Using an SMT solver and Craig interpolation to detect and remove redundant linear constraints in representations of non-convex polyhedra

Authors:
Christoph Scholl;Stefan Disch;Florian Pigorsch;Stefan Kupferschmid
Affiliations:
University of Freiburg, Freiburg, Germany;University of Freiburg, Freiburg, Germany;University of Freiburg, Freiburg, Germany;University of Freiburg, Freiburg, Germany
Venue:
SMT '08/BPR '08 Proceedings of the Joint Workshops of the 6th International Workshop on Satisfiability Modulo Theories and 1st International Workshop on Bit-Precise Reasoning
Year:
2008

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Abstract

We present a method which computes optimized representations for non-convex polyhedra. Our method detects so-called redundant linear constraints in these representations by using an incremental SMT solver and then removes the redundant constraints based on Craig interpolation. The approach is evaluated both for formulas from the model checking context including boolean combinations of linear constraints and boolean variables and for random trees composed of quantifiers, AND-, OR-, NOT-operators, and linear constraints produced by a generator. The results clearly show the advantages of our approach in comparison to state-of-the-art solvers.