We present a novel low-overhead framework for encoding and utilizing structural symmetry in propositional satisfiability algorithms (SAT solvers). We use the notion of complete multi-class symmetry and demonstrate the efficacy of our technique through a solver SymChaff that achieves exponential speedup by using simple tags in the specification of problems from both theory and practice. Efficient implementations of DPLL-based SAT solvers are routinely used in areas as diverse as planning, scheduling, design automation, model checking, verification, testing, and algebra. A natural feature of many application domains is the presence of symmetry, such as that amongst all trucks at a certain location in logistics planning and all wires connecting two switch boxes in an FPGA circuit. Many of these problems turn out to have a concise description in many-sorted first order logic. This description can be easily specified by the problem designer and almost as easily inferred automatically. SymChaff, an extension of the popular SAT solver zChaff, uses information obtained from the "sorts" in the first order logic constraints to create symmetry sets that are used to partition variables into classes and to maintain and utilize symmetry information dynamically. Current approaches designed to handle symmetry include: (A) symmetry breaking predicates (SBPs), (B) pseudo-Boolean solvers with implicit representation for counting, (C) modifications of DPLL that handle symmetry dynamically, and (D) techniques based on ZBDDs. SBPs are prohibitively many, often large, and expensive to compute for problems such as the ones we report experimental results for. Pseudo-Boolean solvers are provably exponentially slow in certain symmetric situations and their implicit counting representation is not always appropriate. Suggested modifications of DPLL either work on limited global symmetry and are difficult to extend, or involve expensive algebraic group computations. Finally, techniques based on ZBDDs often do not compare well even with ordinary DPLL-based solvers. SymChaff addresses and overcomes most of these limitations.
Content Area: 6. Constraint Satisfaction and Satisfiability
Subjects: 15.2 Constraint Satisfaction; 1.11 Planning
Submitted: May 10, 2005