Reversals and alternation

Abstract

Auxiliary pushdown automata have been proven to be a useful tool for the characterization of complexity classes. In this paper we consider the pushdown reversal complexity of these machines, and show that especially in connection with a simultaneous space bound, pushdown reversals provide a uniform measure for the characterization of awide range of complexity classes, located between L and P. It is shown that classes defined by reversal bounds are included in those of restricted pushdown height.

Moreover, the connection between alternating Turing machines (ATMs) and auxiliary pushdown automata (AuxPDAs) is investigated. Applying a technique recently introduced by Neil Immerman and Róbert Szelepcsényi we can generalize a relation shown by Walter Ruzzo which connects the tree-size of ATMs to time of AuxPDAs. Namely we shown that the number of reversals coincides with the alternation-size of and ATM, which is the total number of alternations occurring in an accepting computation tree. Several corollaries relating time and tree-size of ATMs to pushdown height and reversals of AuxPDAs are derived.

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A preliminary version: On Reversal Complexity of Auxiliary Pushdown Automata is contained in the unpublished volume: “Dirk Siefkes zum 50. Geburtstag”, Technische Universität Berlin / Universität Augsburg, Klaus W. Wagner ed., pp. 4–16, April 16, 1988