Error-free affine, unitary, and probabilistic OBDDS

© IFIP International Federation for Information Processing 2018. We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata versions of these models

Lower bounds for Las Vegas automata by information theory

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