The complexity of linear problems in fields
Journal of Symbolic Computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Applying SAT Methods in Unbounded Symbolic Model Checking
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Efficient SAT-based unbounded symbolic model checking using circuit cofactoring
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
DAG-aware AIG rewriting a fresh look at combinational logic synthesis
Proceedings of the 43rd annual Design Automation Conference
Advanced Unbounded Model Checking Based on AIGs, BDD Sweeping, And Quantifier Scheduling
FMCAD '06 Proceedings of the Formal Methods in Computer Aided Design
Scalable exploration of functional dependency by interpolation and incremental SAT solving
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Bi-decomposing large Boolean functions via interpolation and satisfiability solving
Proceedings of the 45th annual Design Automation Conference
Scalable don't-care-based logic optimization and resynthesis
Proceedings of the ACM/SIGDA international symposium on Field programmable gate arrays
To SAT or not to SAT: Ashenhurst decomposition in a large scale
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Interpolant-based transition relation approximation
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
New domains for applied quantifier elimination
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Automatic parallelization of recursive functions using quantifier elimination
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
| Hi-index | 0.00 |
This paper poses the following basic question: Given a quantified Boolean formula *** x . φ , what should a function/formula f be such that substituting f for x in φ yields a logically equivalent quantifier-free formula? Its answer leads to a solution to quantifier elimination in the Boolean domain, alternative to the conventional approach based on formula expansion. Such a composite function can be effectively derived using symbolic techniques and further simplified for practical applications. In particular, we explore Craig interpolation for scalable computation. This compositional approach to quantifier elimination is analyzably superior to the conventional one under certain practical assumptions. Experiments demonstrate the scalability of the approach. Several large problem instances unsolvable before can now be resolved effectively. A generalization to first-order logic characterizes a composite function's complete flexibility, which awaits further exploitation to simplify quantifier elimination beyond the propositional case.