Algebraic complexity theory investigates the computational cost of solving problems with an algebraic flavor. Several cost measures are of interest. We consider arithmetic circuits, which can perform the (exact) arithmetic operations +, -, *, / at unit cost, and take their size ( = sequential time) or their depth (=parallel time) as cost functions. This is a natural "structured" model of comput...

Several proof methods have been successfully employed over the years to prove several important results in Complexity Theory, but no one has been able to settle the question P =?NP. This article surveys three of the main proof methods used in Complexity Theory, and then shows that they cannot be used to prove P =?NP, thus exposing technical barriers to the advance of Complexity Theory. The firs...

Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng (J. ACM, 2004). Classical methods like worst-case or average-case analysis have accompanying complexity classes, like P and Avg-P, respectively. While worst-case or average-case analysis give us a means to talk about the running time of a particular algorithm, complexity classes allows us to talk about the in...

Put differently, let D = {x1, . . . , x`} and consider the random variables Yi = hK(xi) (where K is uniform). If H is pairwise independent then each Yi is uniformly distributed, and moreover the random variables Y1, . . . , Y` are pairwise independent; i.e., for any i 6= j the random variables Yi and Yj are independent. We show a simple construction of a pairwise-independent family for D = R = ...

Noam Nisan constructed pseudo random number generators which convert O(S log R) truly random bits to R bits that appear random to any algorithm that runs in SPACE(S). D Sivakumar, demonstrated that a large class of probabilistic algorithms can be derandomized using Nisan’s construction. This class of algorithms is characterized by the fact that each probabilistic algorithm can thought of as a s...

this paper assumes the cell formation problem as a distributed decision network. it proposes an approach based on application and extension of information theory concepts, in order to analyze informational complexity in an agent- based system, due to interdependence between agents. based on this approach, new quantitative concepts and definitions are proposed in order to measure the amount of t...

XML must work. Here, we argue the construction of e-commerce. We describe a “fuzzy” tool for controlling checksums [114, 114, 188, 62, 70, 179, 70, 68, 95, 70, 54, 54, 68, 152, 191, 59, 168, 54, 148, 99], which we call SLIT.

Complexity theory has come a long way in the thirty years since its inception. It has identiied some of the most fundamental and deep problems related to computation, it has developed a powerful methodology for attacking them, and it is broadly considered as one of the most challenging mathematical frontiers. Considered as a pure mathematical discipline in the pursuit of mathematical insight an...