## UnitWalk: A new SAT solver that uses local search guided by unit clause elimination (2002)

Citations: | 61 - 1 self |

### BibTeX

@MISC{Hirsch02unitwalk:a,

author = {Edward A. Hirsch and Arist Kojevnikov},

title = {UnitWalk: A new SAT solver that uses local search guided by unit clause elimination},

year = {2002}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we present a new randomized algorithm for SAT, i.e., the satisfiability problem for Boolean formulas in conjunctive normal form. Despite its simplicity, this algorithm performs well on many common benchmarks ranging from graph coloring problems to microprocessor verification.

### Citations

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Citation Context ...27, 28] and [30, 31]). We combine the main ideas of these algorithms in one algorithm. The two approaches we use are local search (which is used in many SAT algorithms, e.g., in GSAT [34] and WalkSAT =-=[33]-=-) and unit clause elimination (which is rarely used in local search algorithms). In this paper we do not prove any theoretical bounds. However, we present encouraging results of computational experime... |

206 | Using CSP lookback techniques to solve real-world SAT instances - Bayardo, Schrag - 1997 |

184 | Evidence for Invariants in Local Search
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Citation Context ...rithms, for example, GSAT [34], GWSAT (aka GSAT+w) [33], HSAT [6], HWSAT [7], SDF [32], IDB [29], WalkSAT [33] and various algorithms within WalkSAT framework such as WalkSAT/TABU, Novelty, R-Novelty =-=[23-=-], Novelty+ and R-Novelty+ [14]. Some of these algorithms need restarts because there are initial assignments such that the probability that the random walk (if allowed to run innitely long) hits a sa... |

136 | Towards an understanding of hill-climbing procedures for SAT
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Citation Context ...om walk is long enough, it is restarted from another initial assignment. There is a number of experimentally studied SAT local search algorithms, for example, GSAT [34], GWSAT (aka GSAT+w) [33], HSAT =-=[6]-=-, HWSAT [7], SDF [32], IDB [29], WalkSAT [33] and various algorithms within WalkSAT framework such as WalkSAT/TABU, Novelty, R-Novelty [23], Novelty+ and R-Novelty+ [14]. Some of these algorithms need... |

127 | A probabilistic algorithm for k-SAT and constraint satisfaction problems
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Citation Context ...mon benchmarks ranging from graph coloring problems to microprocessor verication. Our algorithm is inspired by two randomized algorithms having the best current worst-case upper bounds ([27, 28] and [=-=30, 31]-=-). We combine the main ideas of these algorithms in one algorithm. The two approaches we use are local search (which is used in many SAT algorithms, e.g., in GSAT [34] and WalkSAT [33]) and unit claus... |

120 | Heuristics based on unit propagation for satisfiability problems - Li, Anbulagan - 1997 |

96 |
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Citation Context ...\heuristic" algorithms use local search paradigm (this line of research started from experiments of Gu [8] and Selman, Levesque and Mitchell [34] and theoretical work by Koutsoupias and Papadimit=-=riou [19, 26-=-]). Such an algorithm chooses a random initial assignment and then modies it step by step until itsnds a satisfying assignment. If the random walk is long enough, it is restarted from another initial ... |

88 | On the run-time behaviour of stochastic local search algorithms for SAT - Hoos - 1999 |

84 | An improved exponential-time algorithm for k-SAT
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Citation Context ...l on many common benchmarks ranging from graph coloring problems to microprocessor verication. Our algorithm is inspired by two randomized algorithms having the best current worst-case upper bounds ([=-=27, 28]-=- and [30, 31]). We combine the main ideas of these algorithms in one algorithm. The two approaches we use are local search (which is used in many SAT algorithms, e.g., in GSAT [34] and WalkSAT [33]) a... |

77 | SATLIB: An Online Resource for Research on SAT
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Citation Context ...c algorithm (but not for the solver as a whole because it uses WalkSAT-like walks as well). We also give CPU time. Benchmarks. The main source where we took benchmarks was the online library SATLIB 4 =-=[16-=-]; see references there for the description and original sources of these benchmarks. In addition, we ran our algorithm on Velev's microprocessor verication benchmarks 5 [38]. We also used randomly ge... |

66 |
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Citation Context ... n , but it is non-trivial that it can be solved faster). Thesrst such bounds were proved in [3, 22, 24]. Currently, the best known deterministic algorithm for k-SAT has the bound p(n)(2 2=(k + 1)) n =-=[4]-=-. Randomized algorithms achieve even better bounds [30, 27]. If a formula has exactly one satisfying assignment, it can be found even faster: in the time p(n)1:308 n for a formula in 3-CNF [27]. Conce... |

62 | Local search algorithms for SAT: An empirical evaluation
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Citation Context ...ted and mostly concentrates on exponential worst-case lower bounds [11], average-case bounds [9, 19], or properties related to their completeness [2, 13, 14]. Some of these algorithms are surveyed in =-=[10, 15]. In -=-their turn, \heuristic" algorithms may be complete or incomplete. A complete algorithm gives the correct answer with certainty. If an incomplete algorithmsnds a satisfying assignment, it is guara... |

62 | Satisfiability coding lemma
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Citation Context ..., we put its index (in the array of clauses) on a special list of indices of unit clauses. 4.2. Adding resolvents Paturi, Pudlak, Saks and Zane [27] suggest an extension of the original algorithm of [=-=28]-=-, and this extension gives an improvement of the worstcase time upper bound. The extension is a preprocessing step that adds resolvents of logarithmic size to the input formula. In practice, one canno... |

60 |
Stochastic local search - methods, models, applications
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Citation Context ...oretical knowledge about these algorithms is very limited and mostly concentrates on exponential worst-case lower bounds [11], average-case bounds [9, 19], or properties related to their completeness =-=[2, 13, 14]. Som-=-e of these algorithms are surveyed in [10, 15]. In their turn, \heuristic" algorithms may be complete or incomplete. A complete algorithm gives the correct answer with certainty. If an incomplete... |

59 | Local search characteristics of incomplete sat procedures - Schuurmans, Southey |

53 |
Cha#: Engineering an e#cient sat solver
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Citation Context ... (O(2 n ) iterations would do the job for almost all known algorithms, but it is unrealistic in practice). There are several very successful complete algorithms (e.g., satz [21], SATO [39, 40], zCha [=-=25]-=-; see comprehensive experimental results at SAT-Ex web-site 1 [37]). However, solvers based on incomplete algorithms could be faster just because they belong to a wider class of computations. For exam... |

53 | Implementing the davis-putnam method
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Citation Context ...edened constant (O(2 n ) iterations would do the job for almost all known algorithms, but it is unrealistic in practice). There are several very successful complete algorithms (e.g., satz [21], SATO [=-=39, 40-=-], zCha [25]; see comprehensive experimental results at SAT-Ex web-site 1 [37]). However, solvers based on incomplete algorithms could be faster just because they belong to a wider class of computatio... |

46 |
A New Method for Solving Hard Satis Problems
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Citation Context ...e upper bounds ([27, 28] and [30, 31]). We combine the main ideas of these algorithms in one algorithm. The two approaches we use are local search (which is used in many SAT algorithms, e.g., in GSAT =-=[34]-=- and WalkSAT [33]) and unit clause elimination (which is rarely used in local search algorithms). In this paper we do not prove any theoretical bounds. However, we present encouraging results of compu... |

44 | Unsatisfied variables in local search
- Gent, Walsh
- 1995
(Show Context)
Citation Context ...long enough, it is restarted from another initial assignment. There is a number of experimentally studied SAT local search algorithms, for example, GSAT [34], GWSAT (aka GSAT+w) [33], HSAT [6], HWSAT =-=[7]-=-, SDF [32], IDB [29], WalkSAT [33] and various algorithms within WalkSAT framework such as WalkSAT/TABU, Novelty, R-Novelty [23], Novelty+ and R-Novelty+ [14]. Some of these algorithms need restarts b... |

38 | A Continuous Approach to Inductive Inference
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Citation Context ...ata we present in the paper show that our algorithm dominates other contemporary incomplete solvers on some sets of benchmarks (for example, satisable instances of aim [1], ssa [20], par [17] and ii [=-=18]-=- series) and is able to solve some very hard SAT instances (for example, Velev's instances). SAT Competition 2002 has shown that UnitWalk is not a specialized solver; on the contrary, it is able to so... |

32 |
Random generation of test instances with controlled attributes
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Citation Context ...n in the beginning of the period starting with A (note that every permutation is chosen with probability 1 n! ), then the assignment obtained in the end of the period will be closer to S than A. Let [=-=1-=-] = i 1 ; : : : ; [n d] = i n d , where x i 1 ; : : : ; x i n d are the variables on which A agrees with S. Clearly, the values of these variables will not be changed during the period. The remaining ... |

22 |
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Citation Context ...ables are given in Section 5) and, in fact, the implementation details has not changed much since that time. Our data structures are similar to those used in many complete SAT algorithms (e.g., GRASP =-=[35]-=-). The solver is implemented in C and uses only the standard C library. The implementation represents a formula in CNF by an array of clauses, where each clause is represented by its size (i.e., a nat... |

18 |
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Citation Context ... of variables in the input formula, and p is a polynomial (note that SAT can be easily solved in time p(n)2 n , but it is non-trivial that it can be solved faster). Thesrst such bounds were proved in =-=[3, 22, 24]-=-. Currently, the best known deterministic algorithm for k-SAT has the bound p(n)(2 2=(k + 1)) n [4]. Randomized algorithms achieve even better bounds [30, 27]. If a formula has exactly one satisfying ... |

15 |
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Citation Context ...; therefore, throughout this paper we will speak only about satisable formulas. Most incomplete \heuristic" algorithms use local search paradigm (this line of research started from experiments of=-= Gu [8-=-] and Selman, Levesque and Mitchell [34] and theoretical work by Koutsoupias and Papadimitriou [19, 26]). Such an algorithm chooses a random initial assignment and then modies it step by step until it... |

15 | SATEx: a web-based framework for SAT experimentation - Simon, Chatalic |

15 | Solving open quasigroup problems by propositional reasoning - Zhang, Hsiang |

14 |
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Citation Context ... of variables in the input formula, and p is a polynomial (note that SAT can be easily solved in time p(n)2 n , but it is non-trivial that it can be solved faster). Thesrst such bounds were proved in =-=[3, 22, 24]-=-. Currently, the best known deterministic algorithm for k-SAT has the bound p(n)(2 2=(k + 1)) n [4]. Randomized algorithms achieve even better bounds [30, 27]. If a formula has exactly one satisfying ... |

12 |
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Citation Context ...ted and mostly concentrates on exponential worst-case lower bounds [11], average-case bounds [9, 19], or properties related to their completeness [2, 13, 14]. Some of these algorithms are surveyed in =-=[10, 15]. In -=-their turn, \heuristic" algorithms may be complete or incomplete. A complete algorithm gives the correct answer with certainty. If an incomplete algorithmsnds a satisfying assignment, it is guara... |

12 | Local search and backtracking vs non-systematic backtracking
- Prestwich
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(Show Context)
Citation Context ...restarted from another initial assignment. There is a number of experimentally studied SAT local search algorithms, for example, GSAT [34], GWSAT (aka GSAT+w) [33], HSAT [6], HWSAT [7], SDF [32], IDB =-=[29]-=-, WalkSAT [33] and various algorithms within WalkSAT framework such as WalkSAT/TABU, Novelty, R-Novelty [23], Novelty+ and R-Novelty+ [14]. Some of these algorithms need restarts because there are ini... |

10 | local search algorithms: Worst-case study
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(Show Context)
Citation Context ...tances encoding various practical problems like planning or circuit design. Theoretical knowledge about these algorithms is very limited and mostly concentrates on exponential worst-case lower bounds =-=[11], ave-=-rage-case bounds [9, 19], or properties related to their completeness [2, 13, 14]. Some of these algorithms are surveyed in [10, 15]. In their turn, \heuristic" algorithms may be complete or inco... |

9 |
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Citation Context ...hm. The experimental data we present in the paper show that our algorithm dominates other contemporary incomplete solvers on some sets of benchmarks (for example, satisable instances of aim [1], ssa [=-=20]-=-, par [17] and ii [18] series) and is able to solve some very hard SAT instances (for example, Velev's instances). SAT Competition 2002 has shown that UnitWalk is not a specialized solver; on the cont... |

8 | Algorithms for sat and upper bounds on their complexity
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Citation Context ...has exactly one satisfying assignment, it can be found even faster: in the time p(n)1:308 n for a formula in 3-CNF [27]. Concerning other results in this reachseld, we refer the readers to the survey =-=[5]. \He-=-uristic" algorithms. Unfortunately, the worst-case upper bounds currently known for SAT algorithms are still too large for practical purposes. Another direction of research is the design of \heur... |

5 |
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Citation Context ...actical problems like planning or circuit design. Theoretical knowledge about these algorithms is very limited and mostly concentrates on exponential worst-case lower bounds [11], average-case bounds =-=[9, 19], or -=-properties related to their completeness [2, 13, 14]. Some of these algorithms are surveyed in [10, 15]. In their turn, \heuristic" algorithms may be complete or incomplete. A complete algorithm ... |

5 |
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Citation Context ...actical problems like planning or circuit design. Theoretical knowledge about these algorithms is very limited and mostly concentrates on exponential worst-case lower bounds [11], average-case bounds =-=[9, 19], or -=-properties related to their completeness [2, 13, 14]. Some of these algorithms are surveyed in [10, 15]. In their turn, \heuristic" algorithms may be complete or incomplete. A complete algorithm ... |

5 | An improved randomized algorithm for 3-SAT
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Citation Context ...mon benchmarks ranging from graph coloring problems to microprocessor verication. Our algorithm is inspired by two randomized algorithms having the best current worst-case upper bounds ([27, 28] and [=-=30, 31]-=-). We combine the main ideas of these algorithms in one algorithm. The two approaches we use are local search (which is used in many SAT algorithms, e.g., in GSAT [34] and WalkSAT [33]) and unit claus... |

4 |
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Citation Context ...r to any predened constant (O(2 n ) iterations would do the job for almost all known algorithms, but it is unrealistic in practice). There are several very successful complete algorithms (e.g., satz [=-=21-=-], SATO [39, 40], zCha [25]; see comprehensive experimental results at SAT-Ex web-site 1 [37]). However, solvers based on incomplete algorithms could be faster just because they belong to a wider clas... |

4 |
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Citation Context ... of variables in the input formula, and p is a polynomial (note that SAT can be easily solved in time p(n)2 n , but it is non-trivial that it can be solved faster). Thesrst such bounds were proved in =-=[3, 22, 24]-=-. Currently, the best known deterministic algorithm for k-SAT has the bound p(n)(2 2=(k + 1)) n [4]. Randomized algorithms achieve even better bounds [30, 27]. If a formula has exactly one satisfying ... |

4 |
a decision procedure for propositional logic
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Citation Context ...edened constant (O(2 n ) iterations would do the job for almost all known algorithms, but it is unrealistic in practice). There are several very successful complete algorithms (e.g., satz [21], SATO [=-=39, 40-=-], zCha [25]; see comprehensive experimental results at SAT-Ex web-site 1 [37]). However, solvers based on incomplete algorithms could be faster just because they belong to a wider class of computatio... |

4 | On the probabilistic approximate completeness of WalkSAT for 2-SAT - Culberson, Gent, et al. - 2000 |

4 | On the greedy algorithm for satis Information Processing Letters - Koutsoupias, Papadimitriou - 1992 |

3 | Improving SAT using 2SAT
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Citation Context ...-09 6,196 645(0.381) 2,332 439(0.242) 2,697 425,693(69.39) qg7-13 2710 6 1.210 6 (3,598) 2-resolvents after each substitution using a very fast method incBinSat of Zheng and Stuckey [41]. Therefore, we trade the number of possible implications (and simplications) for the time spent for each period. Our choice is partially supported by our experimental results shown in Table II. It t... |

2 |
E.A.: The SAT2002 competition report
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Citation Context ...orithm is probabilistically approximately complete, and its relation to other local search algorithms is discussed. Section 4 contains the details of our solver that took part in SAT Competition 2002 =-=[36]-=-: we discuss its implementation and improvements using other known algorithms. In Section 5 we present comprehensive experimental data describing the execution of our algorithm on various benchmarks i... |

1 |
Hoos: 2000, `On the Probabilistic Approximate Completeness of WalkSAT for 2-SAT
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Citation Context ...oretical knowledge about these algorithms is very limited and mostly concentrates on exponential worst-case lower bounds [11], average-case bounds [9, 19], or properties related to their completeness =-=[2, 13, 14]. Som-=-e of these algorithms are surveyed in [10, 15]. In their turn, \heuristic" algorithms may be complete or incomplete. A complete algorithm gives the correct answer with certainty. If an incomplete... |

1 |
Tricks (eds.): 1996, Cliques, Coloring and Satis ability
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Citation Context ...these series. Our experiments and other sources of data. Most of our experiments were made on a 466MHz Intel Celeron Pentium II running under Linux. The DIMACS hardware benchmark program dfmax r500.5 =-=[17]-=- takes 54.64 seconds on the machine. Some of the experiments were made on a 1GHz Pentium-III machine and the running time was scaled to match our basic machine. The data for other algorithms is partia... |

1 |
Southey: 2000, `Local search characteristics of incomplete SAT procedures
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Citation Context ...gh, it is restarted from another initial assignment. There is a number of experimentally studied SAT local search algorithms, for example, GSAT [34], GWSAT (aka GSAT+w) [33], HSAT [6], HWSAT [7], SDF =-=[32]-=-, IDB [29], WalkSAT [33] and various algorithms within WalkSAT framework such as WalkSAT/TABU, Novelty, R-Novelty [23], Novelty+ and R-Novelty+ [14]. Some of these algorithms need restarts because the... |

1 |
2001, `Eective Use of Boolean Satis
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Citation Context ...e online library SATLIB 4 [16]; see references there for the description and original sources of these benchmarks. In addition, we ran our algorithm on Velev's microprocessor verication benchmarks 5 [=-=38-=-]. We also used randomly generated benchmarks submitted to SAT Competition 2002 [36] by thesrst author, including the smallest satisable benchmark hgen2-v500-s1216665065 remained unsolved during the c... |

1 | A collection of SAT-related resources - SATLIB |

1 | Tricks, editors. Cliques, Coloring and Satis - Johnson, A - 1996 |

1 | The SAT-Ex Site. A collection of experimental results about complete SAT solvers, http: //www.lri.fr/~simon/satex/satex.php3 - Simon |

1 | Benchmark suite SSS-SAT.1.0. Available from: http://www.ece.cmu.edu/~mvelev - Velev |