Truth table invariant cylindrical algebraic decomposition by regular chains

Russell Bradford, Changbo Chen, James H. Davenport, Matthew England, Marc Moreno Maza, David Wilson

Research output: Chapter in Book/Report/Conference proceedingConference proceedingpeer-review

21 Citations (Scopus)
45 Downloads (Pure)


A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of the decomposition. Secondly, the computation uses regular chains theory to first build a cylindrical decomposition of complex space (CCD) incrementally by polynomial. Significant modification of the regular chains technology was used to achieve the more sophisticated invariance criteria. Experimental results on an implementation in the RegularChains Library for Maple verify that combining these advances gives an algorithm superior to its individual components and competitive with the state of the art.

Original languageEnglish
Title of host publicationComputer Algebra in Scientific Computing - 16th International Workshop, CASC 2014, Proceedings
PublisherSpringer Verlag
Number of pages15
Volume8660 LNCS
ISBN (Electronic)978-3-319-10515-4
ISBN (Print)978-3-319-10514-7
Publication statusPublished - 2014
Externally publishedYes
Event16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014 - Warsaw, Poland
Duration: 8 Sept 201412 Sept 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8660 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349


Conference16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014

Bibliographical note

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  • cylindrical algebraic decomposition
  • equational constraint
  • regular chains
  • triangular decomposition

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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