Characterizing the polynomial hierarchy by alternating auxiliary pushdown automata

Abstract

An alternating auxiliary pushdown hierarchy is defined by extending the machine model of the Logarithmic Alternation Hierarchy by a pushdown store while keeping a polynomial time bound. Although recently it was proven by Borodin et al. that the class of languages accepted by nondeterministic logarithmic space bounded auxiliary pushdown automata with a polynomial time bound is closed under complement [Bo et al], it is shown that, surprisingly, the further levels of this alternating auxiliary pushdown hierarchy coincide level by level with the Polynomial Hierarchy. Furthermore, it is shown that PSPACE can be characterized by simultaneously logarithmic space and polynomial time bounded auxiliary pushdown automata with unbounded alternation.