Language recognition power and succintness of affine automata
| Autor: | Villagra, Marcos, Yakaryılmaz, Abuzer |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Natural Computing (2017) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11047-017-9652-z |
| Popis: | In this work we study a non-linear generalization based on affine transformations of probabilistic and quantum automata proposed recently by D\'iaz-Caro and Yakary{\i}lmaz \cite{DCY16A} referred as affine automata. First, we present efficient simulations of probabilistic and quantum automata by means of affine automata which allows us to characterize the class of exclusive stochastic languages. Then, we initiate a study on the succintness of affine automata. In particular, we show that an infinite family of unary regular languages can be recognized by 2-state affine automata but the state numbers of quantum and probabilistic automata cannot be bounded. Finally, we present the characterization of all (regular) unary languages recognized by two-state affine automata. Comment: 19 pages. New results are added. A shorter version will appear in the proceedings of the 15th International Conference on Unconventional Computation and Natural Computation (UCNC 2016) |
| Databáze: | arXiv |
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