Succinct Representation and Leaf Languages

In this paper, we present stronger results in the theory of succinct problem representation and establish a close relationship between succinct problems and leaf languages. As a major tool, we use projection reductions from descriptive complexity theory. A succinct problem is a problem whose high complexity stems from the fact that its instances are not given straightforward, but are themselves encoded by boolean circuits. In [Balc'azar et al. 92, Papa, Yann 85] there have been developed methods to quantify the complexity leap obtained this way. We prove a strictly stronger version of this result which allows iterative application and completeness results under projection reductions. A leaf language [Bovet et al 92, Bovet et al 91] is the language of words accepted by a nondeterministic Turing Machine where for acceptance the word obtained by concatenating the bits at the leaves of the computation graph must fit in a certain pattern. Complexity bounds on the leaf pattern allow to unifo..