A generalized interval package and its use for semantic checking
ACM Transactions on Mathematical Software (TOMS)
On the SUP-INF Method for Proving Presburger Formulas
Journal of the ACM (JACM)
Variable Elimination and Chaining in a Resolution-based Prover for Inequalities
Proceedings of the 5th Conference on Automated Deduction
Spatio-Temporal Reasoning and Linear Inequalitites
Spatio-Temporal Reasoning and Linear Inequalitites
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 1
A new method for proving certain Presburger formulas
IJCAI'75 Proceedings of the 4th international joint conference on Artificial intelligence - Volume 1
A prover for general inequalities
IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 1
Qualitative mathematical reasoning
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
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This paper describes a program called BOUNDER that proves inequalities between functions over finite sets of constraints. Previous inequality algorithms perform well on some subset of the elementary functions, but poorly elsewhere. To overcome this problem, BOUNDER maintains a hierarchy of increasingly complex algorithms. When one fails to resolve an inequality, it tries the next. This strategy resolves more inequalities than any single algorithm. It also performs well on hard problems without wasting time on easy ones. The current hierarchy consists of four algorithms: bounds propagation, substitution, derivative inspection, and iterative approximation. Propagation is an extension of interval arithmetic that takes linear time, but ignores constraints between variables and multiple occurrences of variables. The remaining algorithms consider these factors, but require exponential time. Substitution is a new, provably correct, algorithm for utilizing constraints between variables. The final two algorithms analyze constraints between variables. Inspection examines the signs of partial derivatives. Iteration is based on several earlier algorithms from interval arithmetic.