Truth table invariant cylindrical algebraic decomposition

R. Bradford, J. H. Davenport, Matthew England, S. McCallum, D. Wilson

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    32 Citations (Scopus)
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    When using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is likely not the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae involving them. This observation motivates our article and definition of a Truth Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors presented an algorithm that can efficiently and directly construct a TTICAD for a list of formulae in which each has an equational constraint. This was achieved by generalising McCallum's theory of reduced projection operators. In this paper we present an extended version of our theory which can be applied to an arbitrary list of formulae, achieving savings if at least one has an equational constraint. We also explain how the theory of reduced projection operators can allow for further improvements to the lifting phase of CAD algorithms, even in the context of a single equational constraint. The algorithm is implemented fully in Maple and we present both promising results from experimentation and a complexity analysis showing the benefits of our contributions.
    Original languageEnglish
    Pages (from-to)1-35
    JournalJournal of Symbolic Computation
    Early online date4 Nov 2015
    Publication statusPublished - Sep 2016

    Bibliographical note

    Open Access funded by Engineering and Physical Sciences Research Council
    Under a Creative Commons license


    • Cylindrical algebraic decomposition
    • Equational constraint


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