### Abstract

Original language | English |
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Title of host publication | ISSAC '13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation |

Place of Publication | New York |

Publisher | Association for Computing Machinery |

Pages | 125-132 |

ISBN (Print) | 9781450320597 |

DOIs | |

Publication status | Published - 2013 |

Event | ISSAC 2013: International Symposium on Symbolic and Algebraic Computation - Boston, USA United States Duration: 25 Jun 2013 → 28 Jun 2013 |

### Conference

Conference | ISSAC 2013: International Symposium on Symbolic and Algebraic Computation |
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Country | USA United States |

City | Boston |

Period | 25/06/13 → 28/06/13 |

### Fingerprint

### Keywords

- cylindrical algebraic decomposition
- equational constraint

### Cite this

*ISSAC '13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation*(pp. 125-132). New York: Association for Computing Machinery. https://doi.org/10.1145/2465506.2465516

**Cylindrical algebraic decompositions for Boolean combinations.** / Bradford, Russell; Davenport, James H; England, Matthew; McCallum, Scott; Wilson, David.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ISSAC '13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation.*Association for Computing Machinery, New York, pp. 125-132, ISSAC 2013: International Symposium on Symbolic and Algebraic Computation, Boston, USA United States, 25/06/13. https://doi.org/10.1145/2465506.2465516

}

TY - GEN

T1 - Cylindrical algebraic decompositions for Boolean combinations

AU - Bradford, Russell

AU - Davenport, James H

AU - England, Matthew

AU - McCallum, Scott

AU - Wilson, David

PY - 2013

Y1 - 2013

N2 - This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae involving them. This motivates our definition of a Truth Table Invariant CAD (TTICAD). We generalise the theory of equational constraints to design an algorithm which will efficiently construct a TTICAD for a wide class of problems, producing stronger results than when using equational constraints alone. The algorithm is implemented fully in Maple and we present promising results from experimentation.

AB - This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but rather the truth values of certain quantifier free formulae involving them. This motivates our definition of a Truth Table Invariant CAD (TTICAD). We generalise the theory of equational constraints to design an algorithm which will efficiently construct a TTICAD for a wide class of problems, producing stronger results than when using equational constraints alone. The algorithm is implemented fully in Maple and we present promising results from experimentation.

KW - cylindrical algebraic decomposition

KW - equational constraint

UR - http://www.scopus.com/inward/record.url?scp=84871659975&partnerID=8YFLogxK

UR - http://www.issac-conference.org/2013/

UR - http://dx.doi.org/10.1145/2465506.2465516

U2 - 10.1145/2465506.2465516

DO - 10.1145/2465506.2465516

M3 - Conference contribution

SN - 9781450320597

SP - 125

EP - 132

BT - ISSAC '13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation

PB - Association for Computing Machinery

CY - New York

ER -