Publication detail

A Logic of Singly Indexed Arrays

IOSIF, R. VOJNAR, T. HABERMEHL, P.

Original Title

A Logic of Singly Indexed Arrays

Type

article in a collection out of WoS and Scopus

Language

English

Original Abstract

We present a logic interpreted over integer arrays, which allows difference bound  comparisons between array elements situated within a constant sized window. We show that the satisfiability problem for the logic is undecidable for formulae  with a quantifier prefix $\{\exists,\forall\}^*\forall^*\exists^*\forall^*$. For formulae  with quantifier prefixes in the $\exists^*\forall^*$ fragment, decidability is established  by an automata-theoretic argument. For each formula in the $\exists^*\forall^*$ fragment, we  can build a~flat counter automaton with difference bound transition rules (FCADBM) whose traces correspond to the models of the formula. The construction is modular, following the syntax of  the formula. Decidability of the $\exists^*\forall^*$ fragment of the logic is a consequence  of the fact that reachability of a control state is decidable for FCADBM.

Keywords

mathematical logic, arrays, decidability, decision procedure, formal verification, automata

Authors

IOSIF, R.; VOJNAR, T.; HABERMEHL, P.

RIV year

2008

Released

3. 12. 2008

Publisher

Springer Verlag

Location

Berlin

ISBN

978-3-540-89438-4

Book

Logic for Programming, Artificial Intelligence and Reasoning

Edition

Lecture Notes in Computer Science

Pages from

558

Pages to

573

Pages count

16

BibTex

@inproceedings{BUT34278,
  author="Iosif {Radu} and Tomáš {Vojnar} and Peter {Habermehl}",
  title="A Logic of Singly Indexed Arrays",
  booktitle="Logic for Programming, Artificial Intelligence and Reasoning",
  year="2008",
  series="Lecture Notes in Computer Science",
  volume="5330",
  pages="558--573",
  publisher="Springer Verlag",
  address="Berlin",
  isbn="978-3-540-89438-4"
}