Quantum finite automata with control language
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 2, pp. 315-332.

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.

DOI : 10.1051/ita:2006007
Classification : 68Q10, 68Q19, 68Q45
Mots-clés : quantum computing, quantum finite automata 
@article{ITA_2006__40_2_315_0,
     author = {Mereghetti, Carlo and Palano, Beatrice},
     title = {Quantum finite automata with control language},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {315--332},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {2},
     year = {2006},
     doi = {10.1051/ita:2006007},
     mrnumber = {2252642},
     zbl = {1112.68064},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita:2006007/}
}
TY  - JOUR
AU  - Mereghetti, Carlo
AU  - Palano, Beatrice
TI  - Quantum finite automata with control language
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2006
SP  - 315
EP  - 332
VL  - 40
IS  - 2
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ita:2006007/
DO  - 10.1051/ita:2006007
LA  - en
ID  - ITA_2006__40_2_315_0
ER  - 
%0 Journal Article
%A Mereghetti, Carlo
%A Palano, Beatrice
%T Quantum finite automata with control language
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2006
%P 315-332
%V 40
%N 2
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ita:2006007/
%R 10.1051/ita:2006007
%G en
%F ITA_2006__40_2_315_0
Mereghetti, Carlo; Palano, Beatrice. Quantum finite automata with control language. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 40 (2006) no. 2, pp. 315-332. doi : 10.1051/ita:2006007. http://archive.numdam.org/articles/10.1051/ita:2006007/

[1] A. Ambainis, M. Beaudry, M. Golovkins, A. Kikusts, M. Mercer and D. Thérien, Algebraic Results on Quantum Automata. Theory Comput. Syst. 39 (2006) 165-188. | Zbl

[2] 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.

[3] A. Ambainis, A. Kikusts and M. Valdats, 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. | Zbl

[4] A. Bertoni and M. Carpentieri, Regular languages accepted by quantum automata. Inform. Comput. 165 (2001) 174-182. | Zbl

[5] A. Bertoni, C. Mereghetti and B. Palano, Quantum computing: 1-way quantum automata, in Proc. 7th International Conference on Developments in Language Theory. Lect. Notes Comput. Sci. 2710 (2003) 1-20. | Zbl

[6] A. Bertoni, C. Mereghetti and B. Palano, Golomb Rulers and Difference Sets for Succinct Quantum Automata. Int. J. Found. Comp. Sci. 14 (2003) 871-888. | Zbl

[7] A. Bertoni, C. Mereghetti and B. Palano, Small size quantum automata recognizing some regular languages. Theoret. Comput. Sci. 340 (2005) 394-407. | Zbl

[8] A. Bertoni, C. Mereghetti and B. Palano, Some formal tools for analyzing quantum automata. Theoret. Comput. Sci. 356 (2006) 14-25.

[9] A. Brodsky and N. Pippenger, Characterizations of 1-Way Quantum Finite Automata. SIAM J. Comput. 5 (2002) 1456-1478. | Zbl

[10] M. Golovkins and M. Kravtsev, Probabilistic Reversible Automata and Quantum Automata, in Proc. 8th International Computing and Combinatorics Conference. Lect. Notes Comput. Sci. 2387 (2002) 574-583. | Zbl

[11] J. Gruska, Quantum Computing. McGraw-Hill (1999). | MR

[12] J. Gruska, Descriptional complexity issues in quantum computing. J. Automata, Languages and Combinatorics 5 (2000) 191-218. | Zbl

[13] J. Hopcroft and J. Ullman, Formal Languages and Their Relation to Automata. Addison-Wesley (1969). | MR | Zbl

[14] 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.

[15] C. Moore and J. Crutchfield, Quantum automata and quantum grammars. Theoret. Comput. Sci. 237 (2000) 275-306. | Zbl

[16] M. Marcus and H. Minc, Introduction to Linear Algebra. The Macmillan Company (1965). Reprinted by Dover (1988). | MR | Zbl

[17] M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities. Prindle, Weber & Schmidt (1964). Reprinted by Dover (1992). | MR | Zbl

[18] C. Mereghetti and B. Palano, On the Size of One-way Quantum Finite Automata with periodic behaviors. RAIRO-Inf. Theor. Appl. 36 (2002) 277-291. | EuDML | Numdam | Zbl

[19] C. Mereghetti, B. Palano and G. Pighizzini, Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata. RAIRO-Inf. Theor. Appl. 35 (2001) 477-490. | EuDML | Numdam | Zbl

[20] A. Nayak, Optimal lower bounds for quantum automata and random access codes, in Proc. 40th Symposium on Foundations of Computer Science (1999) 369-376. | MR

[21] 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. | MR | Zbl

Cité par Sources :