Alternating automata, the weak monadic theory of the tree, and its complexity
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Efficient minimization of deterministic weak &ohgr;-automata
Information Processing Letters
Representing Arithmetic Constraints with Finite Automata: An Overview
ICLP '02 Proceedings of the 18th International Conference on Logic Programming
On the Expressiveness of Real and Integer Arithmetic Automata (Extended Abstract)
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Diophantine Equations, Presburger Arithmetic and Finite Automata
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
From Automata to Formulas: Convex Integer Polyhedra
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
An effective decision procedure for linear arithmetic over the integers and reals
ACM Transactions on Computational Logic (TOCL)
A Polynomial Time Presburger Criterion and Synthesis for Number Decision Diagrams
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
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
The Büchi complementation saga
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Flat counter automata almost everywhere!
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
Don't care words with an application to the automata-based approach for real addition
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
The power of hybrid acceleration
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
T(O)RMC: A Tool for (ω)-Regular Model Checking
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Computing Convex Hulls by Automata Iteration
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
On (Omega-)regular model checking
ACM Transactions on Computational Logic (TOCL)
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This paper considers the problem of computing the real convex hull of a finite set of n-dimensional integer vectors. The starting point is a finite-automaton representation of the initial set of vectors. The proposed method consists in computing a sequence of automata representing approximations of the convex hull and using extrapolation techniques to compute the limit of this sequence. The convex hull can then be directly computed from this limit in the form of an automaton-based representation of the corresponding set of real vectors. The technique is quite general and has been implemented. Also, our result fits in a wider scheme whose objective is to improve the techniques for converting automata-based representation of constraints to formulas.