Armin Biere

Giuseppe Spallitta, Roberto Sebastiani, Armin Biere

A basic algorithm for enumerating disjoint propositional models (disjoint AllSAT) is based on adding blocking clauses incrementally, ruling out previously found models. On the one hand, blocking clauses have the potential to reduce the number of generated models exponentially, as they can handle partial models. On the other hand, the introduction of a large number of blocking clauses affects memory consumption and drastically slows down unit propagation. We propose a new approach that allows for enumerating disjoint partial models with no need for blocking clauses by integrating: Conflict-Driven Clause-Learning (CDCL), Chronological Backtracking (CB), and methods for shrinking models (Implicant Shrinking). Experiments clearly show the benefits of our novel approach.

Jean-Marie Lagniez, Pierre Marquis, Armin Biere

In this paper, we explore the application of blocked clause elimination for projected model counting. This is the problem of determining the number of models ||\exists X.Σ|| of a propositional formula Σ after eliminating a given set X of variables existentially. Although blocked clause elimination is a well-known technique for SAT solving, its direct application to model counting is challenging as in general it changes the number of models. However, we demonstrate, by focusing on projected variables during the blocked clause search, that blocked clause elimination can be leveraged while preserving the correct model count. To take advantage of blocked clause elimination in an efficient way during model counting, a novel data structure and associated algorithms are introduced. Our proposed approach is implemented in the model counter d4. Our experiments demonstrate the computational benefits of our new method of blocked clause elimination for projected model counting.

Giuseppe Spallitta, Roberto Sebastiani, Armin Biere

All-Solution Satisfiability (AllSAT) and its extension, All-Solution Satisfiability Modulo Theories (AllSMT), have become more relevant in recent years, mainly in formal verification and artificial intelligence applications. The goal of these problems is the enumeration of all satisfying assignments of a formula (for SAT and SMT problems, respectively), making them useful for test generation, model checking, and probabilistic inference. Nevertheless, traditional AllSAT algorithms face significant computational challenges due to the exponential growth of the search space and inefficiencies caused by blocking clauses, which cause memory blowups and degrade unit propagation performances in the long term. This paper presents two novel solvers: tabularAllSAT, a projected AllSAT solver, and tabularAllSMT, a projected AllSMT solver. Both solvers combine Conflict-Driven Clause Learning (CDCL) with chronological backtracking to improve efficiency while ensuring disjoint enumeration. To retrieve compact partial assignments we propose a novel aggressive implicant shrinking algorithm, compatible with chronological backtracking, to minimize the number of partial assignments, reducing overall search complexity. Furthermore, we extend the solver framework to handle projected enumeration and SMT formulas effectively and efficiently, adapting the baseline framework to integrate theory reasoning and the distinction between important and non-important variables. An extensive experimental evaluation demonstrates the superiority of our approach compared to state-of-the-art solvers, particularly in scenarios requiring projection and SMT-based reasoning.

Peter van der Tak, Marijn J. H. Heule, Armin Biere

Recent work introduced the cube-and-conquer technique to solve hard SAT instances. It partitions the search space into cubes using a lookahead solver. Each cube is tackled by a conflict-driven clause learning (CDCL) solver. Crucial for strong performance is the cutoff heuristic that decides when to switch from lookahead to CDCL. Yet, this offline heuristic is far from ideal. In this paper, we present a novel hybrid solver that applies the cube and conquer steps simultaneously. A lookahead and a CDCL solver work together on each cube, while communication is restricted to synchronization. Our concurrent cube-and-conquer solver can solve many instances faster than pure lookahead, pure CDCL and offline cube-and-conquer, and can abort early in favor of a pure CDCL search if an instance is not suitable for cube-and-conquer techniques.