A polynomial-time algorithm for the equivalence of probabilistic automata
SIAM Journal on Computing
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
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
SIAM Journal on Computing
Undecidability on quantum finite automata
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Descriptional complexity issues in quantum computing
Journal of Automata, Languages and Combinatorics
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
Regulated Rewriting in Formal Language Theory
Regulated Rewriting in Formal Language Theory
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
One-way probabilistic reversible and quantum one-counter automata
Theoretical Computer Science
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
Decidable and Undecidable Problems about Quantum Automata
SIAM Journal on Computing
Introduction to probabilistic automata (Computer science and applied mathematics)
Introduction to probabilistic automata (Computer science and applied mathematics)
Determination of equivalence between quantum sequential machines
Theoretical Computer Science
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Quantum computing: 1-way quantum automata
DLT'03 Proceedings of the 7th international conference on Developments in language theory
Note: A note on quantum sequential machines
Theoretical Computer Science
Hierarchy and equivalence of multi-letter quantum finite automata
Theoretical Computer Science
Languages Recognized with Unbounded Error by Quantum Finite Automata
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
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
Unbounded-error quantum computation with small space bounds
Information and Computation
Languages recognized by nondeterministic quantum finite automata
Quantum Information & Computation
Characterizations of one-way general quantum finite automata
Theoretical Computer Science
Quantum computation with write-only memory
Natural Computing: an international journal
Journal of Computer and System Sciences
On the complexity of minimizing probabilistic and quantum automata
Information and Computation
State succinctness of two-way finite automata with quantum and classical states
Theoretical Computer Science
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Two quantum finite automata are equivalent if for any input string x the two automata accept x with equal probability. In this paper, we first focus on determining the equivalence for one-way quantum finite automata with control language (CL-1QFAs) defined by Bertoni et al., and then, as an application, we address the equivalence problem for measure-many one-way quantum finite automata (MM-1QFAs) introduced by Kondacs and Watrous. More specifically, we obtain that: (i)Two CL-1QFAs A"1 and A"2 with control languages (regular languages) L"1 and L"2, respectively, are equivalent if and only if they are (c"1n"1^2+c"2n"2^2-1)-equivalent, where n"1 and n"2 are the numbers of states in A"1 and A"2, respectively, and c"1 and c"2 are the numbers of states in the minimal DFAs that recognize L"1 and L"2, respectively. Furthermore, if L"1 and L"2 are given in the form of DFAs, with m"1 and m"2 states, respectively, then there exists a polynomial-time algorithm running in time O((m"1n"1^2+m"2n"2^2)^4) that takes as input A"1 and A"2 and determines whether they are equivalent. (ii)(As an application of item (i)): Two MM-1QFAs A"1 and A"2 with n"1 and n"2 states, respectively, are equivalent if and only if they are (3n"1^2+3n"2^2-1)-equivalent. Furthermore, there is a polynomial-time algorithm running in time O((3n"1^2+3n"2^2)^4) that takes as input A"1 and A"2 and determines whether A"1 and A"2 are equivalent.