Random generation of test instances with
                    controlled attributes

Asahiro, Yuichi; Iwama, Kazuo; Miyano, Eiji

doi:10.1090/dimacs/026/18

Cited by 47 publications

(32 citation statements)

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“…This shows that when the number of variables becomes large, the technique using EUP is advantageous. Table 1 shows the number of states and time required in solving AIM benchmark problems [2] by the algorithm using EUP. These problems are the DIMACS Challenge benchmark problems.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The variable and its negation are called literal. The logical sum of literal [e.g., (x 1 + x 2 __ + x 3 )] is called a clause. For a set of clauses C 1 , C 2 , .…”

Section: Satisfiability Problemsmentioning

confidence: 99%

“…(4) If S contains a unit clause, set the value of the variable such that that clause is satisfied, and the clauses contained in S are simplified. Go to (2). (5) Branching: From the variables contained in S, a variable x is selected by using some heuristic.…”

Section: Outline Of Algorithmmentioning

confidence: 99%

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Solving satisfiability problems by using reconfigurable hardware

Suzuki¹,

Yokoo

Sawada

et al. 2003

Electron Comm Jpn Pt II

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SUMMARYIn this paper, we will propose a new solution method for SAT (Satisfiability Problems) using FPGA (Field-Programmable Gate Arrays) and logic synthesis system. This method is distinctive in that a logic circuit specialized to solve each problem instance is configured on FPGA. This approach has become possible due to the progress in reconfigurable computing technology in recent years and opens a new possibility in design principle of algorithms. SAT is a kind of constraint satisfaction problem and is a general framework which can represent many application problems. In this paper, we will propose various algorithms which are suitable for implementation on hardware. Among these algorithms, the one which has the highest performance has a performance equal to the Davis-Putman algorithm which introduced the heuristic with dynamic ordering of variables. From the evaluation results using simulation, we show that by the method proposed herein, the solution of a 3-SAT problem instance with 400 variables generated in a very hard random can be obtained in 1.6 minutes when the circuit is operated at a machine cycle of 10 MHz. Moreover, a very hard problem instance with 128 variables and 256 clauses was packaged on FPGAs and its operation was confirmed.

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Section: Simulation Resultsmentioning

confidence: 99%

“…The variable and its negation are called literal. The logical sum of literal [e.g., (x 1 + x 2 __ + x 3 )] is called a clause. For a set of clauses C 1 , C 2 , .…”

Section: Satisfiability Problemsmentioning

confidence: 99%

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Solving satisfiability problems by using reconfigurable hardware

Suzuki¹,

Yokoo

Sawada

et al. 2003

Electron Comm Jpn Pt II

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show abstract

“…We have used the package SAT4J [34] which contains a java implementation of an exact method based DPLL. In order to assess the efficiency and accuracy of our approach, we have performed several tests taken from the AIM benchmark instances [35]. The AIM instances are all generated with a particular Random-3-SAT instance generator.…”

Section: Implementation and Evaluationmentioning

confidence: 99%

A Hybrid Quantum Genetic Algorithm and Local Search based DPLL for Max 3-SAT Problems

Layeb¹,

Saïdouni²

2014

Appl. Math. Inf. Sci.

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Abstract:In this paper, we present a new framework for combining complete and incomplete methods in order to deal with the Max Sat problem. The objective is to find the best assignment for a set of Boolean variables, which gives the maximum of verified clauses in a Boolean formula. Unfortunately, this problem has been shown to be NP-hard (non-deterministic polynomial-time hard) if the number of variables per clause is greater than 3. The proposed approach is based on quantum inspired genetic principles and the well known exact algorithm DPLL. The underlying idea is to harness the optimization capabilities of quantum genetic algorithm to achieve good quality solutions for Max SAT problem. A new local search based on DPLL algorithm has been embodied in the quantum genetic algorithm leading to an efficient hybrid framework which achieves better balance between diversification and intensification search. The obtained results are very encouraging and show the feasibility and effectiveness of the proposed hybrid approach.

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“…Also, from FACT instances, it is easy to generate SAT instances with a unique solution; thus, by negating the unique solution, we can easily generate "negative" SAT instances. (In general, "negative" instance generation is difficult [AIM96].) Secondly, with efficient reductions, we can analyze the concrete hardness of SAT.…”

Section: Introductionmentioning

confidence: 99%

Hard instance generation for SAT

Horie

Watanabe

1997

Algorithms and Computation

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Abstract. We consider the problem of generating hard instances for the Satisfying Assignment Search Problem (in short, SAT). It is not known whether SAT is difficult on average, while it has been believed that the Factorization Problem (in short, FACT) is hard on average. Thus, one can expect to generate hard-on-average instances by using a reduction from FACT to SAT. Although the asymptotically best reduction is obtained by using the Fast Fourier Transform [SS71] (in short, FFT), its constant factor is too big in practice. Here we propose to use the Chinese Remainder Theorem for constructing efficient yet simple reductions from FACT to SAT. First by using the Chinese Remainder Theorem recursively, we define a reduction that produces, from n bit FACT instances, SAT instances in the conjunctive normal form with O(n 1+ǫ ) variables, where ǫ > 0 is any fixed constant. (Cf. The reduction using FFT yields instances with O(n log n log log n) variables.) Next we demonstrate the efficiency of our approach with some concrete examples; we define a reduction that produces relatively small SAT instances. For example, it is possible to construct SAT instances with about 5,600 variables that is as hard as factorizing 100 bit integers. (Cf. The straightforward reduction yields SAT instances with 7,600 variables.)

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Random generation of test instances with controlled attributes

Cited by 47 publications

References 0 publications

Solving satisfiability problems by using reconfigurable hardware

Solving satisfiability problems by using reconfigurable hardware

A Hybrid Quantum Genetic Algorithm and Local Search based DPLL for Max 3-SAT Problems

Hard instance generation for SAT

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