Abstract:
In this paper we propose the study of a new model of restricted branching programs which we call incremental branching programs. This is in line with the program proposed by Cook in 1974 as an approach for separating the class of problems solvable in logarithmic space from problems solvable in polynomial time, focusing on the P-complete problem GEN. We show that our model captures and possibly supersedes previously studied structured models of computation for GEN, namely marking machines Cook (1994) and Poon's (1993) extension of jumping automata on graphs, that were originally defined by Cook and Rackoff (1980). We show several exponential lower bounds for variants of our model although we are unable to prove any strong lower bounds for the most general variant of incremental branching programs. Some of our techniques also yield exponential lower bounds without the incrementality restriction, under some other conditions. It remains open if incremental branching programs are as powerful as unrestricted branching programs for GEN problems.