An Improved Decision-DNNF Compiler

Lagniez, Jean-Marie; Marquis, Pierre

doi:10.24963/ijcai.2017/93

Cited by 73 publications

(91 citation statements)

References 8 publications

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“…To evaluate the runtime performance and quality of approximations computed by ApproxMC3, we conducted the most comprehensive study of performance evaluation of counting algorithms involving 1896 benchmarks arising from wide range of application areas including probabilistic reasoning, plan recognition, DQMR networks, ISCAS89 combinatorial circuits, quantified information flow, program synthesis, functional synthesis, logistics, and the like as have been previously employed in studies on model counting (Chakraborty, Meel, and Vardi 2016;Lagniez and Marquis 2017). For the sake of space, we discuss results for only a subset of these benchmarks here.…”

Section: Experimental Evaluationmentioning

confidence: 99%

BIRD: Engineering an Efficient CNF-XOR SAT Solver and Its Applications to Approximate Model Counting

Soos

Meel

2019

AAAI

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Given a Boolean formula φ, the problem of model counting, also referred to as #SAT is to compute the number of solutions of φ. Model counting is a fundamental problem in artificial intelligence with a wide range of applications including probabilistic reasoning, decision making under uncertainty, quantified information flow, and the like. Motivated by the success of SAT solvers, there has been surge of interest in the design of hashing-based techniques for approximate model counting for the past decade. We profiled the state of the art approximate model counter ApproxMC2 and observed that over 99.99% of time is consumed by the underlying SAT solver, CryptoMiniSat. This observation motivated us to ask: Can we design an efficient underlying CNF-XOR SAT solver that can take advantage of the structure of hashing-based algorithms and would this lead to an efficient approximate model counter? The primary contribution of this paper is an affirmative answer to the above question. We present a novel architecture, called BIRD, to handle CNF-XOR formulas arising from hashingbased techniques. The resulting hashing-based approximate model counter, called ApproxMC3, employs the BIRD framework in its underlying SAT solver, CryptoMiniSat. To the best of our knowledge, we conducted the most comprehensive study of evaluation performance of counting algorithms involving 1896 benchmarks with computational effort totaling 86400 computational hours. Our experimental evaluation demonstrates significant runtime performance improvement for ApproxMC3 over ApproxMC2. In particular, we solve 648 benchmarks more than ApproxMC2, the state of the art approximate model counter and for all the formulas where both ApproxMC2 and ApproxMC3 did not timeout and took more than 1 seconds, the mean speedup is 284.40 – more than two orders of magnitude.

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Section: Experimental Evaluationmentioning

confidence: 99%

BIRD: Engineering an Efficient CNF-XOR SAT Solver and Its Applications to Approximate Model Counting

Soos

Meel

2019

AAAI

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“…Other benchmarked systems. In our experimental work, we present results for the most recent versions of publicly available #Sat solvers, namely, c2d 2.20 [13], d4 1.0 [30], DSHARP 1.0 [33], miniC2D 1.0.0 [34], cnf2eadt 1.0 [28], bdd minisat all 1.0.2 [42], and sdd 2.0 [14], which are all based on knowledge compilation techniques. We also considered rather recent approximate solvers ApproxMC2, ApproxMC3 [7] and sts 1.0 [20], as well as CDCL-based solvers Cachet 1.21 [37], sharpCDCL 10 , and sharpSAT 13.02 [40].…”

Section: Setupmentioning

confidence: 99%

Exploiting Database Management Systems and Treewidth for Counting

Fichte

Hecher

Thier

et al. 2020

Lecture Notes in Computer Science

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Bounded treewidth is one of the most cited combinatorial invariants, which was applied in the literature for solving several counting problems efficiently. A canonical counting problem is #Sat, which asks to count the satisfying assignments of a Boolean formula. Recent work shows that benchmarking instances for #Sat often have reasonably small treewidth. This paper deals with counting problems for instances of small treewidth. We introduce a general framework to solve counting questions based on state-of-the-art database management systems (DBMS). Our framework takes explicitly advantage of small treewidth by solving instances using dynamic programming (DP) on tree decompositions (TD). Therefore, we implement the concept of DP into a DBMS (PostgreSQL), since DP algorithms are already often given in terms of table manipulations in theory. This allows for elegant specifications of DP algorithms and the use of SQL to manipulate records and tables, which gives us a natural approach to bring DP algorithms into practice. To the best of our knowledge, we present the first approach to employ a DBMS for algorithms on TDs. A key advantage of our approach is that DBMS naturally allow to deal with huge tables with a limited amount of main memory (RAM), parallelization, as well as suspending computation.

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“…Most solvers use the Davis-Putnam-Logemann-Loveland (DPLL) algorithm [53] to exhaustively search for all satisfying assignments of an instance, whereas others use ideas from knowledge compilation [54] to perform the counting. Specifically, we have tested the performance of cachet [55], cnf2eadt [56], CNF2OBDD [57], d4 [58], miniC2D [59], relsat [60], and sharpSAT [61]. For knowledge compilers, we have used -whenever present -appropriate options to skip the compilation step and solely do counting.…”

Section: Sat Counters Used For Benchmarkingmentioning

confidence: 99%

Fast counting with tensor networks

et al. 2019

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We introduce tensor network contraction algorithms for the counting of satisfying assignments in constraint satisfaction problems (#CSP). We represent each arbitrary #CSP instance as a tensor network whose full contraction yields the number of satisfying assignments for that instance. We then use methods of graph theory and computational complexity theory to develop fast tensor contraction protocols. In particular, we employ the tools of multilevel graph partitioning and community structure detection to determine favorable orders of contraction of arbitrary tensor networks. We first prove analytically that full tensor contraction can be performed in subexponential time for #CSP instances defined on graphs with sublinear separators. We then implement numerical heuristics for the solution of general #P-hard counting boolean satisfiability (#SAT) problems, focusing on random instances of #CUBIC-VERTEX-COVER as a concrete example, and show that they outperform stateof-the-art #SAT solvers by a significant margin. Our results promote tensor network contraction algorithms as a powerful practical tool for fast solution of some #CSPs. arXiv:1805.00475v1 [cond-mat.stat-mech] 1 May 2018

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An Improved Decision-DNNF Compiler

Cited by 73 publications

References 8 publications

BIRD: Engineering an Efficient CNF-XOR SAT Solver and Its Applications to Approximate Model Counting

BIRD: Engineering an Efficient CNF-XOR SAT Solver and Its Applications to Approximate Model Counting

Exploiting Database Management Systems and Treewidth for Counting

Fast counting with tensor networks

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