The theory of N,+,Vk,Vl is undecidable
Theoretical Computer Science
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
Verifying Systems with Infinite but Regular State Spaces
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
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)
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
Quantifier elimination for the reals with a predicate for the powers of two
Theoretical Computer Science
Complementation constructions for nondeterministic automata on infinite words
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
| Hi-index | 0.00 |
This paper studies the expressive power of finite-state automata recognizing sets of real numbers encoded positionally. It is known that the sets that are definable in the first-order additive theory of real and integer variables 〈R, Z,+,r 1. In this paper, we prove the reciprocal property, i.e., that a subset of R that is recognizable by weak deterministic automata in every base r 1 is necessarily definable in 〈R, Z,+,