J. Leroux, A Polynomial Time Presburger Criterion and Synthesis for Number Decision Diagrams, in Proc. 20th IEEE Symp. Logic in Computer Science (LICS'2005), Chicago, USA, June 2005.

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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.

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   Author = {Leroux, J.},
   Title = {A Polynomial Time Presburger Criterion and Synthesis for Number Decision Diagrams},
   BookTitle = {Proc. 20th IEEE Symp. Logic in Computer Science (LICS'2005)},
   Address = {Chicago, USA},
   Month = {June},
   Year = {2005}

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