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
Relations Among Complexity Measures
Journal of the ACM (JACM)
Regular languages accepted by quantum automata
Information and Computation
Quantum automata and quantum grammars
Theoretical Computer Science
Analogies and differences between quantum and stochastic automata
Theoretical Computer Science
Quantum computation and quantum information
Quantum computation and quantum information
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Dense quantum coding and quantum finite automata
Journal of the ACM (JACM)
Characterizations of 1-Way Quantum Finite Automata
SIAM Journal on Computing
Two-way finite automata with quantum and classical states
Theoretical Computer Science - Natural computing
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
Characterizations of quantum automata
Theoretical Computer Science
Introduction to probabilistic automata (Computer science and applied mathematics)
Introduction to probabilistic automata (Computer science and applied mathematics)
Determining the equivalence for one-way quantum finite automata
Theoretical Computer Science
Note: A note on quantum sequential machines
Theoretical Computer Science
Hierarchy and equivalence of multi-letter quantum finite automata
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
Characterizations of one-way general quantum finite automata
Theoretical Computer Science
Journal of Computer and System Sciences
State succinctness of two-way finite automata with quantum and classical states
Theoretical Computer Science
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Quantum sequential machines (QSMs) that may be viewed as a quantum variant of stochastic sequential machines (SSMs) are one of the important quantum computing models. A very crucial result on SSMs is that two SSMs with n and n' states, respectively, and the same input and output alphabets are equivalent if and only if they are (n + n' - 1)-equivalent. Therefore, Gudder asked whether or not it holds for QSMs, as an open problem in this direction, since the further study is closely related to this result. Qiu demonstrated that in QSMs this result does not hold, and therefore answered in part the problem. However, as Qiu indicated, the sufficient and necessary conditions for the equivalence between two QSMs are still not discovered. In this paper, we show that if the condition of (n + n' -1)-equivalence is appropriately relaxed, then we can give a sufficient and necessary condition for justifying the equivalence between two QSMs. More precisely, we show that any two QSMs M and M' are equivalent if and only if they are (n + n')2-equivalent, where n and n' are, respectively, the numbers of states in M and M'. We therefore solve the open problem suggested by Gudder, and provide a basic result for further developing QSMs. As well, we discuss strongly factorizable QSMs and present the conditions for the equivalence between two strongly factorizable QSMs.