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Deciding polynomial-exponential problems
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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation table of contents
Linz/Hagenberg, Austria
SESSION: Contributed papers table of contents
Pages 215-222  
Year of Publication: 2008
ISBN:978-1-59593-904-3
Authors
Melanie Achatz  University of Passau, Passau, Germany
Scott McCallum  Macquarie University, Sydney, Australia
Volker Weispfenning  University of Passau, Passau, Germany
Sponsors
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
ACM: Association for Computing Machinery
Publisher
ACM  New York, NY, USA
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ABSTRACT

This paper presents a decision procedure for a certain class of sentences of first order logic involving integral polynomials and the exponential function in which the variables range over the real numbers. The inputs to the decision procedure are prenex sentences in which only the outermost quantified variable can occur in the exponential function. The decision procedure has been implemented in the computer logic system REDLOG. Closely related work is reported in [2, 7, 16, 20, 24].


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
M. Achatz. Deciding polynomial-exponential problems. Diploma thesis, University of Passau, D-94030 Passau, Germany, Sept. 2006.
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D. S. Arnon, G. E. Collins, and S. McCallum. Cylindrical algebraic decomposition i: Basic algorithm. In B. Caviness and J. Johnson, editors, Quantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation, pages 136--151. Springer, Wien, New York, 1998.
 
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G. E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In B. Caviness and J. Johnson, editors, Quantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation, pages 85--121. Springer, Wien, New York, 1998.
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A. Dolzmann and T. Sturm. Redlog user manual, edition 3.0. Technical report, University of Passau, 2004.
 
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J. R. Johnson. Algorithms for polynomial real root isolation. In B. Caviness and J. Johnson, editors, Quantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation, pages 269--299. Springer, Wien, New York, 1998.
 
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A. Macintyre and A. Wilkie. On the decidability of the real exponential field. In Kreiseliana: About and around Georg Kreisel, pages 441--467. A. K. Peters, 1996.
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A. Maignan. Real solving of elementary-algebraic systems. Numerical Algorithms, 27:153--167, 2001.
 
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S. McCallum and V. Weispfenning. Deciding polynomial-exponential problems. Technical report, Macquarie University, 2006.
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21
A. Seidl. Cylindrical decomposition under application-oriented paradigms. Doctoral dissertation. University of Passau, D-94030 Passau, Germany, Nov. 2006.
 
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A. B. Shidlovskii. Transcendental Numbers. Walter de Gruyter, Berlin, New York, 1989.
 
23
A. Tarski. A decision algorithm for elementary algebra and geometry. In B. Caviness and J. Johnson, editors, Quantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation, pages 24--84. Springer, Wien, New York, 1998.
 
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V. Weispfenning. Deciding linear--transcendental problems. In V. Ganzha, E. Mayr, and E. Vorozhtshov, editors, Computer Algebra in Scientific Computation -- CASC 2000, pages 423--438. Springer, 2000.

Collaborative Colleagues:
Melanie Achatz: colleagues
Scott McCallum: colleagues
Volker Weispfenning: colleagues