Lower bound for deterministic semantic-incremental branching programs solving GEN

We answer a problem posed in [GKM08] regarding a restricted model of small-space computation, tailored for solving the GEN problem. They define two variants of “incremental branching programs”, the syntactic variant defined by a restriction on the graph-theoretic paths in the program, and the moregeneral semantic variant in which the same restriction is enforced only on the consistent paths - those that are followed by at least one input. They show that exponential size is required for the syntactic variant, but leave open the problem of superpolynomial lower bounds for the semantic variant. Here we give an exponential lower bound for the semantic variant by generalizing lower bound arguments from [BCM+ 09] [Weh10] for a similar restricted model tailored for solving a special case of GEN called Tree Evaluation. 1 How to read this paper

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Dustin Wehr
• Keywords: CORR 2011, Education, Lower Bound, Restricted Model, Semantic Variant