Abstract
The connection between measure once quantum finite automata (MO-QFA) and logic is studied in this paper. The language class recognized by MO-QFA is compared to languages described by the first order logics and modular logics. And the equivalence between languages accepted by MO-QFA and languages described by formulas using Lindström quantifier is shown.
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References
Aharonov, D., Kitaev, A., Nisan, N.: Quantum Circuits with Mixed States. In: STOC, pp. 20–30 (1998)
Amano, M., Iwama, K.: Undecidability on Quantum Finite Automata. In: STOC, pp. 368–375 (1999)
Ambainis, A., Freivalds, R.: 1-Way Quantum Finite Automata: Strengths, Weaknesses and Generalizations. In: Proc. FOCS, pp. 332–341 (1998)
Ambainis, A., Kikusts, A.: Exact Results for Accepting Probabilities of Quantum Automata. Theoretical Computer Science 295(1), 5–23 (2003)
Ambainis, A., Watrous, J.: Two-Way Finite Automata with Quantum and Classical States. Theoretical Computer Science 287(1), 299–311 (2002)
Baader, F.: Automata and Logic. Technische Universittät Dresden (2003)
Barrington, D.A., Compton, K., Straubing, H., Therien, D.: Regular Languages in NC1, BCCS-88-02 (1988)
Barrington, D.A., Corbett, J.: On the Relative Complexity of Some Languages in NC 1. Inf. Proc. Letters 32, 251–256 (1989)
Brodsky, A., Pippenger, N.: Characterizations of 1-Way Quantum Finite Automata. SIAM Journal on Computing 31(5), 1456–1478 (2002)
Büchi, J.R.: Weak Second-Order Arithmetic and Finite Automata. Z. Math. Logik Grundl. Math. 6, 66–92 (1960)
Büchi, J.R.: On Decision Method in Restricted Second-Order Arithmetic. In: Proc. 1960 Int. Congr. for Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford Univ. Press, Stanford (1962)
Eilenberg, S.: Automata, Languages, and Machines, vol. B. Academic Press, New York (1976)
Elgot, C.C.: Decision Problems of Finite Automata Design and Related Arithmetics. Trans. Amer. Math Soc. 98, 21–52 (1961)
Fagin, R.: Generalized First-Order Spectra and Polynomial-Time Recognizable Sets. In: Complexity of Computation, SIAM-AMS Proceedings, vol. 7, pp. 43–73 (1974)
Gruska, J.: Quantum Computing, vol. 439. McGraw-Hill, New York (1999)
Immerman, N.: Relational Queries Computable in Polynomial Time. Information and Control 68, 86–104 (1986)
Immerman, N.: Languages that Capture Complexity Classes. SIAM J. Comput. 16(4), 760–778 (1987)
Immerman, N.: Nondeterministic Space Is Closed under Complementation. SIAM J. Comput. 17(5), 938–953 (1988)
Kondacs, A., Watrous, J.: On the Power of Quantum Finite State Automata. In: Proc. FOCS 1997, pp. 66–75 (1997)
McNaugton, R.: Symbolic Logic and Automata. Technical Note, 60–244 (1960)
McNaughton, R.: Testing and Generating Infinite Sequences by Finite Automaton. Inform. Contr. 9, 521–530 (1966)
Moore, C., Crutchfield, J.: Quantum Automata and Quantum Grammars. Theoretical Computer Science 237, 275–306 (2000)
Mostowski, A.: On a Generalization of Quantifiers. Fundamenta Mathenaticae 44, 12–36 (1957)
Rabin, M.O.: Decidability of Second-Order Theories and Automata on Infinite Trees. Trans. Amer. Math. Soc. 141, 1–35 (1969)
Schüzenberg, M.P.: On Finite Monoids Having only Trivial Subgroups. Information and Control 8, 283–305 (1965)
Straubing, H., Therien, D., Thomas, W.: Regular Languages Defined with Generalized Quantifiers. In: Lepistö, T., Salomaa, A. (eds.) ICALP 1988. LNCS, vol. 317, pp. 561–575. Springer, Heidelberg (1988)
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Dzelme, I. (2006). Quantum Finite Automata and Logics. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2006: Theory and Practice of Computer Science. SOFSEM 2006. Lecture Notes in Computer Science, vol 3831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11611257_22
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DOI: https://doi.org/10.1007/11611257_22
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