Related papers: A Real World Mechanism for Testing Satisfiability …
This paper is devoted to the complexity of the Boolean satisfiability problem. We consider a version of this problem, where the Boolean formula is specified in the conjunctive normal form. We prove an unexpected result that the…
The following paper proposes a new approach to determine whether a logical (CNF) formula is satisfiable or not using probability theory methods. Furthermore, we will introduce an algorithm that speeds up the standard solution for (CNF-SAT)…
For formulas F of propositional calculus I introduce a "metavariable" MF and show how it can be used to define an algorithm for testing satisfiability. MF is a formula which is true/false under all possible truth assignments iff F is…
In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set…
We study -- within the framework of propositional proof complexity -- the problem of certifying unsatisfiability of CNF formulas under the promise that any satisfiable formula has many satisfying assignments, where ``many'' stands for an…
Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
Knuth (1990) introduced the class of nested formulas and showed that their satisfiability can be decided in polynomial time. We show that, parameterized by the size of a smallest strong backdoor set to the target class of nested formulas,…
These notes contain, among others, a proof that the average running time of an easy solution to the satisfiability problem for propositional calculus is, under some reasonable assumptions, linear (with constant 2) in the size of the input.…
Maximum satisfiability is a canonical NP-hard optimization problem that appears empirically hard for random instances. Let us say that a Conjunctive normal form (CNF) formula consisting of $k$-clauses is $p$-satisfiable if there exists a…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the…
The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are…
While model checking PCTL for Markov chains is decidable in polynomial-time, the decidability of PCTL satisfiability, as well as its finite model property, are long standing open problems. While general satisfiability is an intriguing…
Many procedures for SAT and SAT-related problems -- in particular for those requiring the complete enumeration of satisfying truth assignments -- rely their efficiency on the detection of partial assignments satisfying an input formula. In…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for…
We study the exponential time complexity of approximate counting satisfying assignments of CNFs. We reduce the problem to deciding satisfiability of a CNF. Our reduction preserves the number of variables of the input formula and thus also…
NP-Complete problems have an important attribute that if one NP-Complete problem can be solved in polynomial time, all NP-Complete problems will have a polynomial solution. The 3-CNF-SAT problem is a NP-Complete problem and the primary…