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## PBS: A backtrack search pseudo Boolean solver (2002)

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Venue: | In Symposium on the theory and applications of satisfiability testing (SAT |

Citations: | 86 - 1 self |

### Citations

479 | GRASP: A search algorithm for propositional satisfiability.
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- 1999
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Citation Context ...kallah Department of Electrical Engineering and Computer Science University of Michigan {faloul, ramania, imarkov, karem}@eecs.umich.edu Optimized solvers for the Boolean Satisfiability (SAT) problem =-=[5, 14, 15, 17, 19, 23, 24]-=- found many applications in areas such as hardware and software verification, FPGA routing, planning in AI, etc. Further uses are complicated by the need to express “counting constraints” in conjuncti... |

361 | Boosting combinatorial search through randomization.
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- 1998
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Citation Context ...enerated. 2.4 Random Restarts and Backtracking Besides learning new clauses, recent studies have shown that using randomization and random restarts can be very effective in solving hard SAT instances =-=[2, 10, 15]-=-. A SAT solver may often get stuck in a local non-useful search space. The restart process periodically unassigns all previous decisions and implications and randomly selects a new sequence of decisio... |

348 | Efficient conflict driven learning in a boolean satisfiability solver.
- Zhang, Madigan, et al.
- 2001
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Citation Context ... effective in pruning the search space. Since then, several clause learning schemes have been proposed [14, 15], some of which learn multiple clauses at each conflict. Recently, however, Zhang et al. =-=[25]-=- proved empirically that the 1UIP learning scheme, in which a single clause is learned at each conflict, showed the best performance among a variety of schemes on several hard instances. Nevertheless,... |

329 | Symbolic model checking using SAT procedures instead of BDDs,
- Biere, Cimatti, et al.
- 1999
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Citation Context ... become a promising new technology for a number of applications in the field of electronic design automation (EDA) and has been successfully applied to various problems arising in formal verification =-=[6, 21]-=-, timing analysis [18], routing of field-programmable gate arrays [16], automatic test pattern generation (ATPG) [12, 20], etc. As a result, several powerful SAT solvers [5, 14, 15, 19, 23, 24] have b... |

306 | Test Pattern Generation Using Boolean Satisfiability,”
- Larrabee
- 1992
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Citation Context ...as been successfully applied to various problems arising in formal verification [6, 21], timing analysis [18], routing of field-programmable gate arrays [16], automatic test pattern generation (ATPG) =-=[12, 20]-=-, etc. As a result, several powerful SAT solvers [5, 14, 15, 19, 23, 24] have been proposed, many of which use one or another variation of the Davis-Logemann-Loveland (DLL) [8] approach. A recently de... |

186 |
Using CSP look-back techniques to solve real-world SAT instances.
- Schrag
- 1997
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Citation Context ...kallah Department of Electrical Engineering and Computer Science University of Michigan {faloul, ramania, imarkov, karem}@eecs.umich.edu Optimized solvers for the Boolean Satisfiability (SAT) problem =-=[5, 14, 15, 17, 19, 23, 24]-=- found many applications in areas such as hardware and software verification, FPGA routing, planning in AI, etc. Further uses are complicated by the need to express “counting constraints” in conjuncti... |

163 |
Chaff: Engineering an Efficient
- Moskewicz, Madigan, et al.
(Show Context)
Citation Context ...This technique is implemented in almost all backtrack search SAT solvers and has shown to be very effective in pruning the search space. Since then, several clause learning schemes have been proposed =-=[14, 15]-=-, some of which learn multiple clauses at each conflict. Recently, however, Zhang et al. [25] proved empirically that the 1UIP learning scheme, in which a single clause is learned at each conflict, sh... |

136 |
Combinatorial Test Generation Using Satisfiability”,
- Stephan, Brayton, et al.
- 1996
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Citation Context ...as been successfully applied to various problems arising in formal verification [6, 21], timing analysis [18], routing of field-programmable gate arrays [16], automatic test pattern generation (ATPG) =-=[12, 20]-=-, etc. As a result, several powerful SAT solvers [5, 14, 15, 19, 23, 24] have been proposed, many of which use one or another variation of the Davis-Logemann-Loveland (DLL) [8] approach. A recently de... |

126 | A Davis-Putnam based enumeration algorithm for linear pseudo-Boolean optimization,” Max-Planck-Institut fur Informatik, Im Stadtwald,
- Barth
- 1995
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Citation Context ...es derived from adder and comparator circuits. This problem was addressed in a recent work [23] by an algorithm that handles non-CNF constraints such as cube lists and pseudo-Boolean (PB) constraints =-=[3]-=- of the form: ∑c i x i ≤ n c i , n ∈ Z, x i ∈ { 0, 1} The term pseudo-Boolean constraints refers to arbitrary linear inequalities 0-1 in terms of variables, however many applications require only inte... |

95 | SATIRE: A New Incremental Satisfiability Engine,"
- Whittemore, Kim, et al.
- 2001
(Show Context)
Citation Context ...kallah Department of Electrical Engineering and Computer Science University of Michigan {faloul, ramania, imarkov, karem}@eecs.umich.edu Optimized solvers for the Boolean Satisfiability (SAT) problem =-=[5, 14, 15, 17, 19, 23, 24]-=- found many applications in areas such as hardware and software verification, FPGA routing, planning in AI, etc. Further uses are complicated by the need to express “counting constraints” in conjuncti... |

74 | A Comparative study of two Boolean formulations of FPGA detailed routing constraints. - Nam, Sakallah - 2002 |

72 |
A System for Determining Propositional Logic Theorems by Applying Values and Rules to Triplets that are Generated from a Formula,
- Stalmarck
- 1989
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Citation Context |

60 |
Noise strategies for local search.
- Selman, Kautz, et al.
- 1994
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Citation Context |

58 | Using randomization and learning to solve hard real-world instances of satisfiability’,
- Baptista, Marques-Silva
- 2000
(Show Context)
Citation Context ...enerated. 2.4 Random Restarts and Backtracking Besides learning new clauses, recent studies have shown that using randomization and random restarts can be very effective in solving hard SAT instances =-=[2, 10, 15]-=-. A SAT solver may often get stuck in a local non-useful search space. The restart process periodically unassigns all previous decisions and implications and randomly selects a new sequence of decisio... |

53 | An efficient Algorithm for Unit Propagation.
- Zhang, Stickel
- 1996
(Show Context)
Citation Context ...dentified in recent conflicts, the counters are periodically divided by a constant. 2.2 Improved BCP Enhancements to the implementation of BCP were shown to yield significant performance improvements =-=[15, 26]-=-. Noting that a sizable fraction of a SAT solver’s runtime is spent in the BCP procedure, these enhancements can be viewed as a form of “lazy” evaluation that avoids unnecessary traversals of the clau... |

28 |
Effective Use of Boolean Satisfiability
- Velev, Bryant
- 2001
(Show Context)
Citation Context ... become a promising new technology for a number of applications in the field of electronic design automation (EDA) and has been successfully applied to various problems arising in formal verification =-=[6, 21]-=-, timing analysis [18], routing of field-programmable gate arrays [16], automatic test pattern generation (ATPG) [12, 20], etc. As a result, several powerful SAT solvers [5, 14, 15, 19, 23, 24] have b... |

26 | Faster SAT and smaller BDDs via common function structure
- Aloul, Markov, et al.
- 2001
(Show Context)
Citation Context ...sion Strategy Decision heuristics have played an important role in enhancing the performance of SAT solvers. Several studies have proposed various decision heuristics that can be classified as static =-=[1]-=- or dynamic [14, 15, 24]. For example, the GRASP SAT solver [14] is typically used with the dynamic decision heuristic DLIS which selects the literal that appears in the maximum number of unresolved c... |

24 | On the Energy Efficiency
- Chowdhury, Tornatore, et al.
- 2010
(Show Context)
Citation Context ...and 12 instances, respectively. The results of the Max-ONEs experiment are listed in Table II. Several satisfiable instances from various benchmarks including the DIMACs [9], Bejing [11], quasi-group =-=[24]-=-, and sat-planning [11] were tested. The table of results include the number of variables in each problem (V), the maximum possible number of variables assigned to true in a SAT ’2002 TABLE I: Global ... |

23 | Stochastic systematic search algorithms for satisfiability.
- Lynce, Baptista, et al.
- 2001
(Show Context)
Citation Context ... decisions. This process ensures that different sub-trees are searched every time the search process restarts. Clauses learned between various restarts are kept for future use. Recently, Lynce et al. =-=[13]-=- proposed and empirically evaluated combining randomization with backtracks. Periodically, the diagnosis engine backtracks non-chronologically to a decision level involving any literal in the conflict... |

18 | Timing Analysis Using Propositional Satisfiability,”
- Silva, Silva, et al.
- 1998
(Show Context)
Citation Context ...echnology for a number of applications in the field of electronic design automation (EDA) and has been successfully applied to various problems arising in formal verification [6, 21], timing analysis =-=[18]-=-, routing of field-programmable gate arrays [16], automatic test pattern generation (ATPG) [12, 20], etc. As a result, several powerful SAT solvers [5, 14, 15, 19, 23, 24] have been proposed, many of ... |

7 |
Solving Linear Pseudo-Boolean Constraint Problems with Local Search
- Walsor
- 1997
(Show Context)
Citation Context ...TIRE with those used in the currently best pure CNF solver Chaff [15]. Our new SAT solver, PBS, handles CNF constraints and PB inequalities. Unlike previously proposed stochastic local search solvers =-=[22]-=-, this solver is complete and is based on a backtrack search algorithm. We believe that our proposed algorithms to handle PB constraints can be added to any backtrack SAT solver. To demonstrate the ef... |

1 |
A Machine SAT ’2002 TABLE II: Max-ONEs Experiment Results (in seconds) Satisfiable Instance V
- Davis, Logemann, et al.
- 1962
(Show Context)
Citation Context ... generation (ATPG) [12, 20], etc. As a result, several powerful SAT solvers [5, 14, 15, 19, 23, 24] have been proposed, many of which use one or another variation of the Davis-Logemann-Loveland (DLL) =-=[8]-=- approach. A recently developed solver, Chaff [15], proposed significant enhancements in both algorithm and implementation level to backtrack search algorithms, which has lead to dramatic performance ... |