Structural Presburger digit vector automata

نویسنده

Jérôme Leroux

چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Expressiveness of Real

If read digit by digit, a n-dimensional vector of integers represented in base r can be viewed as a word over the alphabet r n. It has been known for some time that, under this encoding, the sets of integer vectors recognizable by nite automata are exactly those deenable in Presburger arithmetic if independence with respect to the base is required , and those deenable in a slight extension of P...

متن کامل

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...

متن کامل

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...

متن کامل

Counting in trees

We consider automata and logics that allow to reason about numerical properties of unranked trees, expressed as Presburger constraints. We characterize non-deterministic automata by Presburger Monadic Second-Order logic, and deterministic automata by Presburger Fixpoint logic. We show how our results can be used in order to obtain efficient querying algorithms on XML trees.

متن کامل