Note on the succinctness of deterministic, nondeterministic, probabilistic and quantum finite automata
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 5, pp. 477-490.

We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family {L m } of cyclic languages, where L m ={a km |k}. In particular, we show that, for any m, the number of states necessary and sufficient for accepting the unary language L m with isolated cut point on one-way probabilistic finite automata is p 1 α 1 +p 2 α 2 ++p s α s , with p 1 α 1 p 2 α 2 p s α s being the factorization of m. To prove this result, we give a general state lower bound for accepting unary languages with isolated cut point on the one-way probabilistic model. Moreover, we exhibit one-way quantum finite automata that, for any m, accept L m with isolated cut point and only two states. These results are settled within a survey on unary automata aiming to compare the descriptional power of deterministic, nondeterministic, probabilistic and quantum paradigms.

Classification : 68Q10,  68Q19,  68Q45
Mots clés : deterministic, nondeterministic, probabilistic, quantum unary finite automata
@article{ITA_2001__35_5_477_0,
     author = {Mereghetti, Carlo and Palano, Beatrice and Pighizzini, Giovanni},
     title = {Note on the succinctness of deterministic, nondeterministic, probabilistic and quantum finite automata},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {477--490},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {5},
     year = {2001},
     zbl = {1010.68068},
     mrnumber = {1908867},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2001__35_5_477_0/}
}
Mereghetti, Carlo; Palano, Beatrice; Pighizzini, Giovanni. Note on the succinctness of deterministic, nondeterministic, probabilistic and quantum finite automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 5, pp. 477-490. http://www.numdam.org/item/ITA_2001__35_5_477_0/

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