The complexity of linear problems in fields
Journal of Symbolic Computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Simplification of truth-invariant cylindrical algebraic decompositions
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On projection in CAD-based quantifier elimination with equational constraint
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Deciding Hopf bifurcations by quantifier elimination in a software-component architecture
Journal of Symbolic Computation
Simple CAD construction and its applications
Journal of Symbolic Computation
On propagation of equational constraints in CAD-based quantifier elimination
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Efficient projection orders for CAD
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
On using bi-equational constraints in CAD construction
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Investigating Generic Methods to Solve Hopf Bifurcation Problems in Algebraic Biology
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
Verification and synthesis using real quantifier elimination
Proceedings of the 36th international symposium on Symbolic and algebraic computation
On the limits of the classical approach to cost analysis
SAS'12 Proceedings of the 19th international conference on Static Analysis
Hi-index | 0.00 |
This paper presents a framework and prototype implementation for preprocessing quantified input formulas that are intended as input for quantifier elimination algorithms. The framework loosely follows the AI search paradigm — exploring the space of formulas derived from the input by applying various rewriting operators in search of a problem formulation that will be good input for the intended Q.E. program. The only operator provided by the prototype implementation presented here is substitution for variables constrained by equations in which they appear linearly, supported by factorization and a simple check for non-vanishing of denominators in substitutions. Yet we present examples of quantified formulas which can be reduced by our preprocessing method to problems solvable by current quantifier elimination packages, whereas the original formulas had been inaccessible to those.