WebJul 2, 2004 · The first remarkable such dichotomy theorem was proved by Schaefer in 1978. It concerns the class of generalized satisfiability problems SAT(S), whose input is a CNF(S) ... WebSchaefer’s Dichotomy Theorem Schaefer’s dichotomy theorem: Replace Boolean Or by an arbitrary set of Boolean operators in the SAT problem. Then the generalized SAT is either solvable in P or NP-complete. Creignou and Hermann proved a dichotomy theorem for counting SAT problems: Either solvable in P or #P-complete. 15
Proving Dichotomy Theorems for Counting Problems Jin-Yi Cai …
Webdichotomy theorem due to Schaefer. We give a precise definition of those classes in order to state our dichotomy theorems. Definition 1.6. A literal is either a Boolean variable (positive literal), or its negation (neg-ative literal). A clause is a disjunction of literals. A clause is horn if it has at most one WebSchaefer’s Dichotomy Theorem Theorem (Schaefer 78) For any nite set S ofBooleanrelations, the decision problem CSP(S) is either in P or NP-complete. Feder-Vardi Conjecture For any nite set S of relations over any nite domain D, the decision problem CSP(S) is either in P or NP-complete. Theorem (Bulatov 06) A dichotomy theorem for all … chris crissey
Schaefer
WebFeb 1, 1999 · Schaefer's dichotomy theorem is a(n) research topic. Over the lifetime, 84 publication(s) have been published within this topic receiving 6560 citation(s). Popular … WebAbstract. This paper is a contribution to the general investigation into how the complexity of constraint satisfaction problems (CSPs) is determined by the form of the constraints. … Webk at most 2. The dichotomy of k-SAT emerges as a special case of the renowned result of Schaefer (1978) who established a more general dichotomy theorem for satisfiability problems. Concerning more recent results we refer to Kirousis and Kolaitis (2003) where also a brief survey on dichotomy theorems in computational complexity is given. genshin where to buy mushrooms