Deciding polynomial-transcendental problems

Scott McCallum*, Volker Weispfenning

*Corresponding author for this work

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

This paper presents a decision procedure for a certain class of sentences of first order logic involving integral polynomials and a certain specific analytic transcendental function trans. (x) in which the variables range over the real numbers. The list of transcendental functions to which our decision method directly applies includes exp. (x), the exponential function with respect to base e, ln. (x), the natural logarithm of x, and arctan. (x), the inverse tangent function. The inputs to the decision procedure are prenex sentences in which only the outermost quantified variable can occur in the transcendental function. In the case trans. (x) = exp. (x), the decision procedure has been implemented in the computer logic system REDLOG. It is shown how to transform a sentence involving a transcendental function from a much wider collection of functions (such as hyperbolic and Gaussian functions, and trigonometric functions on a certain bounded interval) into a sentence to which our decision method directly applies. Closely related work is reported by Anai and Weispfenning (2000), Collins (1998),Maignan (1998), Richardson (1991), Strzebonski (in press) and Weispfenning (2000).

Original languageEnglish
Pages (from-to)16-31
Number of pages16
JournalJournal of Symbolic Computation
Volume47
Issue number1
DOIs
Publication statusPublished - Jan 2012

Keywords

  • Decision procedure
  • Exponential polynomials

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