Dejan Zivkovic

Bounded-width polynomial-size Boolean formulas compute exactly those functions in AC 0

Abstract We show that the complexity classes AC 0 and NC 1 consist exactly of, respectively, constant and O(log n ) width polynomial-size Boolean formulas.

A fast algorithm for finding the compact sets

Abstract We define and investigate the problem of finding all compact sets in a complete, weighted, undirected graph with n vertices. An algorithm with worst-case complexity of O(n2 log N) is given for the problem.

DMS — Improving Web performance

In this paper we consider the problem of improving Web performance and propose an efficient differencing and merging system (DMS) based on an HTTP protocol extension. To provide for faster information exchange over the Web, the system tries to transfer only computed differences between requested documents and previously retrieved documents from the same site. Analysis and experimental results prove the effectiveness of DMS, but also show bigger processor and memory load on servers and clients. DMS is compatible with most of the existing solutions for improving Web performance. Moreover, SSL security system may be used to provide Web privacy and authenticity. The DMS model is simple to use and can be relatively easily integrated in Web servers and browsers.

A Non-Probabilistic Switching Lemma for the Sipser Function

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 Σ2-circuits), has a large set of prime clauses (i.e., big Π2-circuits). As a corollary, an exponential lower bound was obtained for monotone ΣΠΣ-circuits computing the clique function. The proof technique is the only non-probabilistic super polynomial lower bound method from the literature. We prove, by a non-probabilistic argument as well, a similar switching lemma for the NC1-complete Sipser function. Using this we then show that a monotone depth-3 (i.e., ΣΠΣ or ΠΣΠ) circuit computing the Sipser function must have super quasipolynomial size. Moreover, any depth-d quasipolynomial size non-monotone circuit computing the Sipser function has a depth-(d—1) gate computing a function with exponentially many both prime implicants and (monotone) prime clauses. These results are obtained by a top-down analysis of the circuits.