Showing papers by "Peter Baumgartner published in 2000"

FDPLL - A First Order Davis-Putnam-Longeman-Loveland Procedure

Abstract: FDPLL is a directly lifted version of the well-known Davis-Putnam-Logeman-Loveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. non-ground and complementary literals now.

The Taming of the (X)OR

Abstract: Many key verification problems such as boundedmodel-checking, circuit verification and logical cryptanalysis are formalized with combined clausal and affine logic (i.e. clauses with xor as the connective) and cannot be efficiently (if at all) solved by using CNF-only provers. We present a decision procedure to efficiently decide such problems. The Gauss-DPLL procedure is a tight integration in a unifying framework of a Gauss-Elimination procedure (for affine logic) and a Davis-Putnam-Logeman-Loveland procedure (for usual clause logic). The key idea, which distinguishes our approach from others, is the full interaction bewteen the two parts which makes it possible to maximize (deterministic) simplification rules by passing around newly created unit or binary clauses in either of these parts. We show the correcteness and the termination of Gauss-DPLL under very liberal assumptions.

FDPLL : A first-order Davis-Putnam-Logeman-Loveland procedure

Abstract: FDPLL is a directly lifted version of the well-known Davis-Putnam-Logeman-Loveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. non-ground and complementary literals now. The motivation for this lifting is to bring together successful first-order techniques like unification and subsumption to the propositionally successful DPLL procedure. At the heart of the method is a new technique to represent first-order interpretations, where a literal specifies truth values for all its ground instances, unless there is a more specific literal specifying opposite truth values. Based on this idea, the FDPLL calculus is developed and proven as strongly complete.

Workshop: Model Computation - Principles, Algorithms, Applications

Abstract: Computing models of first-order or propositional logic specifications is the complementary problem of refutational theorem proving. A deduction system capable of producing models significantly extends the functionality of purely refutational systems by providing the user with useful information in case that no refutation exists.