The convex hull of a regular set of integer vectors is polyhedral and effectively computable
Information Processing Letters
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
The convex hull of a regular set of integer vectors is polyhedral and effectively computable
Information Processing Letters
Flat counter automata almost everywhere!
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
From automata to semilinear sets: a logical solution for sets L (C, P)
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
Computing affine hulls over Q and Z from sets represented by number decision diagrams
CIAA'05 Proceedings of the 10th international conference on Implementation and Application of Automata
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Automata-based representations have recently been investigated as a tool for representing and manipulating sets of integer vectors. In this paper, we study some structural properties of automata accepting the encodings (most significant digit first) of the natural solutions of systems of linear Diophantine inequations, i.e., convex polyhedra in N{N}. Based on those structural properties, we develop an algorithm that takes as input an automaton and generates a quantifier-free formula that represents exactly the set of integer vectors accepted by the automaton. In addition, our algorithm generates the minimal Hilbert basis of the linear system. In experiments made with a prototype implementation, we have been able to synthesize in seconds formulas and Hilbert bases from automata with more than 10,000 states.