## Deciding Linear-Transcendental Problems (2000)

Citations: | 2 - 0 self |

### BibTeX

@TECHREPORT{Weispfenning00decidinglinear-transcendental,

author = {Volker Weispfenning},

title = {Deciding Linear-Transcendental Problems},

institution = {},

year = {2000}

}

### OpenURL

### Abstract

We present a decision procedure for linear-transcendental problems formalized in a suitable first-order language. The problems are formalized by formulas with arbitrary quantified linear variables and a block of quantifiers with respect to mixed linear-transcendental variables. Variables may range both over the reals and over the integers. The transcendental functions admitted are characterized axiomatically; they include the exponential function applied to a polynomial, hyperbolic functions and their inverses, and the arcustangent. The decision procedure is explicit and implementable; it is based on mixed real-integer linear elimination, the symbolic test point method, elementary analysis, and Lindemann's theorem. As a byproduct we obtain sample solutions for existential formulas and a qualitative description of the connected components of the satisfaction set wrt. a mixed linear-transcendental variable.