170 research outputs found
On Tackling the Limits of Resolution in SAT Solving
The practical success of Boolean Satisfiability (SAT) solvers stems from the
CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a
propositional proof complexity perspective, CDCL is no more powerful than the
resolution proof system, for which many hard examples exist. This paper
proposes a new problem transformation, which enables reducing the decision
problem for formulas in conjunctive normal form (CNF) to the problem of solving
maximum satisfiability over Horn formulas. Given the new transformation, the
paper proves a polynomial bound on the number of MaxSAT resolution steps for
pigeonhole formulas. This result is in clear contrast with earlier results on
the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper
also establishes the same polynomial bound in the case of modern core-guided
MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard
for CDCL SAT solvers, show that these can be efficiently solved with modern
MaxSAT solvers
On Continuous Local BDD-Based Search for Hybrid SAT Solving
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
binary decision diagrams (BDDs). Our framework accepts all Boolean constraints
that admit compact BDDs, including symmetric Boolean constraints and
small-coefficient pseudo-Boolean constraints as interesting families. We
propose a novel algorithm for efficiently computing the gradient needed by CLS.
We study the capabilities and limitations of our versatile CLS solver, GradSAT,
by applying it on many benchmark instances. The experimental results indicate
that GradSAT can be a useful addition to the portfolio of existing SAT and
MaxSAT solvers for solving Boolean satisfiability and optimization problems.Comment: AAAI 2
A First Step Towards a Framework for the Automated Analysis of Feature Models
Feature modelling is a common mechanism for variability management in the context of software product lines. After years of progress, the number of proposals to automatically analyse feature models is still modest and the data about the performance of the different solvers and logic representations used in such area are practically nonâexistent. Three of the most promising proposals for the automated analysis of feature models are based on the mapping of feature models into CSP, SAT and BDD solvers. in this paper we present a performance test between three off-the-shelf Java CSP, SAT and BDD solvers to analyse feature models which is a novel contribution. in addition, we conclude that the integration of such proposals in a framework will be a key challenge in the future
Generating Extended Resolution Proofs with a BDD-Based SAT Solver
In 2006, Biere, Jussila, and Sinz made the key observation that the
underlying logic behind algorithms for constructing Reduced, Ordered Binary
Decision Diagrams (BDDs) can be encoded as steps in a proof in the extended
resolution logical framework. Through this, a BDD-based Boolean satisfiability
(SAT) solver can generate a checkable proof of unsatisfiability for a set of
clauses. Such a proof indicates that the formula is truly unsatisfiable without
requiring the user to trust the BDD package or the SAT solver built on top of
it.
We extend their work to enable arbitrary existential quantification of the
formula variables, a critical capability for BDD-based SAT solvers. We
demonstrate the utility of this approach by applying a prototype solver to
several problems that are very challenging for search-based SAT solvers,
obtaining polynomially sized proofs on benchmarks for parity formulas, as well
as the Urquhart, mutilated chessboard, and pigeonhole problems.Comment: Extended version of paper published at TACAS 202
Boolean Satisfiability in Electronic Design Automation
Boolean Satisfiability (SAT) is often used as the underlying model for a significant and increasing number of applications in Electronic Design Automation (EDA) as well as in many other fields of Computer Science and Engineering. In recent years, new and efficient algorithms for SAT have been developed, allowing much larger problem instances to be solved. SAT âpackagesâ are currently expected to have an impact on EDA applications similar to that of BDD packages since their introduction more than a decade ago. This tutorial paper is aimed at introducing the EDA professional to the Boolean satisfiability problem. Specifically, we highlight the use of SAT models to formulate a number of EDA problems in such diverse areas as test pattern generation, circuit delay computation, logic optimization, combinational equivalence checking, bounded model checking and functional test vector generation, among others. In addition, we provide an overview of the algorithmic techniques commonly used for solving SAT, including those that have seen widespread use in specific EDA applications. We categorize these algorithmic techniques, indicating which have been shown to be best suited for which tasks
Proof Generation for CDCL Solvers Using Gauss-Jordan Elimination
Traditional Boolean satisfiability (SAT) solvers based on the conflict-driven
clause-learning (CDCL) framework fare poorly on formulas involving large
numbers of parity constraints. The CryptoMiniSat solver augments CDCL with
Gauss-Jordan elimination to greatly improve performance on these formulas.
Integrating the TBUDDY proof-generating BDD library into CryptoMiniSat enables
it to generate unsatisfiability proofs when using Gauss-Jordan elimination.
These proofs are compatible with standard, clausal proof frameworks.Comment: Presented at 2022 Workshop on the Pragmatics of SA
Fast LTL Satisfiability Checking by SAT Solvers
Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step
in checking for possible errors in LTL assertions. Extant LTL satisfiability
checkers use a variety of different search procedures. With the sole exception
of LTL satisfiability checking based on bounded model checking, which does not
provide a complete decision procedure, LTL satisfiability checkers have not
taken advantage of the remarkable progress over the past 20 years in Boolean
satisfiability solving. In this paper, we propose a new LTL
satisfiability-checking framework that is accelerated using a Boolean SAT
solver. Our approach is based on the variant of the \emph{obligation-set
method}, which we proposed in earlier work. We describe here heuristics that
allow the use of a Boolean SAT solver to analyze the obligations for a given
LTL formula. The experimental evaluation indicates that the new approach
provides a a significant performance advantage
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