The Complexity of Logarithmic Space Bounded Counting Classes

TL;DR

This paper provides a comprehensive study of complexity classes defined by logarithmic space-bounded nondeterministic Turing machines, covering key theorems and their implications in computational complexity.

Contribution

It offers an in-depth analysis of logarithmic space bounded counting classes, including proofs of major theorems like the Immerman-Szelepcsenyi Theorem and the Isolating Lemma, serving as a detailed textbook.

Findings

Proves the Immerman-Szelepcsenyi Theorem.

Discusses the Isolating Lemma and its applications.

Explores theorems related to the determinant in this complexity context.

Abstract

In this monograph, we study complexity classes that are defined using $O(\log n)$-space bounded non-deterministic Turing machines. We prove salient results of Computational Complexity in this topic such as the Immerman-Szelepcsenyi Theorem, the Isolating Lemma, theorems of Meena Mahajan and V. Vinay on the determinant and many consequences of these very important results. The manuscript is intended to be a comprehensive textbook on the topic of The Complexity of Logarithmic Space Bounded Counting Classes.