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
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Undecidability on quantum finite automata
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Regular languages accepted by quantum automata
Information and Computation
Quantum automata and quantum grammars
Theoretical Computer Science
Dense quantum coding and quantum finite automata
Journal of the ACM (JACM)
Characterizations of 1-Way Quantum Finite Automata
SIAM Journal on 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
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
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Determining the equivalence for one-way 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
On the complexity of minimizing probabilistic and quantum automata
Information and Computation
Hi-index | 5.23 |
Quantum sequential machines (QSMs) are a quantum version of stochastic sequential machines (SSMs). Recently, we showed that two QSMs M"1 and M"2 with n"1 and n"2 states, respectively, are equivalent iff they are (n"1+n"2)^2-equivalent [L.Z. Li, D.W. Qiu, Determination of equivalence between quantum sequential machines, Theoretical Computer Science 358 (2006) 65-74]. However, using this result to check the equivalence is likely to need exponential expected time. In this note, we consider the time complexity of deciding the equivalence between QSMs and related problems. The main results are as follows: (1) We present a polynomial-time algorithm for deciding the equivalence between QSMs, and, if two QSMs are not equivalent, this algorithm will produce an input-output pair with length not more than (n"1+n"2)^2. (2) We improve the bound for the equivalence between QSMs from (n"1+n"2)^2 to n"1^2+n"2^2-1, by employing Moore and Crutchfield's method [C. Moore, J.P. Crutchfield, Quantum automata and quantum grammars, Theoretical Computer Science 237 (2000) 275-306. Also quant-ph/9707031, 1997]. In addition, by viewing MO-1QFAs as a special case of QSMs, we briefly discuss the equivalence between MO-1QFAs, where the method used and the result obtained are slightly different from those given by Koshiba [T. Koshiba, Polynomial-time algorithms for the equivalence for one-way quantum finite automata, in: Proceedings of the 12th International Symposium on Algorithms and Computation, ISAAC'2001, Christchurch, New Zealand, in: Lecture Notes in Computer Science, vol. 2223, Springer, Berlin, 2001, pp. 268-278].