English

Language recognition power and succintness of affine automata

Formal Languages and Automata Theory 2017-11-15 v2 Computational Complexity Quantum Physics

Abstract

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.

Keywords

Cite

@article{arxiv.1602.05432,
  title  = {Language recognition power and succintness of affine automata},
  author = {Marcos Villagra and Abuzer Yakaryılmaz},
  journal= {arXiv preprint arXiv:1602.05432},
  year   = {2017}
}

Comments

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)