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Volumn 344, Issue 2-3, 2005, Pages 134-207

A theory of computation based on quantum logic (I)

Author keywords

Algebraic semantics; Finite automata; Orthomodular lattice; Quantum computation; Quantum logic; Regular languages

Indexed keywords

COMPUTATIONAL METHODS; FINITE AUTOMATA; FORMAL LANGUAGES; QUANTUM THEORY; SEMANTICS;

EID: 27644550004     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2005.04.001     Document Type: Article
Times cited : (58)

References (52)
  • 1
    • 85047893286 scopus 로고
    • Model-theoretic logics: Background and aims
    • J. Barwise S. Feferman Springer Berlin
    • J. Barwise Model-theoretic logics: background and aims J. Barwise S. Feferman Model Theoretic Logics 1985 Springer Berlin 3 27
    • (1985) Model Theoretic Logics , pp. 3-27
    • Barwise, J.1
  • 2
    • 34250256884 scopus 로고
    • The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computer s as represented by Turing machines
    • P.A. Benioff The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computer s as represented by Turing machines J. Statist. Phys. 22 1980 563 591
    • (1980) J. Statist. Phys. , vol.22 , pp. 563-591
    • Benioff, P.A.1
  • 3
    • 0015680909 scopus 로고
    • Logical reversibility of computation
    • C.H. Bennet Logical reversibility of computation IBM J. Res. Dev. 17 1973 525 532
    • (1973) IBM J. Res. Dev. , vol.17 , pp. 525-532
    • Bennet, C.H.1
  • 4
    • 0000194417 scopus 로고
    • The logic of quantum mechanics
    • G. Birkhoff, and J. von Neumann The logic of quantum mechanics Ann. Math. 37 1936 823 843
    • (1936) Ann. Math. , vol.37 , pp. 823-843
    • Birkhoff, G.1    Von Neumann, J.2
  • 6
    • 4244043498 scopus 로고
    • Quantum computation with cold trapped ions
    • J.I. Cirac, and P. Zoller Quantum computation with cold trapped ions Phys. Rev. Lett. 74 1995 4091 4094
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 4091-4094
    • Cirac, J.I.1    Zoller, P.2
  • 8
    • 27644593596 scopus 로고
    • Some meta-logical pathologies of quantum logic
    • E. Beltrametti B.C. van Fraassen Plenum New York
    • M.L. Dalla Chiara Some meta-logical pathologies of quantum logic E. Beltrametti B.C. van Fraassen Current Issues in Quantum Logics 1981 Plenum New York 147 159
    • (1981) Current Issues in Quantum Logics , pp. 147-159
    • Dalla Chiara, M.L.1
  • 9
    • 0003056266 scopus 로고
    • Quantum logic
    • D. Gabbay, E. Guenthner (Eds.) Reidel, Dordrecht Also see arXiv: quant-ph/0101028 for an extended and revised version
    • M.L. Dalla Chiara, Quantum logic, in: D. Gabbay, E. Guenthner (Eds.), Handbook of Philosophical Logic, Vol. III: Alternatives to Classical Logic, Reidel, Dordrecht, 1986, pp. 427-469. Also see arXiv: quant-ph/0101028 for an extended and revised version.
    • (1986) Handbook of Philosophical Logic, Vol. III: Alternatives to Classical Logic , vol.3 , pp. 427-469
    • Dalla Chiara, M.L.1
  • 10
    • 0022421379 scopus 로고
    • Quantum theory, the Church-Turing principle and the universal quantum computer
    • D. Deutsch Quantum theory, the Church-Turing principle and the universal quantum computer Proc. Roy. Soc. Lond. A 400 1985 97 117
    • (1985) Proc. Roy. Soc. Lond. A , vol.400 , pp. 97-117
    • Deutsch, D.1
  • 11
    • 0002496370 scopus 로고
    • Quantum computational networks
    • D. Deutsch Quantum computational networks Proc. Roy. Soc. Lond. A 425 1989 73 90
    • (1989) Proc. Roy. Soc. Lond. A , vol.425 , pp. 73-90
    • Deutsch, D.1
  • 12
    • 27644578724 scopus 로고
    • The current trend of pure mathematics
    • J. Dieudonne The current trend of pure mathematics Adv. Math. 27 1978 235 255
    • (1978) Adv. Math. , vol.27 , pp. 235-255
    • Dieudonne, J.1
  • 14
    • 51249180339 scopus 로고
    • Simulating physics with computers
    • R.P. Feynman Simulating physics with computers Int. J. Theoret. Phys. 21 1982 467 488
    • (1982) Int. J. Theoret. Phys. , vol.21 , pp. 467-488
    • Feynman, R.P.1
  • 15
    • 5344230456 scopus 로고
    • Quantum mechanical computers
    • R.P. Feynman Quantum mechanical computers Found. Phys. 16 1986 507 531
    • (1986) Found. Phys. , vol.16 , pp. 507-531
    • Feynman, R.P.1
  • 16
    • 0041789202 scopus 로고
    • Quantum logic as an implication algebra
    • P.D. Finch Quantum logic as an implication algebra Bull. Austr. Math. Soc. 2 1970 101 106
    • (1970) Bull. Austr. Math. Soc. , vol.2 , pp. 101-106
    • Finch, P.D.1
  • 17
    • 0029701737 scopus 로고    scopus 로고
    • A fast quantum mechanical algorithm for database search
    • L.K. Grover, A fast quantum mechanical algorithm for database search, in: Proc. 28th ACM STOC, 1996, pp. 212-219.
    • (1996) Proc. 28th ACM STOC , pp. 212-219
    • Grover, L.K.1
  • 18
    • 0442326281 scopus 로고    scopus 로고
    • Basic properties of quantum automata
    • S. Gudder Basic properties of quantum automata Found. Phys. 30 2000 301 319
    • (2000) Found. Phys. , vol.30 , pp. 301-319
    • Gudder, S.1
  • 22
    • 80054165705 scopus 로고
    • Three-valued logics - An introduction, a comparison of various logical lexica, and some philosophical remarks
    • H. Hodes Three-valued logics - an introduction, a comparison of various logical lexica, and some philosophical remarks Ann. Pure Appl. Logic 43 1989 99 145
    • (1989) Ann. Pure Appl. Logic , vol.43 , pp. 99-145
    • Hodes, H.1
  • 24
    • 0039811826 scopus 로고
    • Studies on the foundations of quantum mechanics i
    • K. Husimi Studies on the foundations of quantum mechanics I Proc. Physicomath. Soc. Japan 19 1937 766 789
    • (1937) Proc. Physicomath. Soc. Japan , vol.19 , pp. 766-789
    • Husimi, K.1
  • 29
    • 0027660531 scopus 로고
    • A potentially realizable quantum computer
    • S. Lloyd A potentially realizable quantum computer Science 261 1993 1569 1571
    • (1993) Science , vol.261 , pp. 1569-1571
    • Lloyd, S.1
  • 30
    • 0040686650 scopus 로고
    • The deduction theorem for quantum logic - Some negative results
    • J. Malinowski The deduction theorem for quantum logic - some negative results J. Symbolic Logic 55 1990 615 625
    • (1990) J. Symbolic Logic , vol.55 , pp. 615-625
    • Malinowski, J.1
  • 31
    • 84881829506 scopus 로고
    • Thirty years of foundational studies: Lectures on the development of mathematical logic and the study of the foundations of mathematics in 1930-1964
    • Helsinki
    • A. Mostowski, Thirty Years of Foundational Studies: Lectures on the Development of Mathematical Logic and the Study of the Foundations of Mathematics in 1930-1964, Acta Philosophica Fennica, Vol. 17, Helsinki, 1965.
    • (1965) Acta Philosophica Fennica , vol.17
    • Mostowski, A.1
  • 32
    • 0346104276 scopus 로고
    • Quantum logics (strict- and probability-logics), summarized
    • J. von Neumann (Ed.) Macmillan, New York
    • J. von Neumann, Quantum logics (strict- and probability-logics), summarized in: J. von Neumann (Ed.), Collected Works, Vol. IV, Macmillan, New York, 1962.
    • (1962) Collected Works , vol.4
    • Von Neumann, J.1
  • 33
    • 0348179165 scopus 로고    scopus 로고
    • Orthologic and quantum logic: Models and computational elements
    • J.P. Rawling, and S.A. Selesnick Orthologic and quantum logic: models and computational elements J. ACM 47 2000 721 751
    • (2000) J. ACM , vol.47 , pp. 721-751
    • Rawling, J.P.1    Selesnick, S.A.2
  • 34
    • 0000595671 scopus 로고
    • Quantum logic revisited
    • L. Román, and B. Rumbos Quantum logic revisited Found. Phys. 21 1991 727 734
    • (1991) Found. Phys. , vol.21 , pp. 727-734
    • Román, L.1    Rumbos, B.2
  • 37
    • 0033241364 scopus 로고    scopus 로고
    • Toward quantum mathematics. I. From quantum set theory to universal quantum mechanics
    • K.-G. Schlesinger Toward quantum mathematics. I. From quantum set theory to universal quantum mechanics J. Math. Phys. 40 1999 1344 1358
    • (1999) J. Math. Phys. , vol.40 , pp. 1344-1358
    • Schlesinger, K.-G.1
  • 38
    • 0002642964 scopus 로고
    • Polynomial-time algorithm for prime factorization and discrete logarithms on quantum computer
    • Santa Fe IEEE Computer Society Press Silver Spring, MD
    • P.W. Shor Polynomial-time algorithm for prime factorization and discrete logarithms on quantum computer Proc. 35th Ann. Symp. on Foundations of Computer Science Santa Fe 1994 IEEE Computer Society Press Silver Spring, MD
    • (1994) Proc. 35th Ann. Symp. on Foundations of Computer Science
    • Shor, P.W.1
  • 40
    • 0009295134 scopus 로고
    • Quantum set theory
    • E. Beltrametti B.C. van Fraassen Plenum New York
    • G. Takeuti Quantum set theory E. Beltrametti B.C. van Fraassen Current Issues in Quantum Logics 1981 Plenum New York 303 322
    • (1981) Current Issues in Quantum Logics , pp. 303-322
    • Takeuti, G.1
  • 44
    • 84981433123 scopus 로고
    • Deduction theorem for many-valued inference
    • M.S. Ying Deduction theorem for many-valued inference Z. Math. Logik Grundlagen Math. 37 1991 6
    • (1991) Z. Math. Logik Grundlagen Math. , vol.37 , pp. 6
    • Ying, M.S.1
  • 45
    • 84981425570 scopus 로고
    • The fundamental theorem of ultraproduct in Pavelka's logic
    • M.S. Ying The fundamental theorem of ultraproduct in Pavelka's logic Z. Math. Logik Grundlagen Math. 38 1992 2
    • (1992) Z. Math. Logik Grundlagen Math. , vol.38 , pp. 2
    • Ying, M.S.1
  • 46
    • 84981423150 scopus 로고
    • Compactness, the Lowenheim-Skolem property and the direct product of lattices of truth values
    • M.S. Ying Compactness, the Lowenheim-Skolem property and the direct product of lattices of truth values Z. Math. Logik Grundlagen Math. 38 1992 4
    • (1992) Z. Math. Logik Grundlagen Math. , vol.38 , pp. 4
    • Ying, M.S.1
  • 47
    • 44949276372 scopus 로고
    • A new approach for fuzzy topology (I), (II), (III)
    • M.S. Ying, A new approach for fuzzy topology (I), (II), (III), Fuzzy Sets Systems 39 (1991) 303-321;
    • (1991) Fuzzy Sets Systems , vol.39 , pp. 303-321
    • Ying, M.S.1
  • 48
    • 0000538575 scopus 로고
    • A new approach for fuzzy topology (I), (II), (III)
    • M.S. Ying, A new approach for fuzzy topology (I), (II), (III), Fuzzy Sets Systems 47 (1992) 221-232;
    • (1992) Fuzzy Sets Systems , vol.47 , pp. 221-232
    • Ying, M.S.1
  • 49
    • 0001251564 scopus 로고
    • A new approach for fuzzy topology (I), (II), (III)
    • M.S. Ying, A new approach for fuzzy topology (I), (II), (III), Fuzzy Sets Systems 55 (1993) 193-207.
    • (1993) Fuzzy Sets Systems , vol.55 , pp. 193-207
    • Ying, M.S.1
  • 50
    • 0001746720 scopus 로고
    • Fuzzifying topology based on complete residuated lattice-valued logic (I)
    • M.S. Ying Fuzzifying topology based on complete residuated lattice-valued logic (I) Fuzzy Sets Systems 56 1993 337 373
    • (1993) Fuzzy Sets Systems , vol.56 , pp. 337-373
    • Ying, M.S.1
  • 51
    • 21844523011 scopus 로고
    • A logic for approximate reasoning
    • M.S. Ying A logic for approximate reasoning J. Symbolic Logic 59 1994
    • (1994) J. Symbolic Logic , vol.59
    • Ying, M.S.1
  • 52
    • 0034349194 scopus 로고    scopus 로고
    • Automata theory based on quantum logic (I), (II)
    • M.S. Ying, Automata theory based on quantum logic (I), (II), Internat. J. Theoret. Phys. 39 (2000) 985-995; 2545-2557.
    • (2000) Internat. J. Theoret. Phys. , vol.39 , pp. 985-995
    • Ying, M.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.