On the Class of Languages Recognizable by 1-Way Quantum Finite Automata

  • Andris Ambainis1
  • Arnolds KĶikusts
  • Māris Valdats
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)

Abstract

It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some neces- sary and some sufficient conditions for a (regular) language to be recog- nizable by a QFA. For a subclass of regular languages we get a condition which is necessary and sufficient.

Also, we prove that the class of languages recognizable by a QFA is not closed under union or any other binary Boolean operation where both arguments are significant.

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References

  1. [ABFK 99]
    A. Ambainis, R. Bonner, R. Freivalds, A. Ķikusts. Probabilities to accept languages by quantum finite automata. Proc. COCOON’99, Lecture Notes in Computer Science, 1627:174–183. Also quant-ph/99040664.Google Scholar
  2. [AF 98]
    A. Ambainis, R. Freivalds. 1-way quantum finite automata: strengths, weaknesses and generalizations. Proc. FOCS’98, pp. 332–341. Also quant-ph/9802062.Google Scholar
  3. [ANTV 98]
    A. Ambainis, A. Nayak, A. Ta-Shma, U. Vazirani. Dense quantum coding and a lower bound for 1-way quantum automata. Proc. STOC’99, pp. 376–383. Also quant-ph/9804043.Google Scholar
  4. [AW 99]
    A. Ambainis, J. Watrous. Two-way finite automata with quantum and classical states. cs.CC/9911009. Submitted to Theoretical Computer Science.Google Scholar
  5. [BV 97]
    E. Bernstein, U. Vazirani, Quantum complexity theory. SIAM Journal on Computing, 26:1411–1473, 1997.MATHCrossRefMathSciNetGoogle Scholar
  6. [BP 99]
    A. Brodsky, N. Pippenger. Characterizations of 1-way quantum finite automata. quant-ph/9903014.Google Scholar
  7. [G 00]
    J. Gruska. Descriptional complexity issues in quantum computing. Journal of Automata, Languages and Combinatorics, 5:191–218, 2000.MATHMathSciNetGoogle Scholar
  8. [KS 76]
    J. Kemeny, J. Laurie Snell. Finite Markov Chains. Springer-Verlag, 1976.Google Scholar
  9. [K 98]
    A. Ķikusts. A small 1-way quantum finite automaton. quant-ph/9810065.Google Scholar
  10. [KW 97]
    A. Kondacs, J. Watrous. On the power of quantum finite state automata. Proc. FOCS’97, pp. 66–75.Google Scholar
  11. [MT 69]
    A. Meyer, C. Thompson. Remarks on algebraic decomposition of automata. Mathematical Systems Theory, 3:110–118, 1969.MATHCrossRefMathSciNetGoogle Scholar
  12. [MC 97]
    C. Moore, J. Crutchfield. Quantum automata and quantum grammars. Theoretical Computer Science, 237:275–306, 2000. Also quant-ph/9707031.MATHCrossRefMathSciNetGoogle Scholar
  13. [N 99]
    A. Nayak. Optimal lower bounds for quantum automata and random access codes. Proc. FOCS’99, pp. 369–376. Also quant-ph/9904093.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Andris Ambainis1
    • 1
  • Arnolds KĶikusts
    • 2
  • Māris Valdats
    • 2
  1. 1.Computer Science DivisionUniversity of CaliforniaBerkeleyUSA
  2. 2.Institute of Mathematics and Computer ScienceUniversity of LatviaRīgaLatvia

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