Language Recognition Power and Succinctness of Affine Automata

  • Marcos VillagraEmail author
  • Abuzer YakaryılmazEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9726)


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 [6] 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, whereas the number of states of any quantum and probabilistic automata cannot be bounded. Finally, we present the 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 the anonymous referees for their helpful comments.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Universidad Nacional de Asunción NIDTECSan LorenzoParaguay
  2. 2.National Laboratory for Scientific ComputingPetrópolisBrazil

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