English

The Complexity of Logarithmic Space Bounded Counting Classes

Computational Complexity 2026-03-17 v4

Abstract

In this monograph, we study complexity classes that are defined using O(logn)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.

Keywords

Cite

@article{arxiv.2507.23563,
  title  = {The Complexity of Logarithmic Space Bounded Counting Classes},
  author = {T. C. Vijayaraghavan},
  journal= {arXiv preprint arXiv:2507.23563},
  year   = {2026}
}

Comments

Minors typos, errors in almost all the chapters have been corrected. Some figures have been redrawn. Main results in the last chapter have been checked for correctness and re-written to improve clarity and precision

R2 v1 2026-07-01T04:27:52.572Z