Håstad’s Separation of Constant-Depth Circuits Using Sipser Functions
نویسنده
چکیده
This note contains a proof of the exponential separation of depth-d circuits from depth(d + 1) circuits due to Håstad [Has89]. The separating functions are the Sipser functions, denoted fd+1,n. We use a simplified proof of Håstad’s second switching lemma due to Neil Thapen [Tha09].
منابع مشابه
Monotone Separation of Logarithmic Space from Logarithmic Depth
We show that the monotone analogue of logspace computation is more powerful than monotone log-depth circuits: monotone bounded fanin circuits for a certain function in monotone logspace require depth (lg 2 n).
متن کاملA Non-Probabilistic Switching Lemma for the Sipser Function
Abs t r ac t . Valiant [12] showed that the clique function is structurally different than the majority function by establishing the following "switching lemma ~ : Any function f whose set of prime implicants is a large enough subset of the set of cliques (and thus requiring big ~2-circuits), has a large set of prime clauses (i.e., big II2-circuits). As a corollary, an exponential lower bound w...
متن کامل3 the Switching Lemma
Today we show that PARITY is not in AC0. AC0 is a family of circuits with constant depth, polynomial size, and unbounded fan-in for the AND and OR gates. We establish this result through an application of the Switching Lemma. This result is the first use of randomization in its full power in complexity. Circuits were defined in previous lectures. In this lecture, we always assume that the circu...
متن کاملParameterized Circuit Complexity and the W Hierarchy
A parameterized problem 〈L, k〉 belongs to W [t] if there exists k′ computed from k such that 〈L, k〉 reduces to the weight-k′ satisfiability problem for weft-t circuits. We relate the fundamental question of whether the W [t] hierarchy is proper to parameterized problems for constant-depth circuits. We define classes G[t] as the analogues of AC depth-t for parameterized problems, and N [t] by we...
متن کاملNon-Uniform Automata Over Groups
A new model, non-uniform deterministic finite automata (NUDFA’s) over general tinite monoids, has recently been developed as a strong link between the theory of finite automata and low-level parallel complexity. Achievements of this model include the proof that width 5 branching programs recognize exactly the languages in non-uniform NC’, NUDFA characterizations of several important subclasses ...
متن کامل