Rational series and their languages
Rational series and their languages
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
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Characterizations of 1-Way Quantum Finite Automata
SIAM Journal on Computing
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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
Optimal Lower Bounds for Quantum Automata and Random Access Codes
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Quantum computing: 1-way quantum automata
DLT'03 Proceedings of the 7th international conference on Developments in language theory
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In this paper, we analyze a model of 1-way quantum automaton where only measurements are allowed ( MON -1qfa). The automaton works on a compatibility alphabet $$(\Sigma, E)$$ of observables and its probabilistic behavior is a formal series on the free partially commutative monoid $$\hbox{FI}(\Sigma, E)$$ with idempotent generators. We prove some properties of this class of formal series and we apply the results to analyze the class $${\bf LMO}(\Sigma, E)$$ of languages recognized by MON -1qfa's with isolated cut point. In particular, we prove that $${\bf LMO}(\Sigma, E)$$ is a boolean algebra of recognizable languages with finite variation, and that $${\bf LMO}(\Sigma, E)$$ is properly contained in the recognizable languages, with the exception of the trivial case of complete commutativity.