Branching programs provide lower bounds on the areas of multilective deterministic and nondeterministic VLSI-circuits

Abstract

Each (nondeterministic) multilective VLSI-circuit C of area A can be simulated by an oblivious (disjunctive) branching program of width exp( O ( A )) which has the same multiplicity of reading as C . That is why exponential lower bounds on the width of (disjunctive) oblivious branching programs of linear depth provide lower bounds of order Ω(n 1–2α ) , 0≤α< 1 2 , on the area of (nondeterministic) multilective VLSI-circuits computing explicitly defined one-output Boolean functions, if the multiplicity of reading is bounded by O (log α n ). Lower bounds are derived for the sequence equality problem (SEQ) and the graph accessibility problem (GAP).