The power of nondeterminism in polynomial-size bounded-width branching programs

Abstract

Nondeterministic branching programs introduced in /Me86,1/ spelt out to be an interesting computational tool for describing higher complexity classes /Me86,2/. The investigation of the power of nondeterminism in the case of bounded-width nondeterministic branching programs yields: while polynomial-size bounded-width 1-time-only-nondeterministic branching programs are not more powerful than polynomial-size (usual) bounded-width branching programs, polynomial-size, bounded-width k-times-only-nondeterministic branching programs, k>1, are as powerful as polynomialsize, unbounded-width, nondeterministic branching programs. I.e. $$\mathcal{P}_{bw - n_1 BP} = NC^1 and\mathcal{P}_{bw - n_k BP} = NP/poly,k > 1.$$ .KeywordsBoolean FunctionTuring MachineComplexity ClassPolynomial SizeBoolean CircuitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.