The established techniques of computational complexity can be applied to the new problems posed by very !urge-scale integrated (VLSI) circuits. This thesis develops a "VLSI model of computation" and derives upper and lower bounds on the silicon area and time required to snlve the problems of sorting and discrete Fourier transformation. In particular, the area (A) and time (T) taken by any VLSI ...

Algebraic complexity theory, the study of the minimum number of operations suficient o perform algebraic computations, is surveyed with emphasis on the general theory of bilinear forms and two of its applications: polynomial multiplication and matrix multiplication. Though by no means exhausting algebraic complexity theory, these topics illustrate well its development and its methods, and ...

Complexity theory of numerical analysis is the study of the number of arithmetic operations required to pass from the input to the output of a numerical problem. To a large extent this requires the (global) analysis of the basic algorithms of numerical analysis. This analysis is complicated by the existence of ill-posed problems, conditioning and roundoff error. A complementary aspect (“lower b...

Bob Frank, Giorgio Satta, and Lauri Karttunen stunned the computational OT community some years ago when they pointed out that unidirectional optimization is essentially a finite state technique. If all components of an OT system can be modeled by a finite state machine, then the complexity of the entire system does not exceed the complexity of its components. There has been some debate in past...

A Boolean circuit C on n inputs x1, . . . , xn is a directed acyclic graph (DAG) with n nodes of in-degree 0 (the inputs x1, . . . , xn), one node of out-degree 0 (the output), and every node of the graph except the input nodes is labeled by AND, OR, or NOT; it has in-degree 2 (for AND and OR), or 1 (for NOT). The Boolean circuit C computes a Boolean function f(x1, . . . , xn) in the obvious wa...

In this paper we give an introduction to the connection between complexity theory and the study of randomized algorithms. In particular, we will define and study probabilistic complexity classes, survey the basic results, and show how they relate to the notion of randomized algorithms.