Related papers: Understanding the complexity of #SAT using knowled…
A delta-model is a satisfying assignment of a Boolean formula for which any small alteration, such as a single bit flip, can be repaired by flips to some small number of other bits, yielding a new satisfying assignment. These satisfying…
3-SAT problem is of great importance to many technical and scientific applications. This paper presents a new hybrid evolutionary algorithm for solving this satisfiability problem. 3-SAT problem has the huge search space and hence it is…
A canonical result about satisfiability theory is that the 2-SAT problem can be solved in linear time, despite the NP-hardness of the 3-SAT problem. In the quantum 2-SAT problem, we are given a family of 2-qubit projectors $\Pi_{ij}$ on a…
In this paper, we provide a deterministic polynomial time algorithm that determines satisfiability of 3-SAT. The complexity analysis for the algorithm takes into account no efficiency and yet provides a low enough bound, that efficient…
Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in…
The circuit satisfaction problem CSAT(A) of an algebra A is the problem of deciding whether an equation over A (encoded by two circuits) has a solution or not. While solving systems of equations over finite algebras is either in P or…
The field of fine-grained complexity aims at proving conditional lower bounds on the time complexity of computational problems. One of the most popular assumptions, Strong Exponential Time Hypothesis (SETH), implies that SAT cannot be…
In this paper we propose a structural parameter of CNF formulas and use it to identify instances of weighted MaxSAT and #SAT that can be solved in polynomial time. Given a CNF formula we say that a set of clauses is precisely satisfiable if…
In this paper the reason why entropy reduction (negentropy) can be used to measure the complexity of any computation was first elaborated both in the aspect of mathematics and informational physics. In the same time the equivalence of…
In this paper, I consider a fine-grained dichotomy of Boolean counting constraint satisfaction problem (#CSP), under the exponential time hypothesis of counting version (#ETH). Suppose $\mathscr{F}$ is a finite set of algebraic…
An analysis of the average-case complexity of solving random 3-Satisfiability (SAT) instances with backtrack algorithms is presented. We first interpret previous rigorous works in a unifying framework based on the statistical physics…
Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…
We apply the splitting method to three well-known counting problems, namely 3-SAT, random graphs with prescribed degrees, and binary contingency tables. We present an enhanced version of the splitting method based on the capture-recapture…
We consider semidefinite programming (SDP) approaches for solving the maximum satisfiability problem (MAX-SAT) and the weighted partial MAX-SAT. It is widely known that SDP is well-suited to approximate the (MAX-)2-SAT. Our work shows the…
In this paper we propose the approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance…
Symmetries are intrinsic to many combinatorial problems including Boolean Satisfiability (SAT) and Constraint Programming (CP). In SAT, the identification of symmetry breaking predicates (SBPs) is a well-known, often effective, technique…
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…
In quantum computation we are given a finite set of gates and we have to perform a desired operation as a product of them. The corresponding computational problem is approximating an arbitrary unitary as a product in a topological…
Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview…
In this article we consider the inversion problem for polynomially computable discrete functions. These functions describe behavior of many discrete systems and are used in model checking, hardware verification, cryptanalysis, computer…