ABSTRACT We address satisfiability checking for the first-order theory of the real-closed field (RCF) using satisfiability-modulo-theories (SMT) solving. SMT solvers combine a SAT solver to resolve the Boolean structure of a given formula... more
ABSTRACT We address satisfiability checking for the first-order theory of the real-closed field (RCF) using satisfiability-modulo-theories (SMT) solving. SMT solvers combine a SAT solver to resolve the Boolean structure of a given formula with theory solvers to verify the consistency of sets of theory constraints. In this paper, we report on an integration of Gröbner bases as a theory solver so that it conforms with the requirements for efficient SMT solving: (1) it allows the incremental adding and removing of polynomials from the input set and (2) it can compute an inconsistent subset of the input constraints if the Gröbner basis contains 1. We modify Buchberger’s algorithm by implementing a new update operator to optimize the Gröbner basis and provide two methods to handle inequalities. Our implementation uses special data structures tuned to be efficient for huge sets of sparse polynomials. Besides solving, the resulting module can be used to simplify constraints before being passed to other RCF theory solvers based on, e.g., the cylindrical algebraic decomposition.
Publication Date: 2013
Publication Name: Lecture Notes in Computer Science
Page 1. Reviewers The Program Committee Co-Chairs are very grateful for the substantial effort put in by the many reviewers outside of the Technical Program Committee. Samy Abbes Jan Krcal S. Akshay Thomas Krieger Hind Alhakami Yousra... more
Page 1. Reviewers The Program Committee Co-Chairs are very grateful for the substantial effort put in by the many reviewers outside of the Technical Program Committee. Samy Abbes Jan Krcal S. Akshay Thomas Krieger Hind Alhakami Yousra Lembachar Mario S. Alvim Michele Loreti Alessio Angius Ulrich Loup Cornel Barna Alexandru Mereacre Damián Barsotti Linar Mikeev Saddek Bensalem Malcolm Mumme Marco Bernardo Johanna Nellen Pieter-Tjerk de Boer Gethin Norman Luca Bortolussi David Parker Thomas Brihaye Sylvain Peyronnet ...
This paper connects research in computer science in the field of SAT-modulo-theories (SMT) solving and research in mathematics on decision procedures for real algebra. We consider a real algebraic decision procedure computing all... more
This paper connects research in computer science in the field of SAT-modulo-theories (SMT) solving and research in mathematics on decision procedures for real algebra. We consider a real algebraic decision procedure computing all realizable sign conditions of a set of polynomials. We modify this procedure so that it satisfies certain requirements needed for the embedding into an SMT-solver.
