Guiding SAT Diagnosis with Tree Decompositions

Lecture Notes in Computer Science

2005

This paper presents a new technique to derive an initial static variable ordering for efficient SAT search. Our approach not only exploits variable activity and connectivity information simultaneously, but it also analyzes how tightly the variables are related to each other. For this purpose, a new metric is proposed -the degree of correlation among pairs of variables. Variable activity and correlation information is modeled (implicitly) as a weighted graph. A topological analysis of this graph generates an order for SAT search. An algorithm called ACCORD (ACtivity -CORrelation -ORDering) is proposed for this purpose.While ACCORD rigorously analyzes constraint-variable dependencies, it does not account for the effect of decision-assignments on clause-variable dependencies. This issue motivates further refinements to our approach using literal activity and correlation measures -giving rise to the L'ACCORD algorithm. Using efficient implementations of the above, experiments are conducted over a wide range of benchmarks. The results demonstrate that: (i) the variable order generated by our approach significantly improves the performance of SAT solvers; (ii) time to derive this order is a fraction of the overall solving time. As a result, our approach delivers faster performance (often, by orders of magnitude) as compared to contemporary approaches.

Section: Limitations Of Previous Workmentioning

confidence: 99%

“…al. [21] proposed tree decomposition based approaches to guide variable selection and conflict clause generation. Aloul et.…”

Section: Introductionmentioning

confidence: 99%

Variable Ordering for Efficient SAT Search by Analyzing Constraint-Variable Dependencies

Lecture Notes in Computer Science

2005

“…Our recent work [13] employs hypergraph partitioning methods to derive a tree decomposition. Various other approaches operate on such partitioned tree structures by deriving an order in which the partitioned set of constraints are resolved [14] [15] [10].…”

Section: A Related Workmentioning

confidence: 99%

“…As a result, these techniques are somewhat impractical for solving large and hard CNF-SAT problems [10] as often encountered in design and validation problems in VLSI-CAD.…”

Section: B Limitationsmentioning

confidence: 99%

Dynamic analysis of constraint-variable dependencies to guide SAT diagnosis

Proceedings. Ninth IEEE International High-Level Design Validation and Test Workshop (IEEE Cat. No.04EX940)

2004

An important aspect of the Boolean Satisfiability problem is to derive an ordering of variables such that branching on that order results in a faster, more efficient search. Contemporary techniques employ either variable-activity or clauseconnectivity based heuristics, but not both, to guide the search. This paper advocates for simultaneous analysis of variableactivity and clause-connectivity to derive an order for SAT search. Preliminary results demonstrate that the variable order derived by our approach can significantly expedite the search.As the search proceeds, clause database is updated due to added conflict clauses. Therefore, the variable activity and connectivity information changes dynamically. Our technique analyzes this information and re-computes the variable order whenever the search is restarted. Preliminary experiments show that such a dynamic analysis of constraint-variable relationships significantly improves the performance of the SAT solvers. Our technique is very fast and this analysis time is a negligible (in milliseconds) even for instances that contain a large number of variables and constraints. This paper presents preliminary experiments, analyzes the results and comments upon future research directions.

“…al. [10] proposed tree decomposition based approaches to guide variable selection and conflict clause generation. Aloul et.…”

Section: Introductionmentioning

confidence: 99%

Guiding CNF-SAT Search by Analyzing Constraint-Variable Dependencies and Clause Lengths

2006 IEEE International High Level Design Validation and Test Workshop

2006

The type of decision strategies employed for CNF-SAT have a profound effect on the efficiency and performance of SAT engines. Over the years, a variety of decision heuristics have been proposed; each has its own achievements and limitations. This paper re-visits the issue of decision heuristics and engineers a new approach that takes an integrated view of the overall problem structure. Our approach qualitatively analyzes clause-variable dependencies by accounting for variable/literal activity, clause connectivity, distribution of variables among clauses of different lengths, and correlation among variables, to derive an initial static ordering for SAT search. To account for conflict clauses and their resolution, a corresponding dynamic variable order update strategy is also presented. Quantitative metrics are proposed that are used to devise an algorithmic approach to guide overall SAT search. Experimental results demonstrate that our strategy significantly outperforms conventional approaches.