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 polynomial-size, unbounded-width, nondeterministic branching programs. I.e.(formula presented).