Hostname: page-component-8448b6f56d-wq2xx Total loading time: 0 Render date: 2024-04-25T04:34:54.843Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantum finite automata with control language

Published online by Cambridge University Press:  20 July 2006

Carlo Mereghetti  and
Beatrice Palano
Carlo Mereghetti
Affiliation:
Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39, 20135 Milano, Italy; mereghetti@dsi.unimi.it, palano@dsi.unimi.it
Beatrice Palano
Affiliation:
Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39, 20135 Milano, Italy; mereghetti@dsi.unimi.it, palano@dsi.unimi.it
Get access

Abstract

Bertoni et al.  introduced in Lect. Notes Comput. Sci.2710 (2003) 1–20 a new model of 1-way quantum finite automaton (1qfa) called 1qfa with control language (1qfc). This model, whose recognizing power is exactly the class of regular languages, generalizes main models of 1qfa's proposed in the literature. Here, we investigate some properties of 1qfc's. In particular, we provide algorithms for constructing 1qfc's accepting the inverse homomorphic images and quotients of languages accepted by 1qfc's. Moreover, we give instances of binary regular languages on which 1qfc's are proved to be more succinct (i.e. , to have less states) than the corresponding classical (deterministic) automata.

Keywords

Quantum computingquantum finite automata.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 2: Alberto Bertoni: Climbing summits , April 2006 , pp. 315 - 332
Copyright
© EDP Sciences, 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ambainis, A., Beaudry, M., Golovkins, M., Kikusts, A., Mercer, M. and Thérien, D., Algebraic Results on Quantum Automata. Theory Comput. Syst. 39 (2006) 165–188. CrossRef
A. Ambainis and R. Freivalds, 1-way Quantum Finite Automata: Strengths, Weaknesses and Generalizations, in Proc. 39th Annual Symposium on Foundations of Computer Science. IEEE Computer Society Press (1998) 332–342.
Ambainis, A., Kikusts, A. and Valdats, M., On the class of languages recognizable by 1–way quantum finite automata, in Proc. 18th Annual Symposium on Theoretical Aspects of Computer Science. Lect. Notes Comput. Sci. 2010 (2001) 305–316.
Bertoni, A. and Carpentieri, M., Regular languages accepted by quantum automata. Inform. Comput. 165 (2001) 174–182. CrossRef
Bertoni, A., Mereghetti, C. and Palano, B., Quantum computing: 1-way quantum automata, in Proc. 7th International Conference on Developments in Language Theory. Lect. Notes Comput. Sci. 2710 (2003) 1–20. CrossRef
Bertoni, A., Mereghetti, C. and Palano, B., Golomb Rulers and Difference Sets for Succinct Quantum Automata. Int. J. Found. Comp. Sci. 14 (2003) 871–888.
Bertoni, A., Mereghetti, C. and Palano, B., Small size quantum automata recognizing some regular languages. Theoret. Comput. Sci. 340 (2005) 394–407. CrossRef
Bertoni, A., Mereghetti, C. and Palano, B., Some formal tools for analyzing quantum automata. Theoret. Comput. Sci. 356 (2006) 14–25. CrossRef
Brodsky, A. and Pippenger, N., Characterizations of 1-Way Quantum Finite Automata. SIAM J. Comput. 5 (2002) 1456–1478. CrossRef
Golovkins, M. and Kravtsev, M., Probabilistic Reversible Automata and Quantum Automata, in Proc. 8th International Computing and Combinatorics Conference. Lect. Notes Comput. Sci. 2387 (2002) 574–583. CrossRef
J. Gruska, Quantum Computing. McGraw-Hill (1999).
J. Gruska, Descriptional complexity issues in quantum computing. J. Automata, Languages and Combinatorics 5 (2000) 191–218.
J. Hopcroft and J. Ullman, Formal Languages and Their Relation to Automata. Addison-Wesley (1969).
A. Kondacs and J. Watrous, On the Power of Quantum Finite State Automata, in Proc. 38th Annual Symposium on Foundations of Computer Science. IEEE Computer Society Press (1997) 66–75.
Moore, C. and Crutchfield, J., Quantum automata and quantum grammars. Theoret. Comput. Sci. 237 (2000) 275–306. CrossRef
M. Marcus and H. Minc, Introduction to Linear Algebra. The Macmillan Company (1965). Reprinted by Dover (1988).
M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities. Prindle, Weber & Schmidt (1964). Reprinted by Dover (1992).
Mereghetti, C. and Palano, B., On the Size of One-way Quantum Finite Automata with periodic behaviors. RAIRO-Inf. Theor. Appl. 36 (2002) 277–291. CrossRef
Mereghetti, C., Palano, B. and Pighizzini, G., Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata. RAIRO-Inf. Theor. Appl. 35 (2001) 477–490. CrossRef
A. Nayak, Optimal lower bounds for quantum automata and random access codes, in Proc. 40th Symposium on Foundations of Computer Science (1999) 369–376.
J.E. Pin, On Languages Accepted by finite reversible automata, in Proc. 14th Int. Coll. Automata, Languages and Programming. Lect. Notes Comput. Sci. 267 (1987) 237–249.