Detail publikace

# A Logic of Singly Indexed Arrays

Originální název

A Logic of Singly Indexed Arrays

Anglický název

A Logic of Singly Indexed Arrays

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

BibTex

``````
@inproceedings{BUT34278,
author="Iosif {Radu} and Tomáš {Vojnar} and Peter {Habermehl}",
title="A Logic of Singly Indexed Arrays",
annote="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
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