Conference paperHABERMEHL Peter, IOSIF Radu and VOJNAR Tomáš. What else is decidable about integer arrays?. In: Foundations of Software Science and Computation Structures. Berlin: Springer Verlag, 2008, pp. 475490. ISBN 9783540784975.  Publication language:  english 

Original title:  What else is decidable about integer arrays? 

Title (cs):  Co dále je rozhodnutelné o polích? 

Pages:  475490 

Proceedings:  Foundations of Software Science and Computation Structures 

Conference:  European Joint Conferences on Theory and Practice of Software  ETAPS'08 (TACAS'08, FoSSaCS'08) 

Series:  LNCS 4962 

Place:  Berlin, DE 

Year:  2008 

ISBN:  9783540784975 

Publisher:  Springer Verlag 

Keywords 

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

Annotation 

We introduce a new decidable logic for reasoning about infinite arrays of integers. The logic is in the $\exists^* \forall^*$ firstorder fragment and allows (1) Presburger constraints on existentially quantified variables, (2) difference constraints as well as periodicity constraints on universally quantified indices, and (3) difference constraints on values. In particular, using our logic, one can express constraints on consecutive elements of arrays (e.g., $\forall i ~.~ 0 \leq i < n \rightarrow a[i+1]=a[i]1$) as well as periodic facts (e.g., $\forall i ~.~ i \equiv_2 0 \rightarrow a[i] = 0$). The decision procedure follows the automatatheoretic approach: we translate formulae into a special class of B\"uchi counter automata such that any model of a formula corresponds to an accepting run of an automaton, and vice versa. The emptiness problem for this class of counter automata is shown to be decidable as a consequence of earlier results on counter automata with a flat control structure and transitions based on difference constraints.

BibTeX: 

@INPROCEEDINGS{
author = {Peter Habermehl and Radu Iosif and Tom{\'{a}}{\v{s}} Vojnar},
title = {What else is decidable about integer arrays?},
pages = {475490},
booktitle = {Foundations of Software Science and Computation Structures},
series = {LNCS 4962},
year = {2008},
location = {Berlin, DE},
publisher = {Springer Verlag},
ISBN = {9783540784975},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=8574}
} 
