Related papers: A Complete Diagrammatic Calculus for Boolean Satis…
Synthesis of models and strategies is a very important problem in software engineering. The main element here is checking the satisfiability of formulae expressing the specification of a system to be implemented. This paper puts forward a…
Programs must be correct with respect to their application domain. Yet, the program specification and verification approaches so far only consider correctness in terms of computations. In this work, we present a two-tier Hoare Logic that…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
The complete reason behind a decision is a Boolean formula that characterizes why the decision was made. This recently introduced notion has a number of applications, which include generating explanations, detecting decision bias and…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
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…
The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…
Machine learning approaches to solving Boolean Satisfiability (SAT) aim to replace handcrafted heuristics with learning-based models. Graph Neural Networks have emerged as the main architecture for SAT solving, due to the natural graph…
In this work, we consider the satisfiability problem in a logic that combines word equations over string variables denoting words of unbounded lengths, regular languages to which words belong and Presburger constraints on the length of…
This paper reviews the recent literature on solving the Boolean satisfiability problem (SAT), an archetypal NP-complete problem, with the help of machine learning techniques. Despite the great success of modern SAT solvers to solve large…
We study the typical case properties of the 1-in-3 satisfiability problem, the boolean satisfaction problem where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and…
In this paper, we present a novel algorithm to solve the Boolean Satisfiability (SAT) problem, using noise-based logic (NBL). Contrary to what the name may suggest, NBL is not a random/fuzzy logic system. In fact, it is a completely…
We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by…
A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…
Automatically verifying safety properties of programs is hard, and it is even harder if the program acts upon arrays or other forms of maps. Many approaches exist for verifying programs operating upon Boolean and integer values (e.g.…
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof…
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…