Weak alternating automata give a simple explanation of why most temporal and dynamic logics are decidable in exponential time

The authors give a very simple uniform explanation of the persistence of exponential decidability. They follow M. Vardi and P. Wolper´s theory (1986) that given a formula gamma of a temporal or dynamic logic, it is important to construct an equivalent automation M/sub gamma /. They characterize the weak monadic theory of the tree; it turns out that weak alternating automata greatly simplify design procedures.<>