Related papers: Efficient Solution of Boolean Satisfiability Probl…
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…
The Boolean satisfiability problem (SAT) can be solved efficiently with variants of the DPLL algorithm. For industrial SAT problems, DPLL with conflict analysis dependent dynamic decision heuristics has proved to be particularly efficient,…
We consider the decision problem for quantifier-free formulas whose atoms are linear inequalities interpreted over the reals or rationals. This problem may be decided using satisfiability modulo theory (SMT), using a mixture of a SAT solver…
Satisfiability Modulo Theory (SMT) has recently emerged as a powerful tool for solving various automated reasoning problems across diverse domains. Unlike traditional satisfiability methods confined to Boolean variables, SMT can reason on…
We explore the potential of continuous local search (CLS) in SAT solving by proposing a novel approach for finding a solution of a hybrid system of Boolean constraints. The algorithm is based on CLS combined with belief propagation on…
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…
In this manuscript, we derive the principle of conservation of computational complexity. We measure computational complexity as the number of binary computations (decisions) required to solve a problem. Every problem then defines a unique…
It was shown before that the NP-hard problem of deterministic finite automata (DFA) identification can be effectively translated to Boolean satisfiability (SAT). Modern SAT-solvers can tackle hard DFA identification instances efficiently.…
We present novel algorithms for design and design space exploration. The designs discovered by these algorithms are compositions of function types specified in component libraries. Our algorithms reduce the design problem to quantified…
Digital memcomputing machines (DMMs) are a novel, non-Turing class of machines designed to solve combinatorial optimization problems. They can be physically realized with continuous-time, non-quantum dynamical systems with memory (time…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
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…
To check the satisfiability of (non-linear) real arithmetic formulas, modern satisfiability modulo theories (SMT) solving algorithms like NLSAT depend heavily on single cell construction, the task of generalizing a sample point to a…
Boolean matching is an important problem in logic synthesis and verification. Despite being well-studied for conventional Boolean circuits, its treatment for reversible logic circuits remains largely, if not completely, missing. This work…
Modern conflict-driven clause-learning (CDCL) Boolean SAT solvers provide efficient automatic analysis of real-world feature models (FM) of systems ranging from cars to operating systems. It is well-known that solver-based analysis of…
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their…
Efficiently determining the satisfiability of a boolean equation -- known as the SAT problem for brevity -- is crucial in various industrial problems. Recently, the advent of deep learning methods has introduced significant potential for…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
Modern high-performance SAT solvers quickly solve large satisfiability instances that occur in practice. If the instance is satisfiable, then the SAT solver can provide a witness which can be checked independently in the form of a…