Convex Hull of Arithmetic Automata
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Computing Convex Hulls by Automata Iteration
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Structural Presburger digit vector automata
Theoretical Computer Science
A generalization of Cobham's theorem to automata over real numbers
Theoretical Computer Science
TaPAS: The Talence Presburger Arithmetic Suite
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Automatic Verification of Counter Systems With Ranking Function
Electronic Notes in Theoretical Computer Science (ENTCS)
A Generalization of Semenov's Theorem to Automata over Real Numbers
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Finite automata and the writing of numbers
DLT'07 Proceedings of the 11th international conference on Developments in language theory
LATA'11 Proceedings of the 5th international conference on Language and automata theory and applications
Enumeration and decidable properties of automatic sequences
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Post correspondence problem with partially commutative alphabets
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
A generalization of Cobham's theorem to automata over real numbers
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Computing minimal separating DFAs and regular invariants using SAT and SMT solvers
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
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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.