Related papers: The fast parallel algorithm for CNF SAT without al…
Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure of satisfiable and unsatisfiable sentences. In previous work…
Over the last two decades, we have seen a dramatic improvement in the efficiency of conflict-driven clause-learning Boolean satisfiability (CDCL SAT) solvers on industrial problems from a variety of domains. The availability of such…
We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in…
There are a huge number of problems, from various areas, being solved by reducing them to SAT. However, for many applications, translation into SAT is performed by specialized, problem-specific tools. In this paper we describe a new system…
This paper introduces the XOR-OR-AND normal form (XNF) for logical formulas. It is a generalization of the well-known Conjunctive Normal Form (CNF) where literals are replaced by XORs of literals. As a first theoretic result, we show that…
The Model-Constructing Satisfiability Calculus (MCSAT) framework has been applied to SMT problems over various arithmetic theories. NLSAT, an implementation using cylindrical algebraic decomposition (CAD) for explanation, is especially…
The Boolean satisfiability problem (SAT) holds a central place in computational complexity theory as the first shown NP-complete problem. Due to this role, SAT is often used as the benchmark for polynomial-time reductions: if a problem can…
We present a new algorithm for deciding formula entailment in orthologic (a sound approximation of classical logic) that avoids the costly preprocessing phase of prior implementations while retaining the same $\mathcal{O}(n^2(1+|A|))$…
The solution-space structure of the 3-Satisfiability Problem (3-SAT) is studied as a function of the control parameter alpha (ratio of number of clauses to the number of variables) using numerical simulations. For this purpose, one has to…
Boolean satisfiability (SAT) has an extensive application domain in computer science, especially in electronic design automation applications. Circuit synthesis, optimization, and verification problems can be solved by transforming original…
In this paper, we discussed CNF-SAT problem (NP-Complete problem) and analysis two solutions that can solve the problem, the PL-Resolution algorithm and the WalkSAT algorithm. PL-Resolution is a sound and complete algorithm that can be used…
Boolean Satisfiability (SAT) solving underpins a wide range of applications in Electronic Design Automation (EDA), particularly formal verification. However, this paper observes that the mainstream clause reduction heuristic in modern SAT…
We propose to use local search algorithms to produce SAT instances which are harder to solve than randomly generated k-CNF formulae. The first results, obtained with rudimentary search algorithms, show that the approach deserves further…
In the maximum satisfiability problem (MAX-SAT) we are given a propositional formula in conjunctive normal form and have to find an assignment that satisfies as many clauses as possible. We study the parallel parameterized complexity of…
Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there…
Discrete variables are common in many applications, such as probabilistic reasoning, planning and explainable AI. When symbolic reasoning techniques are brought in to bear on these applications, a standard technique for handling discrete…
Resource sharing is a crucial part of a multi-robot system. We propose a Boolean satisfiability based approach to resource sharing. Our key contributions are an algorithm for converting any constrained assignment to a weighted-SAT based…
Earlier we introduced the notion of a stable set of points (SSP). We proved that a CNF formula is unsatisfiable iff there is a set of points (i.e. complete assignments) that is stable with respect to this formula. Experiments showed that…
Previous efforts on making Satisfiability (SAT) solving fit for high performance computing (HPC) have lead to super-linear speedups on particular formulae, but for most inputs cannot make efficient use of a large number of processors.…
Existing methods provide varying algorithms for different types of Boolean satisfiability problems (SAT), lacking a general solution framework. Accordingly, this study proposes a unified framework DCSAT based on integer programming and…