Deciding Linear-Transcendental Problems

Volker Weispfenning ()
Additional contact information
Volker Weispfenning: Universität Passau, Fakultät für Mathematik und Informatik

A chapter in Computer Algebra in Scientific Computing, 2000, pp 423-437 from Springer

Abstract: 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. Potential applications include reachability problems for linear differential systems.

Date: 2000
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-57201-2_32

Ordering information: This item can be ordered from
http://www.springer.com/9783642572012

DOI: 10.1007/978-3-642-57201-2_32

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().