Abstract
The regular language (a + b)* a (the words in alphabet {a, b} having a as the last letter) is at the moment a classical example of a language not recognizable by a one-way quantum finite automaton (QFA). Up to now, there have been introduced many different models of QFAs, with increasing capabilities, but none of them can cope with this language.
We introduce a new, quite simple modification of the QFA model (actually even a deterministic reversible FA model) which is able to recognize this language. We also completely characterise the set of languages recognizable by the new model FAs, by finding a “forbidden construction” whose presence or absence in the minimal deterministic (not necessarily reversible) finite automaton of the language decides the recognizability.
Thus, the new model still cannot recognize the whole set of regular languages, however it enhances the understanding of what can be done in a finite-state real-time quantum process.
Supported by the European Social Fund.
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References
Ambainis, A., Beaudry, M., Golovkins, M., Kikusts, A., Mercer, M., Thérien, D.: Algebraic results on quantum automata. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 93–104. Springer, Heidelberg (2004)
Ambainis, A., Freivalds, R.: 1-way quantum finite automata: strengths, weaknesses and generalizations. In: Proceedings of the 39th Annual Symposium on Foundations of Computer Science. pp. 332–341 (1998)
Bertoni, A., Mereghetti, C., Palano, B.: Quantum computing: 1-way quantum automata. In: Ésik, Z., Fülöp, Z. (eds.) DLT 2003. LNCS, vol. 2710, pp. 1–20. Springer, Heidelberg (2003)
Brodsky, A., Pippenger, N.: Characterizations of 1-way quantum finite automata. SIAM Journal on Computing 31(5), 1456–1478 (2002) Appeared earlier as Technical Report TR-99-03, University of British Columbia, 1999
Ciamarra, M.P.: Quantum reversibility and a new model of quantum automaton. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, pp. 376–379. Springer, Heidelberg (2001)
Dzelme, I.: Kvantu automāti ar jauktajiem stāvokļiem. Technical Report, University of Latvia (2003)
Hromkovič, J.: One-way multihead deterministic finite automata. Acta. Informatica 19, 377–384 (1983)
Kondacs, A., Watrous, J.: On the power of quantum finite state automata. In: Kondacs, A., Watrous, J. (eds.) Proceedings of the 38th IEEE Conference on Foundations of Computer Science, pp. 66–75 (1997)
Moore, C., Crutchfield, J.: Quantum automata and quantum grammars. Theoretical Computer Science 237, 97–97 (1997) Appeared in preprint form as Santa-Fe Institute Working Paper 97-07-062, 1997
Nayak, A.: Optimal lower bounds for quantum automata and random access codes. In: Proceedings of the 40th Annual Symposium on Foundations of Computer Science, pp. 369–377 (1999)
Paschen, K.: Quantum finite automata using ancilla qubits. Technical Report,University of Karlsruhe (2000)
Sipser, M.: Introduction to the Theory of Computation, pp. 31–90. PWS, Boston (1997)
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Belovs, A., Rosmanis, A., Smotrovs, J. (2007). Multi-letter Reversible and Quantum Finite Automata. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_9
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DOI: https://doi.org/10.1007/978-3-540-73208-2_9
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