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Heuristic search strategies for Cylindrical Algebraic Decomposition

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Artificial Intelligence and Symbolic Mathematical Computing (AISMC 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 737))

Abstract

In this paper, we report how certain AI techniques can be used to speed up an algebraic algorithm for deciding the satisfiability of a system of polynomial equations, dis-equations, and inequalities. The algebraic algorithm (a restructured version of Cylindrical Algebraic Decomposition) is non-deterministic, in the sense that it can often achieve the same goal, but following different paths requiring different amounts of computing times. Obviously one wishes to follow the least time-consuming path. However, in practice it is not possible to determine such an optimal path. Thus it naturally renders itself to the heuristic search techniques of AI. In particular we experimented with Best-First strategy. The experimental results indicate that such AI techniques can often help in speeding up the algebraic method, sometimes dramatically.

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Authors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes Kepler University, A-4040, Linz, Austria

    Hoon Hong

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  1. Hoon Hong
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Editor information

Jacques Calmet John A. Campbell

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© 1993 Springer-Verlag Berlin Heidelberg

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Hong, H. (1993). Heuristic search strategies for Cylindrical Algebraic Decomposition. In: Calmet, J., Campbell, J.A. (eds) Artificial Intelligence and Symbolic Mathematical Computing. AISMC 1992. Lecture Notes in Computer Science, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57322-4_10

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  • DOI: https://doi.org/10.1007/3-540-57322-4_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57322-7

  • Online ISBN: 978-3-540-48063-1

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