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.
Similar content being viewed by others
REFERENCES
G. Birkhoff and J. von Neumann, The logic of quantum mechanics, Ann. Math. 37 (1936) 823–843.
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.
D. Deutsch, Quantum theory, the Church¶Turing principle and the universal quantum computer, Proc. R. Soc. Lond. A 400 (1985) 97–117.
S. Eilenberg, Automata, Languages, and Machines, Volume A, Academic Press, New York, 1974.
R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21 (1982) 467–488.
R. P. Feynman, Quantum mechanical computers, Found. Phys. 16 (1986) 507–531.
L. Román and B. Rumbos, Quantum logic revisited, Found. Phys. 21 (1991) 727–734.
L. Román and R. E. Zuazua, Quantum implication, Int. J. Theor. Phys. 38 (1999) 793–797.
J. B. Rosser and A. R. Turquette, Many-Valued Logics, North-Holland, Amsterdam, 1952.
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.
K. Svozil, Quantum Logic, Springer-Verlag, Berlin, 1998.
V. Vedral and M. B. Plenio, Basics of quantum computation, Prog. Quant. Electron. 22 (1998) 1.
M. S. Ying, Deduction theorem for many-valued inference, Z. Math. Logik Grundl. Math. 37 (1991) 6.
M. S. Ying, The fundamental theorem of ultraproduct in Pavelka's logic, Z. Math. Logik Grundl. Math. 38 (1992) 2.
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.
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.
M. S. Ying, Fuzzifying topology based on complete residuated lattice-valued logic (I), Fuzzy Sets Systems 56 (1993) 337–373.
M. S. Ying, A logic for approximate reasoning, J. Symbolic Logic 59 (1994) 3.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ying, M. Automata Theory Based on Quantum Logic. (I). International Journal of Theoretical Physics 39, 985–995 (2000). https://doi.org/10.1023/A:1003642222321
Issue Date:
DOI: https://doi.org/10.1023/A:1003642222321