On the languages accepted by finite reversible automata
14th International Colloquium on Automata, languages and programming
The complexity of linear problems in fields
Journal of Symbolic Computation
Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Regular languages accepted by quantum automata
Information and Computation
Quantum automata and quantum grammars
Theoretical Computer Science
Characterizations of 1-Way Quantum Finite Automata
SIAM Journal on Computing
Some Recursive Unsolvable Problems Relating to Isolated Cutpoints in Probabilistic Automata
Proceedings of the Fourth Colloquium on Automata, Languages and Programming
Probabilistic Reversible Automata and Quantum Automata
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
1-way quantum finite automata: strengths, weaknesses and generalizations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Small size quantum automata recognizing some regular languages
Theoretical Computer Science - The art of theory
Quantum automata and algebraic groups
Journal of Symbolic Computation
Quantum computing: 1-way quantum automata
DLT'03 Proceedings of the 7th international conference on Developments in language theory
Quantum automata for some multiperiodic languages
Theoretical Computer Science
Revisiting the power and equivalence of one-way quantum finite automata
ICIC'10 Proceedings of the Advanced intelligent computing theories and applications, and 6th international conference on Intelligent computing
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Results in the area of compact monoids and groups are useful in the analysis of quantum automata (lqfa's). In this paper: (1) We settle isolated cut point Rabin's theorem in the context of compact monoids, and we prove a lower bound on the state complexity of lqfa's accepting regular languages. (2) We use a method pointed out by Blondel et al. [Decidable and undecidable problems about quantum automata, Technical Report RR2003-24, LIP, ENS Lyon, 2003] based on compact groups theory to design an algorithm for testing whether a k-tuple of lqfa's is a classifier of words in Σ*; this problem turns out to be undecidable if the completeness of the classifier is required. (3) In the unary case, we give an exponential time algorithm for computing the descriptional complexity of periodic languages. Moreover, we present a probabilistic method to construct lqfa's exponentially succinct in the period and polynomially succinct in the inverse of the bounded error.