A lower bound for probabilistic algorithms for finite state machines
Journal of Computer and System Sciences
A time complexity gap for two-way probabilistic finite-state automata
SIAM Journal on Computing
Finite state verifiers I: the power of interaction
Journal of the ACM (JACM)
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum automata and quantum grammars
Theoretical Computer Science
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
Probabilistic Two-Way Machines
Proceedings on Mathematical Foundations of Computer Science
Running Time to Recognize Nonregular Languages by 2-Way Probabilistic Automata
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
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
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Some Observations on Two-Way Finite Automata with Quantum and Classical States
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Theoretical and Methodological Issues
Quantum computing: 1-way quantum automata
DLT'03 Proceedings of the 7th international conference on Developments in language theory
Some Observations on Two-Way Finite Automata with Quantum and Classical States
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Theoretical and Methodological Issues
Some algebraic properties of measure-once two-way quantum finite automata
Quantum Information Processing
Characterizations of one-way general quantum finite automata
Theoretical Computer Science
State succinctness of two-way finite automata with quantum and classical states
Theoretical Computer Science
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Two-way finite automata with quantum and classical states(2qcfa's) were introduced by Ambainis and Watrous. Though this computing model is more restricted than the usual two-way quantum finite automata(2qfa's) first proposed by Kondacs and Watrous, it is still more powerful than the classical counterpart. In this note, we focus on dealing with the operation properties of 2qcfa's. We prove that the Boolean operations (intersection, union, and complement) and the reversal operation of the class of languages recognized by 2qcfa's with error probabilities are closed; also, we verify that the catenation operation of such class of languages is closed under certain restricted condition. The numbers of states of these 2qcfa's for the above operations are presented. Some examples are included, and $\{xx^{R}|x\in \{a,b\}^{*},\#_{x}(a)=\#_{x}(b)\}$ is shown to be recognized by 2qcfa with one-sided error probability, where xRis the reversal of x, and #x(a) denotes the a's number in string x.