Random Generation of Nondeterministic Tree Automata

Algorithms for (nondeterministic) finite-state tree automata (NTA) are often tested on random NTA, in which all internal transitions are equiprobable. The run-time results obtained in this manner are usually overly optimistic as most such generated random NTA are trivial in the sense that the number of states of an equivalent minimal deterministic finite-state tree automaton is extremely small. It is demonstrated that nontrivial random NTA are obtained only for a narrow band of transition probabilities. Moreover, an analytical analysis yields a formula to approximate the transition probability that yields the most complex random NTA.