Abstract
We develop a theory of communication within branching programs that provides exponential lower bounds on the size of branching programs that are bounded alternating. Our theory is based on the algebraic concept of Ω-branching programs, ω: ℕ → ℝ, a semiring homomorphism, that generalizes ordinary branching programs, Ω-branching programs [M2] andMOD p-branching programs [DKMW]. Due to certain exponential lower and polynomial upper bounds on the size of bounded alternating ω-branching programs we are able to separate the corresponding complexity classesNℒ ba ,co-Nℒ ba ⊕ℒ ba , andMOD p -ℒ ba ,p prime, from each other, and from that classes corresponding to oblivious linear length-bounded branching programs investigated in the past.
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