Fast simplifications for Tarski formulas based on monomial inequalities

Authors:
Christopher W. Brown
Affiliations:
-
Venue:
Journal of Symbolic Computation
Year:
2012

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Abstract

We define the ''combinatorial part'' of a Tarski formula in which equalities and inequalities are in factored or partially-factored form. The combinatorial part of a formula contains only ''monomial inequalities'', which are sign conditions on monomials. We give efficient algorithms for answering some basic questions about conjunctions of monomial inequalities and prove the NP-Completeness/Hardness of some others. By simplifying the combinatorial part of a Tarski formula, and mapping the simplified combinatorial part back to a Tarski formula, we obtain non-trivial simplifications without algebraic operations.