Natural Computing

, Volume 17, Issue 2, pp 283–293 | Cite as

Language recognition power and succinctness of affine automata

  • Marcos VillagraEmail author
  • Abuzer Yakaryılmaz


In this work we study a non-linear generalization based on affine transformations of probabilistic and quantum automata proposed recently by Díaz-Caro and Yakaryılmaz (in: Computer science—theory and applications, LNCS, vol 9691. Springer, pp 1–15, 2016. ArXiv:1602.04732) referred to as affine automata. First, we present efficient simulations of probabilistic and quantum automata by means of affine automata which characterizes 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, whereas the number of inner states of quantum and probabilistic automata cannot be bounded. Finally, we present a characterization of all (regular) unary languages recognized by two-state affine automata.


Probabilistic automata Quantum automata Affine automata State complexity Stochastic language Bounded-error One-sided error 



We thank to the anonymous referees for their helpful comments. Yakaryılmaz was partially supported by CAPES with Grant 88881.030338/2013-01 and ERC Advanced Grant MQC.


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Núcleo de Investigación y Desarrollo TecnológicoUniversidad Nacional de Asunción Campus UniversitarioSan LorenzoParaguay
  2. 2.Center of Quantum Computer ScienceUniversity of LatviaRigaLatvia

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