Alternating automata play a key role in the automata-theoretic approach to specification, verification, and synthesis of reactive systems. Many algorithms on alternating automata, and in particular, their nonemptiness test, involve removal of alternation: a translation of the alternating automaton to an equivalent nondeterministic one. For alternating Büchi automata, the best known translation ...

1. Introduction This paper investigates the effect of changing syntactic categories on speaker choice, using the needs to be done ∼ needs doing alternation as the testing ground. The two alternants in this alternation have different syntactic properties , and so we hypothesize that the syntactic preferences of the alternation's environment influence alternant choice. Our hypothesis is that, all...

We deene the sharply bounded hierarchy, SBH (QL), a hierarchy of classes within P , using quasilinear-time computation and quantiication over values of length log n. It generalizes the limited nondeterminism hierarchy introduced by Buss and Gold-smith, while retaining the invariance properties. The new hierarchy has several alternative characterizations. We deene both SBH (QL) and its correspon...

Toda proved a remarkable connection between the polynomial hierarchy and the counting classes. Tarui improved Toda’s result to show the connection to a weak form of counting and provided an elegant proof. This paper shows that a key step in Tarui’s proof can be done uniformly using the depth-first traversal and provides the algorithm that generalizes Toda’s result to arbitrary alternating Turin...