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/logn). We improve this to [email protected][email protected] for a constant @e>0. This also gives an alternative and simpler proof of an exponential lower bound for ([email protected])n time branching programs for a constant @e>0. We prove these lower bounds for quadratic functions of Ramanujan graphs.

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