Decreasing the Bandwidth of a Transition Matrix

Abstract

Adapting the competitions method of Freivalds to the setting of unbounded-error probabilistic computation, we prove that, for any ffl 2 (0; 1], Band-Mat-Inv(n ffl ) is log-space complete for the class of languages recognized by log-space unbounded-error probabilistic Turing machines (PL). This extends the result of Jung that Band-Mat-Inv(n) is log-space complete for PL, and may open new possibilities for space-efficient deterministic simulation of space-bounded probabilistic Turing machines. Key words: computational complexity, log-space probabilistic Turing machines, log-space complete problem. This research was supported by the National Science Foundation under Grant No. CDA 8822724. 1 Introduction For an arbitrary function f , such that 8n 2 N , f(n) 2 (0; n], Band-Mat-Inv(f) denotes the following problem: for each positive integer n and a diagonally dominant n-by-n f(n)- banded matrix A whose elements are n-bit rational numbers, compare with 1/2 the element from the position ..