Algebraic Elimination of epsilon-transitions

TL;DR

This paper introduces algebraic formulas to convert k-epsilon-automata into equivalent k-automata, relying on matrix star operations and semiring properties, ensuring they exhibit identical behavior.

Contribution

It provides a new algebraic method for eliminating epsilon-transitions in automata using matrix star operations within semirings.

Findings

Equivalence of k-epsilon-automata and k-automata established

Algebraic formulas enable epsilon-elimination

Transformation preserves automaton behavior

Abstract

We present here algebraic formulas associating a k-automaton to a k-epsilon-automaton. The existence depends on the definition of the star of matrices and of elements in the semiring k. For this reason, we present the theorem which allows the transformation of k-epsilon-automata into k-automata. The two automata have the same behaviour.