Related papers: Lower bound for the Complexity of the Boolean Sati…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
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…
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…
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…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…
The aim of the paper is to answer a long-standing open problem on the relationship between NP and BQP. The paper shows that BQP contains NP by proposing a BQP quantum algorithm for the MAX-E3-SAT problem which is a fundamental NP-hard…
In this paper we present a new approach to solve the satisfiability problem (SAT), based on boolean networks (BN). We define a mapping between a SAT instance and a BN, and we solve SAT problem by simulating the BN dynamics. We prove that BN…
We refine the formulation of the Boolean satisfiability problem with $n$ Boolean variables in Clifford algebra ${\cal C}\ell(\mathbb{R}^{n,n})$ [3] and exploit this continuous setting to outline a new unsatisfiability test. This algorithm…
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
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.…
We study here several variants of the covariates fine balance problem where we generalize some of these problems and introduce a number of others. We present here a comprehensive complexity study of the covariates problems providing…
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version,…
We address lower bounds on the time complexity of algorithms solving the propositional satisfiability problem. Namely, we consider two DPLL-type algorithms, enhanced with the unit clause and pure literal heuristics. Exponential lower bounds…
Boolean satisfiability is a propositional logic problem of interest in multiple fields, e.g., physics, mathematics, and computer science. Beyond a field of research, instances of the SAT problem, as it is known, require efficient solution…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
First of all we give some reasons that "natural proofs" built not a barrier to prove P $\not=$ NP using Boolean complexity. Then we investigate the approximation method for its extension to prove super-polynomial lower bounds for the…
We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatizable unless P = NP. Indeed, we show it is…