Derived-Term Automata of Multitape Rational Expressions (Long version)

TL;DR

This paper introduces a new formalism for multitape rational expressions using an operator to combine tapes, along with expansions and an algorithm to construct multitape automata from these expressions.

Contribution

It presents a novel operator for multitape expressions, generalizes derivatives through expansions, and provides an algorithm to derive automata from multitape rational expressions.

Findings

Defined the operator $|$ for multitape expressions

Introduced expansions as a generalization of derivatives

Developed an algorithm to construct multitape automata

Abstract

We introduce (weighted) rational expressions to denote series over Cartesian products of monoids. To this end, we propose the operator $|$ to build multitape expressions such as $(a^+|x + b^+|y)^*$. We define expansions, which generalize the concept of derivative of a rational expression, but relieved from the need of a free monoid. We propose an algorithm based on expansions to build multitape automata from multitape expressions.