ORACLE BRANCHING PROGRAMS AND LOGSPACE VERSUS P

Abstract

AbstractWe define the notion of an oracle branching program in order to investigate space-bounded computation. Within this new framework we examine the P-complete problem GEN which consists of determining membership in a subalgebra of a general (not necessarily associative) binary algebra (input as a multiplication table). Our work begins with the statement of a conceptually simple conjecture highlighting the combinatorics which underlie the relationship between Logspace and P. We show that natural subclasses of P can be expressed as natural subproblems for GEN. Finally, we prove optimal lower bounds on the size of branching programs for GEN with certain natural oracles