International Journal of Theoretical Physics

, Volume 39, Issue 11, pp 2545–2557 | Cite as

Automata Theory Based on Quantum Logic II

  • Mingsheng Ying


We establish the pumping lemma in automata theory based on quantum logicunder certain conditions on implication, and discuss the recognizability by theproduct and union of orthomodular lattice-valued (quantum) automata. Inparticular, we show that the equivalence between the recognizabilty by the productof automata and the conjunction of the recognizabilities by the factor automatais equivalent to the distributivity of meet over union in the truth-value set.


Field Theory Elementary Particle Quantum Field Theory Quantum Logic Automaton Theory 
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  1. G. Birkhoff and J. von Neumann (1936). Ann. Math. 37 823–843.Google Scholar
  2. M. L. Dalla Chiara, In D. Gabbay and E. Guenthner (eds.), Handbook of Philosophical Logic, Vol. III: Alternatives to Classical Logic, Reidel, Dordrecht (1986) pp. 427–469.Google Scholar
  3. D. Deutsch (1985). Proc. R. Soc. Lond. A 400 97–11.Google Scholar
  4. S. Eilenberg, Automata, Languages, and Machines, Vol. A, Academic Press, New York (1974).Google Scholar
  5. R. P. Feynman (1982). Int. J. Theor. Phys. 21 467–488.Google Scholar
  6. R. P. Feynman (1986). Found. Phys. 16 507–531.Google Scholar
  7. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, Massachusetts (1979).Google Scholar
  8. C. Moore and J. P. Crutchfield, Quantum automata and quantum grammars, Theor. Computer Sci., to appear.Google Scholar
  9. L. Román and B. Rumbos (1991). Found. Phys. 21 727–734.Google Scholar
  10. L. Román and R. E. Zuazua (1999). Int. J. Theor. Phys. 38 793–797.Google Scholar
  11. J. B. Rosser and A. R. Turquette, Many-Valued Logics, North-Holland, Amsterdam (1952).Google Scholar
  12. K. Svozil, Quantum Logic, Springer-Verlag, Berlin (1998).Google Scholar
  13. M. S. Ying (1991). Fuzzy Sets Syst. 39 303–321; (1992). 47 221-232; (1993). 55 193-207.Google Scholar
  14. M. S. Ying (1993). Fuzzy Sets Syst. 56 337–373.Google Scholar
  15. M. S. Ying (2000). Int. J. Theor. Phys. 39 981–991.Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Mingsheng Ying
    • 1
    • 2
  1. 1.Department of Computer ScienceState Key Laboratory of Intelligent Technology and Systemschina
  2. 2.Tsinghua UniversityBeijingChina

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