Handbook of theoretical computer science (vol. B)
Mixed real-integer linear quantifier elimination
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
On the Expressiveness of Real and Integer Arithmetic Automata (Extended Abstract)
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Locally Threshold Testable Languages of Infinite Words
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
An Automata-Theoretic Approach to Presburger Arithmetic Constraints (Extended Abstract)
SAS '95 Proceedings of the Second International Symposium on Static Analysis
An Improved Reachability Analysis Method for Strongly Linear Hybrid Systems (Extended Abstract)
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
An effective decision procedure for linear arithmetic over the integers and reals
ACM Transactions on Computational Logic (TOCL)
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
A Generalization of Cobham's Theorem to Automata over Real Numbers
ICALP '07 Proceedings of the 34th international colloquium on Automata, Languages and Programming
The Büchi complementation saga
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
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
A Generalization of Semenov's Theorem to Automata over Real Numbers
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
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This paper studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers . This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases.In this paper, we first generalize this result to multiplicatively independentbases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this setting, Cobham's theorem does not generalize to multiplicatively independent bases. Finally, we prove that the sets of reals that are recognizable by Muller automata in two bases that do not share the same set of prime factors are exactly those definable in . These sets are thus also recognizable by weak deterministic automata. This result leads to a precise characterization of the sets of real numbers that are recognizable in multiple bases, and provides a theoretical justification to the use of weak automata as symbolic representations of sets.