Algebraic acceptance mechanisms for polynomial time machines

Abstract

We present several results, mainly taken from the author's recent conference articles [Her97a, Her97b, Her99], whose common theme is the application of (quite basic) algebraic techniques to describe complexity classes, which appear in the many ways nondeterministic polynomial time machines can be used (or abused).One possibility to motivate this is an exact characterization of the (at first glance) rather weak (2 out of 3)-P-set paradigm (see the Introduction for a description), which we will prove to be as powerful as PSPACE.