
A Refutation of Guinea's "Understanding SAT is in P"
In this work, we summarize and critique the paper "Understanding SAT is ...
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Necessary and sufficient conditions for Boolean satisfiability
The study in this article seeks to find conditions that are necessary an...
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From Hall's Marriage Theorem to Boolean Satisfiability and Back
Motivated by the application of Hall's Marriage Theorem in various LPro...
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Deciding the Closure of Inconsistent Rooted Triples is NPComplete
Interpreting threeleaf binary trees or rooted triples as constraints y...
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A Symbolic SATbased Algorithm for Almostsure Reachability with Small Strategies in POMDPs
POMDPs are standard models for probabilistic planning problems, where an...
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On the tractability of the maximum independent set problem
The maximum independent set problem is a classical NPcomplete problem i...
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Definable isomorphism problem
We investigate the isomorphism problem in the setting of definable sets ...
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About a certain NP complete problem
In this article, we introduce the concept of special decomposition of a set under the given pairs of subsets of that set, and the concept of special covering of a set under such a decomposition. We study the conditions for existence of special coverings of sets, under special decomposition of the set. Such conditions of formulated problem have important applications in the field of satisfiability of functions. Our goal is to study the relationship between sat CNF problem and the problem of existance of special covering of te set. We also study the relationship between classes of computational complexity by searching for special coverings of the sets. We prove, that the decidability of sat CNF problem, in polynomial time reduces to the problem of existence of a special covering of a set. We also prove, that the problem of existence of a special covering of a set, in polynomial time reduces to the decidability of the sat CNF problem. Therefore, the mentioned problems are polynomially equivalent. And then, the problem of existence of a special covering of a set is NPcomplete problem.
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