Related papers: Necessary and sufficient conditions for Boolean sa…
We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…
We intend to create new concepts aimed at finding necessary and sufficient conditions for Boolean satisfiability so that these conditions can be verified in polynomial time. Based on these conditions it will be possible to create 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…
This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra $B_{0}=\{0,1\}$ and find all satisfying assignments. The algorithm is based…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
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…
In 1978, Schaefer proved his famous dichotomy theorem for generalized satisfiability problems. He defined an infinite number of propositional satisfiability problems (nowadays usually called Boolean constraint satisfaction problems) and…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
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,…
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
We study the complexity of satisfiability problems in probabilistic and causal reasoning. Given random variables $X_1, X_2,\ldots$ over finite domains, the basic terms are probabilities of propositional formulas over atomic events $X_i =…
In this paper we explore whether or not deep neural architectures can learn to classify Boolean satisfiability (SAT). We devote considerable time to discussing the theoretical properties of SAT. Then, we define a graph representation for…
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…
We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…
We develop necessary and sufficient conditions and a novel provably consistent and efficient algorithm for discovering topics (latent factors) from observations (documents) that are realized from a probabilistic mixture of shared latent…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
Given the family $P$ of all nonempty subsets of a set $U$ of alternatives, a choice over $U$ is a function $c \colon \Omega \to P$ such that $\Omega \subseteq P$ and $c(B) \subseteq B$ for all menus $B \in \Omega$. A choice is total if…
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…
A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…