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Register a new userURSA: A System for Uniform Reduction to SAT
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Predrag Janicic
Publication date
2010
fields
Informatics Engineering
and research's language is
English
Authors
Predrag Janicic
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There are a huge number of problems, from various areas, being solved by reducing them to SAT. However, for many applications, translation into SAT is performed by specialized, problem-specific tools. In this paper we describe a new system for uniform solving of a wide class of problems by reducing them to SAT. The system uses a new specification language URSA that combines imperative and declarative programming paradigms. The reduction to SAT is defined precisely by the semantics of the specification language. The domain of the approach is wide (e.g., many NP-complete problems can be simply specified and then solved by the system) and there are problems easily solvable by the proposed system, while they can be hardly solved by using other programming languages or constraint programming systems. So, the system can be seen not only as a tool for solving problems by reducing them to SAT, but also as a general-purpose constraint solving system (for finite domains). In this paper, we also describe an open-source implementation of the described approach. The performed experiments suggest that the system is competitive to state-of-the-art related modelling systems.
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Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. Its worst-case hardness lies at the core of computational complexity theory, for example in the form of NP-hardness and the (Strong) Exponential Time Hypothesis. In practice however, SAT instances can often be solved efficiently. This contradicting behavior has spawned interest in the average-case analysis of SAT and has triggered the development of sophisticated rigorous and non-rigorous techniques for analyzing random structures. Despite a long line of research and substantial progress, most theoretical work on random SAT assumes a uniform distribution on the variables. In contrast, real-world instances often exhibit large fluctuations in variable occurrence. This can be modeled by a non-uniform distribution of the variables, which can result in distributions closer to industrial SAT instances. We study satisfiability thresholds of non-uniform random $2$-SAT with $n$ variables and $m$ clauses and with an arbitrary probability distribution $(p_i)_{iin[n]}$ with $p_1 ge p_2 ge ldots ge p_n > 0$ over the n variables. We show for $p_1^2=Theta(sum_{i=1}^n p_i^2)$ that the asymptotic satisfiability threshold is at $m=Theta( (1-sum_{i=1}^n p_i^2)/(p_1cdot(sum_{i=2}^n p_i^2)^{1/2}) )$ and that it is coarse. For $p_1^2=o(sum_{i=1}^n p_i^2)$ we show that there is a sharp satisfiability threshold at $m=(sum_{i=1}^n p_i^2)^{-1}$. This result generalizes the seminal works by Chvatal and Reed [FOCS 1992] and by Goerdt [JCSS 1996].
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