Expanders and time-restricted branching programs

The replication number of a branching program is the minimum number R such that along every accepting computation at most R variables are tested more than once; the sets of variables re-tested along different computations may be different. For every branching program, this number lies between 0 (read-once programs) and the total number n of variables (general branching programs). The best results so far were exponential lower bounds on the size of branching programs with R = o(n/ log n). We improve this to R n for a constant > 0. This also gives an alternative and simpler proof of an exponential lower bound for (1 + )n time branching programs for a constant > 0. We prove these lower bounds for quadratic functions of Ramanujan graphs. Key words: Computational complexity; Branching programs; Time versus space; Lower bounds; Expander graphs; Ramanujan graphs

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Stasys Jukna
• Keywords: Branching Programs, General Branching Programs, Lower Bounds, TCS 2008, Theoretical Computer Science