## Dynamic Scoring Functions with Variable Expressions: New SLS Methods for Solving SAT

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Citations: | 6 - 2 self |

### BibTeX

@MISC{Tompkins_dynamicscoring,

author = {Dave A. D. Tompkins and Holger H. Hoos},

title = {Dynamic Scoring Functions with Variable Expressions: New SLS Methods for Solving SAT},

year = {}

}

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### Abstract

Abstract. We introduce a new conceptual model for representing and designing Stochastic Local Search (SLS) algorithms for the propositional satisfiability problem (SAT). Our model can be seen as a generalization of existing variable weighting, scoring and selection schemes; it is based upon the concept of Variable Expressions (VEs), which use properties of variables in dynamic scoring functions. Algorithms in our model are constructed from conceptually separated components: variable filters, scoring functions (VEs), variable selection mechanisms and algorithm controllers. To explore the potential of our model we introduce the Design Architecture for Variable Expressions (DAVE), a software framework that allows users to specify arbitrarily complex algorithms at runtime. Using DAVE, we can easily specify rich design spaces of SLS algorithms and subsequently explore these using an automated algorithm configuration tool. We demonstrate that by following this approach, we can achieve significant improvements over previous state-of-the-art SLS-based SAT solvers on software verification benchmark instances from the literature. 1

### Citations

690 | A new method for solving hard satisfiability problems
- Selman, Levesque, et al.
- 1992
(Show Context)
Citation Context ...ies of a variable in combination with constants, operators and functions. The variable properties that can appear in VEs include well-known concepts from the literature, such as GSAT’s score property =-=[17]-=- and the age property used by NOVELTY and WALKSAT/TABU [14]. A VE can be a simple property (e.g., 〈age〉) or any mathematical expression with one or more properties, such as 〈score + 3 · log(age)〉. Mos... |

370 | Noise strategies for improving local search
- Selman, Kautz, et al.
- 1994
(Show Context)
Citation Context ...ake − break〉 where the properties make and break measure the number of clauses that would become satisfied and unsatisfied, respectively, if the variable were to be flipped. The WALKSAT/SKC algorithm =-=[16]-=- was the first algorithm to use the even simpler VE 〈break〉 for scoring variables and also introduced a Boolean freebie property that is true if, and only if, break equals zero. Algorithms with dynami... |

247 |
Stochastic Local Search Foundations and Applications
- Hoos, Stützle
- 2005
(Show Context)
Citation Context ...e are typically incomplete, i.e., they cannot determine with certainty that a given propositional formula is unsatisfiable, but they often find models of satisfiable formulae surprisingly effectively =-=[9]-=-. SLS algorithms for SAT typically start by randomly assigning to every variable appearing in a given formula a value of either true or false; then, in each subsequent search step a variable is select... |

216 | A tool for checking ANSI-C programs
- Clarke, Kroening, et al.
- 2004
(Show Context)
Citation Context ...s, we mostly focused on the CBMC software verification instance set generated, and used as a benchmark, by KhudaBukhsh et al. [12]. The instances were generated by a Bounded Model Checking (BMC) tool =-=[4]-=- and were pre-processed with SATELITE [5]. This set is interesting to us primarily because it has some of the structural properties of larger and more complicated software verification problems (that ... |

188 | Evidence for Invariants in Local Search
- McAllester, Selman, et al.
- 1997
(Show Context)
Citation Context ...and functions. The variable properties that can appear in VEs include well-known concepts from the literature, such as GSAT’s score property [17] and the age property used by NOVELTY and WALKSAT/TABU =-=[14]-=-. A VE can be a simple property (e.g., 〈age〉) or any mathematical expression with one or more properties, such as 〈score + 3 · log(age)〉. Most existing SLS algorithms for SAT select variables based on... |

139 | Effective Preprocessing in SAT Through Variable and Clause Elimination
- Eén, Biere
- 2005
(Show Context)
Citation Context ... verification instance set generated, and used as a benchmark, by KhudaBukhsh et al. [12]. The instances were generated by a Bounded Model Checking (BMC) tool [4] and were pre-processed with SATELITE =-=[5]-=-. This set is interesting to us primarily because it has some of the structural properties of larger and more complicated software verification problems (that are still somewhat intractable for SLS so... |

137 | Towards an understanding of hill-climbing procedures for SAT
- Gent, Walsh
- 1993
(Show Context)
Citation Context ...ned as the number of search steps that have occurred since the given variable was last flipped. The age property is closely related to the flips property (a.k.a. flipcount) used by the HSAT algorithm =-=[7]-=- as a tie-breaking mechanism; the flips property measures how many times a variable has been flipped. An interesting and effective combination of the freebie, break, age and flips properties is used i... |

96 | ParamILS: an automatic algorithm configuration framework
- Hutter, Hoos, et al.
- 2009
(Show Context)
Citation Context ...e provided at run-time. We provided this flexibility in DAVE from the outset, with the goal of leveraging existing automated algorithm configuration tools (henceforth, configurators) such as PARAMILS =-=[11]-=-. With the combination of DAVE and a configurator, designers have an unprecedented amount of flexibility and power to help automate the design of new high-performance SLS algorithms and algorithm hybr... |

89 | PicoSAT essentials
- Biere
(Show Context)
Citation Context ...ger and more complicated software verification problems (that are still somewhat intractable for SLS solvers). For example, many of the complete solvers from the 2009 SAT Competition (such as PICOSAT =-=[3]-=-) can solve the hardest CBMC instance in less than one second, whereas well-known state-of-the-art SLS solvers from the competition such as ADAPTG 2 WSAT and GNOVELTY + require over an hour to solve t... |

54 | UBCSAT: An implementation and experimentation environment for SLS algorithms for SAT and MAX-SAT
- Tompkins, Hoos
- 2004
(Show Context)
Citation Context ...mplex VEs can be very effective. To explore the potential of our model, we introduce the Design Architecture for Variable Expressions (DAVE), a software extension of our versatile UBCSAT architecture =-=[18]-=-. No programming is required to develop new algorithms in DAVE; the complete algorithm specification (including arbitrarily complex VEs) can be provided at run-time. We provided this flexibility in DA... |

46 | Boosting Verification by Automatic Tuning of Decision Procedures
- Hutter, Babić, et al.
- 2007
(Show Context)
Citation Context ...irst time experimental data for SLS algorithms on the software verification benchmark set SWV generated by the CALYSTO static checker [2] and used as a benchmark for complete solvers by Hutter et al. =-=[10]-=-. A more detailed description of our experimental methodologies, PARAMILS settings, specifications of our run-time environment, further details of our instance sets and algorithm configurations in DAV... |

36 | W.Q.: Diversification and Determinism in Local Search for Satisfiability - Li, Huang - 2005 |

34 | Calysto: Scalable and Precise Extended Static Checking
- Babić, Hu
- 2008
(Show Context)
Citation Context ... for extensive experiments.In Section 5 we also provide for the first time experimental data for SLS algorithms on the software verification benchmark set SWV generated by the CALYSTO static checker =-=[2]-=- and used as a benchmark for complete solvers by Hutter et al. [10]. A more detailed description of our experimental methodologies, PARAMILS settings, specifications of our run-time environment, furth... |

32 | SATenstein: Automatically building local search SAT solvers from components
- KhudaBukhsh, Xu, et al.
- 2009
(Show Context)
Citation Context ... final performance measurements presented in this paper. In our experiments, we mostly focused on the CBMC software verification instance set generated, and used as a benchmark, by KhudaBukhsh et al. =-=[12]-=-. The instances were generated by a Bounded Model Checking (BMC) tool [4] and were pre-processed with SATELITE [5]. This set is interesting to us primarily because it has some of the structural proper... |

28 |
Automated discovery of local search heuristics for satisfiability testing
- Fukunaga
(Show Context)
Citation Context ...rts arbitrarily complex algorithms in a potentially unbounded space. In that latter respect, DAVE is similar in nature to the Composite heuristic Learning Algorithm for SAT Search (CLASS) by Fukunaga =-=[6]-=-. CLASS is a genetic programming system that constructs new variable selection heuristics. Our work with VEs is somewhat orthogonal to the research direction underlying CLASS; our goal has been to dec... |

11 | Random walk with continuously smoothed variable weights
- Prestwich
- 2005
(Show Context)
Citation Context ...echanism; the flips property measures how many times a variable has been flipped. An interesting and effective combination of the freebie, break, age and flips properties is used in the VW2 algorithm =-=[15]-=-. 3.1 Deconstructing VW2 In many ways, Prestwich’s VW2 algorithm [15] provided the starting point for our work on VEs, and we describe VW2 in the following. 1 Each variable is assigned a weight (which... |

9 | Computer-aided design of high-performance algorithms
- Hoos
- 2008
(Show Context)
Citation Context ...ought might be effective. Our goal with VE-SAMPLER was to make very few decisions at design time and to configure the resulting, highly paramaterized algorithm automatically for optimized performance =-=[8]-=-. In total, VE-SAMPLER has over 10 50 possible configurations, which, to the best of our knowledge, is the largest design space searched using PARAMILS [11]10 7 10 1 VE-Sampler [steps] 10 6 10 5 10 4... |

4 | A switching criterion for intensification and diversification in local search for SAT
- Wei, Li, et al.
(Show Context)
Citation Context ...echanism can achieve very robust performance. 6 Related Work The manner in which SLS algorithm hybrids can be implemented in DAVE can be seen as a generalization of the HYBRID algorithm by Wei et al. =-=[20]-=-. HYBRID implements a clever heuristic to select between the algorithms VW2-SAT05 and ADAPTG 2 WSAT at each search step. Their heuristic corresponds to a specific algorithm controller in our model, an... |

2 | On the structure of industrial sat instances
- Ansótegui, Bonet, et al.
- 2009
(Show Context)
Citation Context ...two properties. Because the difference in scale between the two properties becomes increasingly larger as the search progresses, we decided to normalize the values of these properties to the interval =-=[0, 1]-=-. We achieved p max(p) this using the formula , where max(p) refers to the maximum value of the property p for all flip candidates, which for VW2 would be those variables in the currently selected cla... |