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Recent formal approaches towards causality have made the concept ready for incorporation into the technical world. However, causality reasoning is computationally hard; and no general algorithmic approach exists that efficiently infers the…

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…

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…

Boolean satisfiability (SAT) is a fundamental NP-complete problem with many applications, including automated planning and scheduling. To solve large instances, SAT solvers have to rely on heuristics, e.g., choosing a branching variable in…

Reinforcement learning with verifiable rewards has significantly advanced reasoning in large language models (LLMs), but such signals remain coarse, offering only binary correctness feedback. This limitation often results in inefficiencies,…

Satisfiability problem (SAT) is a cornerstone of computational complexity with broad industrial applications, and it remains challenging to optimize modern SAT solvers in real-world settings due to their intricate architectures. While…

Boolean satisfiability (SAT) solvers are widely used in hardware verification, cryptanalysis, automatic test-pattern generation, and side-channel reasoning workflows. Modern conflict-driven clause-learning (CDCL) solvers are highly…

It has become standard that, when a SAT solver decides that a CNF $\Gamma$ is unsatisfiable, it produces a certificate of unsatisfiability in the form of a refutation of $\Gamma$ in some proof system. The system typically used is DRAT,…

This paper introduces several techniques that improve the scalability of the deductive verification of data-level programs working on arrays and matrices. First of all, we introduce a technique to rewrite expressions with (nested)…

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 present a hardware-accelerated SAT solver targeting processor/Field Programmable Gate Arrays (FPGA) SoCs. Our solution accelerates the most expensive subroutine of the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, Boolean Constraint…

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…

In this paper, we present ReaS, a technique that combines numerical optimization with SAT solving to synthesize unknowns in a program that involves discrete and floating point computation. ReaS makes the program end-to-end differentiable by…

Constrained-random simulation is the predominant approach used in the industry for functional verification of complex digital designs. The effectiveness of this approach depends on two key factors: the quality of constraints used to…

We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms…

This paper introduces SATFuL, a SAT solver for fuzzy logics. In contrast to the Boolean case, for which numerous SAT solvers exist, the SAT problem for fuzzy logics has attracted less attention, even though these tools have interesting…

Satisfiability Modulo Theories (SMT) solvers are integral to program analysis techniques like concolic and symbolic execution, where they help assess the satisfiability of logical formulae to explore execution paths of the program under…

Boolean Satisfiability (SAT) problems are critical in fields such as artificial intelligence and cryptography, where efficient solutions are essential. Conventional probabilistic solvers often encounter scalability issues due to complex…

Optimization problems pervade essentially every scientific discipline and industry. Many such problems require finding a solution that maximizes the number of constraints satisfied. Often, these problems are particularly difficult to solve…

Previous studies have demonstrated that encoding a Bayesian network into a SAT formula and then performing weighted model counting using a backtracking search algorithm can be an effective method for exact inference. In this paper, we…