We show that the size of a Las Vegas automatonand the size of a complete, minimal deterministicautomaton accepting a regularlanguage are polynomially related. More precisely, we showthat if a regular language L is accepted by aLas Vegas automaton having r states such thatthe probability for a definite answer to occur is at least p,then r ≥ np , where n is the number of the statesof the minimal deterministic automaton accepting L.Earlier this result has been obtainedin [2] by using a reduction to one-way Las Vegas communicationprotocols, but here we give a direct proof based on information theory.
