GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
A comparative study of two Boolean formulations of FPGA detailed routing constraints
Proceedings of the 2001 international symposium on Physical design
Proceedings of the 38th annual Design Automation Conference
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Generic ILP versus specialized 0-1 ILP: an update
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
A fast pseudo-boolean constraint solver
Proceedings of the 40th annual Design Automation Conference
Shatter: efficient symmetry-breaking for boolean satisfiability
Proceedings of the 40th annual Design Automation Conference
BerkMin: A Fast and Robust Sat-Solver
Proceedings of the conference on Design, automation and test in Europe
ShatterPB: symmetry-breaking for pseudo-Boolean formulas
Proceedings of the 2004 Asia and South Pacific Design Automation Conference
Solving difficult instances of Boolean satisfiability in the presence of symmetry
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
The heuristic theorem prover: yet another SMT modulo theorem prover
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
| Hi-index | 0.00 |
With impressive progress in Boolean Satisfiability (SAT) solving and several extensions to pseudo-Boolean (PB) constraints, many applications that use SAT, such as high-performance formal verification techniques are still restricted to checking satisfiability of certain conditions. However, there is also frequently a need to express a preference for certain solutions. Extending SAT-solving to Boolean optimization allows the use of objective functions to describe a desirable solution. Although recent work in 0-1 Integer Linear Programming (ILP) offers extensions that can optimize a linear objective function, this is often achieved by solving a series of SAT or ILP decision problems. Our work articulates some pitfalls of this approach. An objective function may complicate the use of any symmetry that might be present in the given constraints, even when the constraints are unsatisfiable and the objective function is irrelevant. We propose several new techniques that treat objective functions differently from CNF/PB constraints and accelerate Boolean optimization in many practical cases. We also develop an adaptive flow that analyzes a given Boolean optimization problem and picks the symmetry-breaking technique that is best suited to the problem characteristics. Empirically, we show that for non-trivial objective functions that destroy constraint symmetries, the benefit of static symmetry-breaking is lost but dynamic symmetry-breaking accelerates problem-solving in many cases. We also introduce a new objective function, Localized Bit Selection (LBS), that can be used to specify a preference for bit values in formal verification applications.