Details:
Title  Deciding polynomialtranscendental problems  Author(s)  Scott McCallum, Volker Weispfenning  Type  Article in Journal  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).  Keywords  Decision procedure, Exponential polynomials  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111001167 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  1  Pages  16  31  Year  2012  Edition  0  Translation 
No  Refereed 
No 
