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Normal forms for unary probabilistic automata

Published online by Cambridge University Press:  02 August 2012

Maria Paola Bianchi  and
Giovanni Pighizzini
Maria Paola Bianchi
Affiliation:
Dipartimento di Informatica, Università degli Studi di Milano, Via Comelico 39, 20135 Milano, Italy. bianchi@di.unimi.it, pighizzini@di.unimi.it
Giovanni Pighizzini
Affiliation:
Dipartimento di Informatica, Università degli Studi di Milano, Via Comelico 39, 20135 Milano, Italy. bianchi@di.unimi.it, pighizzini@di.unimi.it
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Abstract

We investigate the possibility of extending Chrobak normal form to the probabilistic case. While in the nondeterministic case a unary automaton can be simulated by an automaton in Chrobak normal form without increasing the number of the states in the cycles, we show that in the probabilistic case the simulation is not possible by keeping the same number of ergodic states. This negative result is proved by considering the natural extension to the probabilistic case of Chrobak normal form, obtained by replacing nondeterministic choices with probabilistic choices. We then propose a different kind of normal form, namely, cyclic normal form, which does not suffer from the same problem: we prove that each unary probabilistic automaton can be simulated by a probabilistic automaton in cyclic normal form, with at most the same number of ergodic states. In the nondeterministic case there are trivial simulations between Chrobak normal form and cyclic normal form, preserving the total number of states in the automata and in their cycles.

Keywords

Unary languagesnormal formprobabilistic automata
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 4: Special Issue: Non-Classical Models of Automata and Applications III (NCMA-2011) , October 2012 , pp. 495 - 510
Copyright
© EDP Sciences 2012

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References

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