Nonoverlap of the Star Unfolding.
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...
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...
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...
We investigate the complexity of several problems concerning Las Vegas finite automata. Our results are as follows. (1) The membership problem for Las Vegas finite automata is in NL. (2) The nonemptiness and inequivalence problems for Las Vegas finite automata are NL-complete. (3) Constructing for a given Las Vegas finite automaton a minimum state deterministic finite automaton is in NP. These results provide partial answers to some open problems posed by Hromkovič and Schnitger [Theoret....
We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family of cyclic languages, where . In particular, we show that, for any , the number of states necessary and sufficient for accepting the unary language with isolated cut point on one-way probabilistic finite automata is , with being the factorization of . To prove this result, we give a general state lower bound for accepting unary languages with isolated cut point on...
We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family {Lm} of cyclic languages, where Lm = akm | k ∈ N. In particular, we show that, for any m, the number of states necessary and sufficient for accepting the unary language Lm with isolated cut point on one-way probabilistic finite automata is , with being the factorization of m. To prove this result, we give a general state lower bound for accepting unary languages...
A property of n-vertex graphs is called evasive if every algorithm testing this property by asking questions of the form “is there an edge between vertices u and v” requires, in the worst case, to ask about all pairs of vertices. Most “natural” graph properties are either evasive or conjectured to be such, and of the few examples of nontrivial nonevasive properties scattered in the literature the smallest one has n = 6. We exhibit a nontrivial, nonevasive property of 5-vertex graphs and show that...