Efficient Oblivious Branching Programs for Threshold Functions
نویسندگان
چکیده
In his survey paper on branching programs, Razborov [RazSl] asked the following question: Does every rectifier-switching network computing the majority of n bits have size n l+n( l )? We answer this question in the negative by constructing a simple oblivious branching program of size n log3 n log log n log log log n for computing any threshold function. This improves the previously best known upper bound of O(n3I2) due to Lupanov [Lup65].
منابع مشابه
Efficient Oblivious Branching Programs for Threshold and Mod Functions
In his survey paper on branching programs, Razborov Raz91] asked the following question: Does every rectiier-switching network computing the majority of n bits have size n 1++(1) ? We answer this question in the negative by constructing a simple oblivious branching program of size O n log 3 n log log n log log log n ! for computing any threshold function. This improves the previously best known...
متن کاملTwo types of branching programs with bounded repetition that cannot efficiently compute monotone 3-CNFs
We prove exponential lower bounds for two classes of non-deterministic branching programs (nbps) with bounded repetition computing a class of functions representable by monotone 3-cnfs. The first class significantly generalizes monotone read-k-times nbps and the second class generalizes oblivious read k times branching programs. To the best of our knowledge, this is the first separation of mono...
متن کاملLinear Codes are Hard for Oblivious Read-Once Parity Branching Programs
We show that the characteristic functions of linear codes are exponentially hard for the model of oblivious read-once branching programs with parity accepting mode, known also as Parity OBDDs. The proof is extremely simple, and employs a particular combinatorial property of linear codes { their universality.
متن کاملA very simple function that requires exponential size nondeterministic graph-driven read-once branching programs
Branching programs are a well-established computation model for boolean functions, especially read-once branching programs (BP1s) have been studied intensively. A very simple function f in n variables is exhibited such that both the function f and its negation ¬f can be computed by Σ p-circuits, the function f has nondeterministic BP1s (with one nondeterministic node) of linear size and ¬f has ...
متن کاملBranching Program Uniformization, Rewriting Lower Bounds, and Geometric Group Theory
Geometric group theory is the study of the relationship between the algebraic, geometric, and combinatorial properties of finitely generated groups. Here, we add to the dictionary of correspondences between geometric group theory and computational complexity. We then use these correspondences to establish limitations on certain models of computation. In particular, we establish a connection bet...
متن کامل