The Complexity of Probabilistic versus Deterministic Finite Automata
ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation
Probabilistic Reversible Automata and Quantum Automata
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
On the power of quantum finite state automata
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
1-way quantum finite automata: strengths, weaknesses and generalizations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The Mathematics of Coding Theory
The Mathematics of Coding Theory
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Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.