On Holant Theorem and Its Proof

TL;DR

This paper presents a simpler proof of the Holant theorem, a key component of holographic algorithms, and introduces a new mathematical tool called c-tensor with potential broad applications.

Contribution

It provides a more straightforward proof of the Holant theorem and develops the novel concept of c-tensor for analysis in holographic algorithms.

Findings

Simpler and more direct proof of the Holant theorem.

Introduction of the c-tensor mathematical tool.

Potential wide applicability of c-tensor in analysis.

Abstract

Holographic algorithms are a recent breakthrough in computer science and has found applications in information theory. This paper provides a proof to the central component of holographic algorithms, namely, the Holant theorem. Compared with previous works, the proof appears simpler and more direct. Along the proof, we also develop a mathematical tool, which we call c-tensor. We expect the notion of c-tensor may be applicable over a wide range of analysis.