u4e00\u76ee\u6807\u662f\u5426\u8fbe\u6210\u201d\uff0c\u8fd8\u80fd\u8bc4\u4f30 \u201c\u4eba\u673a\u4efb\u52a1\u662f\u5426\u80fd\u6301\u7eed\u6ee1\u8db3\u201d\u3002<\/p>\n\n\n\n<p>\u6211\u4eec\u6309\u7167 2.1 \u8282\u7684\u5b9a\u4e49\uff0c\u5c06 Overcooked-AI \u73af\u5883\u5efa\u6a21\u4e3a\u53cd\u5e94\u578b\u89c4\u5212\u57df\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u72b6\u6001<\/strong>\uff1a\u7f16\u7801 \u201c\u4eba\u673a\u4f4d\u7f6e\u201d\u201c\u98df\u6750\u4f4d\u7f6e\u201d\u201c\u6c64\u54c1\u70f9\u996a\u72b6\u6001\u201d\uff1b<\/li>\n\n\n\n<li><strong>\u52a8\u4f5c<\/strong>\uff1a\u5bf9\u5e94\u53cc\u65b9\u53ef\u6267\u884c\u7684 \u201c\u79fb\u52a8\u201d \u548c \u201c\u4ea4\u4e92\u6307\u4ee4\u201d\uff1b<\/li>\n\n\n\n<li><strong>\u03c9- \u6b63\u5219\u4efb\u52a1<\/strong>\uff1a\u901a\u8fc7 \u201c\u72b6\u6001\u4e0a\u7684 parity \u6761\u4ef6\u201d \u5b9a\u4e49\uff08\u53ef\u4ece\u98df\u8c31\u89c4\u8303\u63a8\u5bfc\u5f97\u51fa\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8be5\u57df\u5305\u542b\u7ea6 68000 \u4e2a\u72b6\u6001\u548c 200 \u591a\u4e2a\u547d\u9898\uff08\u7f16\u7801\u73af\u5883\u76f8\u5173\u7279\u5f81\uff09\u3002\u6211\u4eec\u901a\u8fc7\u547d\u9898 2 \u4e2d\u7684\u5408\u6210\u8fc7\u7a0b\uff0c\u8ba1\u7b97\u5f97\u5230\u4eba\u673a\u7b56\u7565\u6a21\u677f\u5bf9\\((\\Pi_r, \\Pi_h)\\)\uff08\u6355\u6349\u534f\u4f5c\u884c\u4e3a\uff09\u2014\u2014 \u8be5\u8fc7\u7a0b\u9700\u7ea6 3 \u5206\u949f\uff08\u6267\u884c\u524d\u79bb\u7ebf\u5b8c\u6210\uff09\u3002\u6267\u884c\u9636\u6bb5\uff0c\u673a\u5668\u4eba\u6309\u7167 3.3 \u8282\u63cf\u8ff0\u7684 \u201c\u9002\u5e94\u4e0e\u53cd\u9988\u673a\u5236\u201d \u8fd0\u884c\uff0c\u4eba\u7c7b\u884c\u4e3a\u5219\u901a\u8fc7 \u201c\u7b26\u5408\u5176\u98df\u8c31\u7684\u6982\u7387\u7b56\u7565\u201d \u6a21\u62df\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">4.2.3 \u5b9e\u9a8c\u53c2\u6570\u4e0e\u6307\u6807<\/h4>\n\n\n\n<p>\u6211\u4eec\u5728\u4e09\u7c7b\u573a\u666f\u4e2d\uff0c\u5206\u522b\u91c7\u7528\u4e0d\u540c\u7684\u53cd\u9988\u9608\u503c\\(\\alpha\\)\uff08\u8303\u56f4\u4e3a 0.00-0.10\uff09\u8fdb\u884c\u5b9e\u9a8c\u3002\u6bcf\u4e2a\u573a\u666f\u7684\u5b9e\u9a8c\u6d41\u7a0b\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8fd0\u884c\u7cfb\u7edf\u76f4\u81f3\u4ea4\u4ed8 10 \u4efd\u6c64\u54c1\uff1b<\/li>\n\n\n\n<li>\u6bcf\u6b21\u8fd0\u884c\u6700\u591a 500 \u6b65\u52a8\u4f5c\uff0c\u6267\u884c\u65f6\u95f4\u7ea6 1 \u5206\u949f\uff1b<\/li>\n\n\n\n<li>\u4e3a\u6d88\u9664 \u201c\u4eba\u673a\u52a8\u4f5c\u9009\u62e9\u968f\u673a\u6027\u201d \u7684\u5f71\u54cd\uff0c\u6bcf\u4e2a\u573a\u666f\u91cd\u590d\u8fd0\u884c 10 \u6b21\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u6bcf\u6b21\u8fd0\u884c\u4e2d\uff0c\u6211\u4eec\u8bb0\u5f55\u4ee5\u4e0b\u6307\u6807\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7b26\u5408\u673a\u5668\u4eba\u98df\u8c31\u7684\u6c64\u54c1\u5360\u6bd4\uff1b<\/li>\n\n\n\n<li>\u7b26\u5408\u4eba\u7c7b\u98df\u8c31\u7684\u6c64\u54c1\u5360\u6bd4\uff1b<\/li>\n\n\n\n<li>\u540c\u65f6\u7b26\u5408\u53cc\u65b9\u98df\u8c31\u7684\u6c64\u54c1\u5360\u6bd4\uff1b<\/li>\n\n\n\n<li>\u673a\u5668\u4eba\u63d0\u4f9b\u53cd\u9988\u7684\u9891\u7387\u3002<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"482\" height=\"936\" src=\"https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/\u622a\u5c4f2025-10-15-21.40.57.png\" alt=\"\" class=\"wp-image-275\" srcset=\"https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/\u622a\u5c4f2025-10-15-21.40.57.png 482w, https:\/\/smartaiunion.com\/wp-content\/uploads\/2025\/10\/\u622a\u5c4f2025-10-15-21.40.57-154x300.png 154w\" sizes=\"auto, (max-width: 482px) 100vw, 482px\" \/><\/figure>\n\n\n\n<p>\u56fe 3 \u5c55\u793a\u4e86\u6240\u6709\u573a\u666f\u4e2d\u8fd9\u4e9b\u6307\u6807\u7684\u65f6\u95f4\u6f14\u5316\u8fc7\u7a0b\uff0c\u4f53\u73b0\u4e86 \u201c\u9002\u5e94\u80fd\u529b\u201d \u548c \u201c\u53cd\u9988\u201d \u5bf9 \u201c\u6301\u7eed\u4efb\u52a1\u6ee1\u8db3\u201d \u7684\u5f71\u54cd\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">4.2.4 \u5b9e\u9a8c\u7ed3\u679c\u5206\u6790<\/h4>\n\n\n\n<h5 class=\"wp-block-heading\">\uff081\uff09\u5b8c\u5168\u4e00\u81f4\u573a\u666f<\/h5>\n\n\n\n<p>\u5728\u8be5\u573a\u666f\u4e2d\uff0c\u4eba\u673a\u5728\u4e0d\u77e5\u60c5\u7684\u60c5\u51b5\u4e0b\u6267\u884c\u76f8\u540c\u98df\u8c31\u89c4\u8303\u3002\u5982\u56fe 3\uff08a\uff09\u6240\u793a\uff0c\u6240\u6709\u8fd0\u884c\u4e2d\uff0c\u4eba\u673a\u98df\u8c31\u5747\u80fd\u6301\u7eed\u6ee1\u8db3\uff0c\u4e14\u673a\u5668\u4eba\u4ece\u672a\u63d0\u4f9b\u53cd\u9988\u3002\u8fd9\u4e00\u7ed3\u679c\u4f53\u73b0\u4e86 \u201c\u9002\u5e94\u80fd\u529b\u201d \u7684\u4f18\u52bf\uff1a\u5373\u4fbf\u4eba\u673a\u521d\u59cb\u91c7\u7528\u4e0d\u540c\u7b56\u7565\u6267\u884c\u540c\u4e00\u98df\u8c31\uff0c\u673a\u5668\u4eba\u4e5f\u80fd\u901a\u8fc7\u5728\u7ebf\u8c03\u6574\uff0c\u4f7f\u53cc\u65b9\u884c\u4e3a\u81ea\u7136\u5bf9\u9f50\u3002\u82e5\u7cfb\u7edf\u7f3a\u4e4f\u9002\u5e94\u80fd\u529b\uff0c\u53ef\u80fd\u9700\u8981\u901a\u8fc7\u53cd\u9988\u534f\u8c03\u53cc\u65b9\u7b56\u7565\uff1b\u800c\u6211\u4eec\u7684\u6846\u67b6\u80fd\u8ba9\u534f\u4f5c\u5728\u8fd0\u884c\u65f6\u81ea\u4e3b\u6d8c\u73b0\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u4e00\u7ed3\u679c\u4e5f\u51f8\u663e\u4e86\u672c\u6587\u6846\u67b6\u76f8\u6bd4 [22] \u4e2d 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\u201c\u53cc\u65b9\u98df\u8c31\u6700\u7ec8\u5747\u80fd\u88ab\u65e0\u9650\u6b21\u6267\u884c\u201d \u5373\u53ef\u6ee1\u8db3\u8981\u6c42\u3002\u56e0\u6b64\uff0c\u4eba\u673a\u53ef\u901a\u8fc7 \u201c\u8f6e\u6d41\u5236\u4f5c\u7b26\u5408\u5404\u81ea\u98df\u8c31\u7684\u6c64\u54c1\u201d \u5b9e\u73b0\u534f\u4f5c\u3002\u56fe 3\uff08b\uff09\u8868\u660e\uff0c\u8fd9\u79cd\u76f4\u89c2\u7684\u534f\u4f5c\u884c\u4e3a\u786e\u5b9e\u80fd\u81ea\u4e3b\u6d8c\u73b0\uff0c\u4e14\u53d7\u53cd\u9988\u9608\u503c\\(\\alpha\\)\u5f71\u54cd\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5f53\\(\\alpha\\)\u589e\u5927\u65f6\uff0c\u673a\u5668\u4eba\u5bf9 \u201c\u4eba\u7c7b\u4e0d\u534f\u4f5c\u884c\u4e3a\u201d \u7684\u5bb9\u5fcd\u5ea6\u63d0\u9ad8\uff0c\u5bfc\u81f4 \u201c\u7b26\u5408\u4eba\u7c7b\u98df\u8c31\u7684\u6c64\u54c1\u5360\u6bd4\u201d \u4e0a\u5347\uff0c\u201c\u7b26\u5408\u673a\u5668\u4eba\u98df\u8c31\u7684\u6c64\u54c1\u5360\u6bd4\u201d \u4e0b\u964d\uff1b<\/li>\n\n\n\n<li>\u5f53\\(\\alpha = 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