A separation of syntactic and nonsyntactic (1,+k)-branching programs

Abstract.

For (1,+k)-branching programs and read-k-times branching programs syntactic and nonsyntactic variants can be distinguished. The nonsyntactic variants correspond in a natural way to sequential computations with restrictions on reading the input while lower bound proofs are easier for the syntactic variants. In this paper it is shown that nonsyntactic (1,+k)-branching programs are really more powerful than syntactic (1,+k)-branching programs by presenting an explicitly defined function with polynomial size nonsyntactic (1,+1)-branching programs but only exponential size syntactic (1,+k)-branching programs. Another separation of these variants of branching programs is obtained by comparing the complexity of the satisfiability test for both variants.