International Journal of Theoretical Physics

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

Automata Theory Based on Quantum Logic. (I)

  • Mingsheng Ying


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.


Field Theory Elementary Particle Quantum Field Theory Fundamental Property Quantum Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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