The Complexity of 3-Valued Lukasiewicz Rules
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چکیده
It is known that determining the satisfiability of n-valued ?ukasiewicz rules is NP-complete for n?4, as well as that it can be solved in time linear in the length of the formula in the Boolean case (when n=2). However, the complexity for n=3 is an open problem. In this paper we formally prove that the satisfiability problem for 3-valued ?ukasiewicz rules is NP-complete. Moreover, we also prove that when the consequent of the rule has at most one element, the problem is polynomially solvable URL http://link.springer.com/chapter/10.1007/978-3-319-23240-9_18 [5] Source URL: https://www.iiia.csic.es/en/node/54423 Links [1] https://www.iiia.csic.es/en/bibliography?f[author]=657 [2] https://www.iiia.csic.es/en/staff/felip-many%C3%A0 [3] https://www.iiia.csic.es/en/staff/amanda-vidal [4] https://www.iiia.csic.es/en/staff/mateu-villaret [5] http://link.springer.com/chapter/10.1007/978-3-319-23240-9_18
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It is known that determining the satisfiability of n-valued ?ukasiewicz rules is NP-complete for n?4, as well as that it can be solved in time linear in the length of the formula in the Boolean case (when n=2). However, the complexity for n=3 is an open problem. In this paper we formally prove that the satisfiability problem for 3-valued ?ukasiewicz rules is NP-complete. Moreover, we also prove...
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