International Journal of Theoretical Physics

, Volume 39, Issue 4, pp 985–995 | Cite as

Automata Theory Based on Quantum Logic. (I)

  • Mingsheng Ying
Article

Abstract

We present a basic framework of automata theory based on quantum logic. Inparticular, we introduce the orthomodular lattice-valued (quantum) predicate ofrecognizability and establish some of its fundamental properties.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. [BN36]
    G. Birkhoff and J. von Neumann, The logic of quantum mechanics, Ann. Math. 37 (1936) 823–843.Google Scholar
  2. [DC86]
    M. L. Dalla Chiara, Quantum logic, in: D. Gabbay and E. Guenthner (eds.), Handbook of Philosophical Logic, Volume III: Alternatives to Classical Logic, Reidel, Dordrecht, 1986, pp. 427–469.Google Scholar
  3. [D85]
    D. Deutsch, Quantum theory, the Church¶Turing principle and the universal quantum computer, Proc. R. Soc. Lond. A 400 (1985) 97–117.Google Scholar
  4. [E74]
    S. Eilenberg, Automata, Languages, and Machines, Volume A, Academic Press, New York, 1974.Google Scholar
  5. [F82]
    R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21 (1982) 467–488.Google Scholar
  6. [F86]
    R. P. Feynman, Quantum mechanical computers, Found. Phys. 16 (1986) 507–531.Google Scholar
  7. [RR91]
    L. Román and B. Rumbos, Quantum logic revisited, Found. Phys. 21 (1991) 727–734.Google Scholar
  8. [RZ99]
    L. Román and R. E. Zuazua, Quantum implication, Int. J. Theor. Phys. 38 (1999) 793–797.Google Scholar
  9. [RT52]
    J. B. Rosser and A. R. Turquette, Many-Valued Logics, North-Holland, Amsterdam, 1952.Google Scholar
  10. [S94]
    P. W. Shor, Polynomial-time algorithm for prime factorization and discrete logarithms on quantum computer, in Proceedings 35th Annual Symposium on Foundations of Computer Science, Santa Fe, IEEE Computer Society Press, 1994.Google Scholar
  11. [Sv98]
    K. Svozil, Quantum Logic, Springer-Verlag, Berlin, 1998.Google Scholar
  12. [VP]
    V. Vedral and M. B. Plenio, Basics of quantum computation, Prog. Quant. Electron. 22 (1998) 1.Google Scholar
  13. [Y91]
    M. S. Ying, Deduction theorem for many-valued inference, Z. Math. Logik Grundl. Math. 37 (1991) 6.Google Scholar
  14. [Y92a]
    M. S. Ying, The fundamental theorem of ultraproduct in Pavelka's logic, Z. Math. Logik Grundl. Math. 38 (1992) 2.Google Scholar
  15. [Y92b]
    M. S. Ying, Compactness, the Lowenheim¶Skolem property and the direct product of lattices of truth values, Z. Math. Logik Grundl. Math. 38 (1992) 4.Google Scholar
  16. [Y91¶93]
    M. S. Ying, A new approach for fuzzy topology (I), (II), (III), Fuzzy Sets Systems 39 (1991) 303–321; 47 (1992) 221¶232; 55 (1993) 193¶207.Google Scholar
  17. [Y93]
    M. S. Ying, Fuzzifying topology based on complete residuated lattice-valued logic (I), Fuzzy Sets Systems 56 (1993) 337–373.Google Scholar
  18. [Y94]
    M. S. Ying, A logic for approximate reasoning, J. Symbolic Logic 59 (1994) 3.Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Mingsheng Ying
    • 1
  1. 1.State Key Laboratory of Intelligent Technology and Systems, Department of ComputerScience and TechnologyTsinghua UniversityBeijingChina

Personalised recommendations