%0 Conference Proceedings
%F leroux05d
%A Leroux, J.
%T A Polynomial Time Presburger Criterion and Synthesis for Number Decision Diagrams
%B Proc. 20th IEEE Symp. Logic in Computer Science (LICS'2005)
%P 147-156
%C Chicago, USA
%X Number Decision Diagrams (NDD) are the automatabased symbolic representation for manipulating sets of integer vectors encoded as strings of digit vectors (least or most significant digit first). Since 1969 [8, 29], we know that any Presburger-definable set [26] (a set of integer vectors satisfying a formula in the first-order additive theory of the integers) can be represented by a NDD, and efficient algorithm for manipulating these sets have been recently developed [31, 4]. However, the problem of deciding if a NDD represents such a set, is a well-known hard problem first solved by Muchnik in 1991 [23, 24, 5] with a quadruplyexponential time algorithm. In this paper, we show how to determine in polynomial time whether a NDD represents a Presburger-definable set, and we provide in this positive case a polynomial time algorithm that constructs from the NDD a Presburger-formula that defines the same set
%U http://www.irisa.fr/vertecs/Publis/Ps/2005-LICS.pdf
%U http://dx.doi.org/10.1109/LICS.2005.2
%8 June
%D 2005