A Free Energy Foundation of Semantic Similarity in Automata and Languages

TL;DR

This paper introduces a free energy theoretical framework for automata and languages, providing algorithms for energy computation and a semantic similarity metric, with potential applications in analyzing real-world programs.

Contribution

It develops a novel free energy theory for automata and languages, including algorithms for energy calculation and a semantic similarity metric.

Findings

Algorithms for computing free energy in automata

Efficient estimation of nondeterminism in automata

A new semantic similarity metric for automata and languages

Abstract

This paper develops a free energy theory from physics including the variational principles for automata and languages and also provides algorithms to compute the energy as well as efficient algorithms for estimating the nondeterminism in a nondeterministic finite automaton. This theory is then used as a foundation to define a semantic similarity metric for automata and languages. Since automata are a fundamental model for all modern programs while languages are a fundamental model for the programs' behaviors, we believe that the theory and the metric developed in this paper can be further used for real-word programs as well.