Quantum versus Classical Pushdown Automata in Exact Computation

Even though quantum computation is useful for solving certain problems, classical computation is more powerful in some cases. Thus, it is significant to compare the abilities of quantum computation and its classical counterpart, based on such a simple computation model as automata. In this paper we focus on the quantum pushdown automata which were defined by Golovkins in 2000, who showed that the class of languages recognized by quantum pushdown automata properly contains the class of languages recognized by finite automata. However, no one knows the entire relationship between the recognitive abilities of quantum and classical pushdown automata. As a part, we show a proposition that quantum pushdown automata can deterministically solve a certain problem that cannot be solved by any deterministic pushdown automata.

[1]  James P. Crutchfield,et al.  Quantum automata and quantum grammars , 2000, Theor. Comput. Sci..

[2]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[3]  Arnaldo Moura,et al.  A Generalization of Ogden's Lemma , 1982, JACM.

[4]  Ran Raz,et al.  Exponential separation of quantum and classical communication complexity , 1999, STOC '99.

[5]  Rusins Freivalds,et al.  Quantum versus Probabilistic One-Way Finite Automata with Counter , 2001, SOFSEM.

[6]  Hiroshi Imai,et al.  Quantum versus Deterministic Counter Automata , 2002, COCOON.

[7]  Raymond H. Putra,et al.  Exploiting the Difference in Probability Calculation between Quantum and Probabilistic Computations , 2002, UMC.

[8]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[9]  Daniel R. Simon.  On the Power of Quantum Computation , 1997, SIAM J. Comput..

[10]  John Watrous,et al.  On the power of quantum finite state automata , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[11]  Andris Ambainis,et al.  1-way quantum finite automata: strengths, weaknesses and generalizations , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[12]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[13]  R. Cleve,et al.  Quantum algorithms revisited , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  Maksim Kravtsev.  Quantum Finite One-Counter Automata , 1999, SOFSEM.

[15]  Avi Wigderson,et al.  Quantum vs. classical communication and computation , 1998, STOC '98.

[16]  Hiroshi Imai,et al.  One-way probabilistic reversible and quantum one-counter automata , 2002, Theor. Comput. Sci..