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CAV

2008

Springer

2008

Springer

We consider an extension of integer linear arithmetic with a "star" operator takes closure under vector addition of the solution set of a linear arithmetic subformula. We show that the satisfiability problem for this extended language remains in NP (and therefore NP-complete). Our proof uses semilinear set characterization of solutions of integer linear arithmetic formulas, as well as a generalization of a recent result on sparse solutions of integer linear programming problems. As a consequence of our result, we present worst-case optimal decision procedures for two NP-hard problems that were previously not known to be in NP. The first is the satisfiability problem for a logic of sets, multisets (bags), and cardinality constraints, which has applications in verification, interactive theorem proving, and description logics. The second is the reachability problem for a class of transition systems whose transitions increment the state vector by solutions of integer linear arith...

Related Content

Added |
12 Oct 2010 |

Updated |
12 Oct 2010 |

Type |
Conference |

Year |
2008 |

Where |
CAV |

Authors |
Ruzica Piskac, Viktor Kuncak |

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