What Else Is Decidable about Integer Arrays?

We introduce a new decidable logic for reasoning about infinite arrays of integers. The logic is in the first-order 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. i . 0 i < n a[i+1] = a[i]-1) as well as periodic facts (e.g. i . i 2 0 a[i] = 0). The decision procedure follows the automata-theoretic approach: we translate formulae into a special class of B

• Type: Conference
• Year: 2008
• Where: FOSSACS
• Authors: Peter Habermehl, Radu Iosif, Tomás Vojnar
• Keywords: Counter Automata, Difference Constraints, FOSSACS 2008, Periodicity Constraints, Software Engineering