Technical reportHABERMEHL Peter, IOSIF Radu and VOJNAR Tomáš. What else is decidable about integer arrays?. TR20078, Grenoble: VERIMAG, 2008.  Publication language:  english 

Original title:  What else is decidable about integer arrays? 

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

Pages:  36 

Place:  TR20078, Grenoble, FR 

Year:  2008 

Publisher:  VERIMAG 

URL:  http://www.fit.vutbr.cz/~vojnar/Publications/hivarraystr07.pdf [PDF] 

Keywords 

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

This report is the full version of the corresponding FOSSCAS'08 paper, including full proofs of the achived results. In the work, 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: 

@TECHREPORT{
author = {Peter Habermehl and Radu Iosif and Tom{\'{a}}{\v{s}} Vojnar},
title = {What else is decidable about integer arrays?},
pages = {36},
year = {2008},
location = {TR20078, Grenoble, FR},
publisher = {VERIMAG},
language = {english},
url = {http://www.fit.vutbr.cz/research/view_pub.php?id=8819}
} 
