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In this paper, we revisit an important issue of CDCL-based SAT solvers, namely the learned clauses database management policies. Our motivation takes its source from a simple observation on the remarkable performances of both random and size-bounded reduction strategies. We first derive a simple reduction strategy, called Size-Bounded Randomized strategy (in short SBR), that combines maintaining short clauses (of size bounded by k), while deleting randomly clauses of size greater than k. The resulting strategy outperform the state-of-the-art on SAT instances taken from the SAT competitions 2013 and 2018, and remains competitive on a broad range of SAT instances of the SAT Competition 2014. Reinforced by the interest of keeping short clauses, we propose several new dynamic variants, and we discuss their performance. We also propose different ways for adjusting dynamically the size-bounded parameter of the strategy. [ABSTRACT FROM AUTHOR]

This paper explores several polynomial fragments of SAT that are based on the unit propagation (UP) mechanism. As a first case study, one Tovey's polynomial fragment of SAT is extended through the use of UP. Then, we answer an open question about connections between the so-called UP-Horn class (and other UP-based polynomial variants) and Dalal's polynomial Quad class. Finally, we introduce an extended UP-based pre-processing procedure that allows us to prove that some series of benchmarks from the SAT competitions are polynomial ones. Moreover, our experimentations show that this pre-processing can speed-up the satisfiability check of other instances. [ABSTRACT FROM AUTHOR]

Learning is a general concept, playing an important role in many Artificial intelligence domains. In this paper, we address the learning paradigm used to explain failures or conflicts encountered during search. This explanation, derived by conflict analysis, and generally expressed as a new constraint, is usually used to dynamically avoid future occurrences of similar situations. Before focusing on clause learning in Boolean satisfiability (SAT), we first overview some important works on this powerful reasoning tool in other domains such as constraint satisfaction and truth maintenance systems. Then, we present a comprehensive survey of the most important works having led to what is called today-conflict driven clause learning-which is one of the key components of modern SAT solvers. We also overview some of the original extensions or variants of clauses learning. In theory, current SAT solvers with clause learning are as powerful as general resolution proof systems. In practice, real-world SAT instances with millions of variables and clauses are now in the scope of this solving paradigm. [ABSTRACT FROM AUTHOR]

Learning is a general concept, playing an important role in many Artificial intelligence domains. In this paper, we address the learning paradigm used to explain failures or conflicts encountered during search. This explanation, derived by conflict analysis, and generally expressed as a new constraint, is usually used to dynamically avoid future occurrences of similar situations. Before focusing on clause learning in Boolean satisfiability (SAT), we first overview some important works on this powerful reasoning tool in other domains such as constraint satisfaction and truth maintenance systems. Then, we present a comprehensive survey of the most important works having led to what is called today-conflict driven clause learning (CDCL)-which is one of the key components of modern SAT solvers. In theory, current SAT solvers with clause learning are as powerful as general resolution proof systems. In practice, real-world SAT instances with millions of variables and clauses are now in the scope of this solving paradigm. [ABSTRACT FROM AUTHOR]

This paper presents an original dynamic subsumption technique for Boolean CNF formulae. It exploits simple and sufficient conditions to detect, during conflict analysis, clauses from the formula that can be reduced by subsumption. During the learnt clause derivation, and at each step of the associated resolution process, checks for backward subsumption between the current resolvent and clauses from the original formula are efficiently performed. The resulting method allows the dynamic removal of literals from the original clauses. Experimental results show that the integration of our dynamic subsumption technique within the state-of-the-art SAT solvers Minisat and Rsat particularly benefits to crafted problems. [ABSTRACT FROM AUTHOR]

In this paper, the use of local search to validate first-order knowledge-based systems is investigated. It is well known that such techniques can prove efficient in showing that consistency constraints do hold, at least in the propositional case. Powerful heuristics about the trace of local search allow proofs of inconsistency to be obtained as well. However, how local search can be applied to first-order knowledge bases without giving rise to a combinatorial space explosion remains an open issue. In this paper, a partial instantiation schema is proposed in the context of the incremental consistency–inconsistency problem. It allows forms of depth-limited consistency and inconsistency to be handled in an effective manner, showing promising paths for the development of new efficient consistency checking techniques for first-order knowledge bases. © 2001 John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

In this paper, we address a fundamental problem in the formalization and implementation of cooperative knowledge bases: the difficulty of preserving consistency while interacting or combining them. Indeed, knowledge bases that are individually consistent can exhibit global inconsistency. This stumbling-block problem is an even more serious drawback when knowledge and reasoning are expressed using logical terms. Indeed, on the one hand, two contradictory pieces of information lead to global inconsistency under complete standard rules of deduction: every assertion and its contrary can be deduced. On the other hand, checking the logical consistency of a propositional knowledge base is an NP-complete problem and is often out of reach for large real-life applications. In this paper, a new practical technique to locate inconsistent interacting pieces of information is presented in the context of cooperative logical knowledge bases. Based on a recently discovered heuristic about the work performed by local search techniques, it can be applied in the context of large interacting knowledge bases. [ABSTRACT FROM AUTHOR]

In this paper, an efficient heuristic allowing one to localize inconsistent kernels in propositional knowledge bases is described. Then, it is shown that local search techniques can boost the performance of logically complete methods for SAT. More precisely, local search techniques can be used to guide the branching strategy of logically complete techniques like Davis and Putnam's one, giving rise to significant performance improvements, in particular when addressing locally inconsistent problems. Moreover, this approach appears very competitive in the context of consistent SAT instances, too. [ABSTRACT FROM AUTHOR]