Derived terms without derivation a shifted perspective on the derived-term automaton

TL;DR

This paper introduces a new construction method for derived term automata that simplifies the process by avoiding derivation operations, especially benefiting weighted rational expressions.

Contribution

It proposes a novel inductive approach to construct derived term automata without referencing derivation operations, enhancing applicability to weighted rational expressions.

Findings

Simplifies automaton construction process

Applicable to weighted rational expressions

Avoids traditional derivation operations

Abstract

We present here a construction for the derived term automaton (aka partial derivative, or Antimirov, automaton) of a rational (or regular) expression based on a sole induction on the depth of the expression and without making reference to an operation of derivation of the expression. It is particularly well-suited to the case of weighted rational expressions.