The purpose of this paper is to survey the correspondence between bounded arithmetic and
propositional proof systems. In addition, it also contains some new results which have …

Efficient characteristic set methods for computing solutions of a polynomial equation system
in a finite field are proposed. We introduce the concept of proper triangular sets and prove …

Complexity theory asks what makes certain problems computationally difficult. It also
investigates the relationship between computability and provability; indeed, the famous P …

As the title indicates, this thesis is concerned with the strength of non-uniformity in proof
complexity. The non-uniform part is there because we look at quantified propositional proof …

A number of theories have been developed to characterize ALogTime (or uniform NC 1, or
just NC 1), the class of languages accepted by alternating logtime Turing machines, in the …

We show that the bounded arithmetic theory V0 does not prove that the polynomial time
hierarchy collapses to the linear time hierarchy (without parameters). The result follows from …

Conservative Fragments of S1 and R1 Page 1 Conservative Fragments of S1 2 and R1 2 Chris
Pollett 214 MacQuarrie Hall Department of Computer Science San Jose State University 1 …