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- W2402962222 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 nor- mal 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 sim- ulated 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 nor- mal form, preserving the total number of states in the automata and in their cycles. Mathematics Subject Classification. 68Q45, 68Q10." @default.
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- W2402962222 date "2011-01-01" @default.
- W2402962222 modified "2023-09-23" @default.
- W2402962222 title "Normal forms for unary probabilistic automata" @default.
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