Least Significant Digit First Presburger Automata
Abstract
Since 1969 \cite{C-MST69,S-SMJ77}, we know that any Presburger-definable set \cite{P-PCM29} (a set of integer vectors satisfying a formula in the first-order additive theory of the integers) can be represented by a state-based symmbolic representation, called in this paper Finite Digit Vector Automata (FDVA). Efficient algorithms for manipulating these sets have been recently developed. However, the problem of deciding if a FDVA represents such a set, is a well-known hard problem first solved by Muchnik in 1991 with a quadruply-exponential time algorithm. In this paper, we show how to determine in polynomial time whether a FDVA represents a Presburger-definable set, and we provide in this positive case a polynomial time algorithm that constructs a Presburger-formula that defines the same set.
Cite
@article{arxiv.cs/0612037,
title = {Least Significant Digit First Presburger Automata},
author = {Jérôme Leroux},
journal= {arXiv preprint arXiv:cs/0612037},
year = {2016}
}