Abstract
We describe a simple algebraic semi-decision procedure for detecting unsatisfiability of a (quantifier-free) conjunction of nonlinear equalities and inequalities. The procedure consists of Gröbner basis computation plus extension rules that introduce new definitions, and hence it can be described as a critical-pair completion-based logical procedure. This procedure is shown to be sound and refutationally complete. When projected onto the linear case, our procedure reduces to the Simplex method for solving linear constraints. If only finitely many new definitions are introduced, then the procedure is also terminating. Such terminating, but potentially incomplete, procedures are used in “incompleteness-tolerant” applications.
Research supported in part by the National Science Foundation under grants CCR-0311348 and ITR-CCR-0326540.
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Tiwari, A. (2005). An Algebraic Approach for the Unsatisfiability of Nonlinear Constraints. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_18
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DOI: https://doi.org/10.1007/11538363_18
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