Structural Presburger digit vector automata

Structural Presburger digit vector automata

The least significant digit first decomposition of integer vectors into words of digit vectors provides a natural way for representing sets of integer vectors by automata. In this paper, the minimal automata representing Presburger sets are proved structurally Presburger: automata obtained by moving the initial state and replacing the accepting condition represent Presburger sets.

Least Significant Digit First Presburger Automata

1 Introduction Presburger arithmetic [Pre29] is a decidable logic used in a large range of applications. As described in [Lat04], this logic is central in many areas including integer programming problems [Sch87], compiler optimization techniques [Ome], program analysis tools [BGP99, FO97, Fri00] and model-checking [BFL04, Fas, Las]. Different techniques [GBD02] and tools have been developed fo...

Diophantine Equations, Presburger Arithmetic and Finite Automata

We show that the use of nite automata provides a decision procedure for Presburger Arithmetic with optimal worst case complexity.

On Presburger Liveness of Discrete Timed Automata

Using an automata-theoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburger clock constraints is undecidable, we show that there are various classes of Presburger liveness...

Analyzing Automata with Presburger Arithmetic and Uninterpreted Function Symbols