Regular Expressions and Transducers over Alphabet-invariant and User-defined Labels

TL;DR

This paper introduces a generalized framework for regular expressions and transducers that are invariant under alphabet changes, enabling more flexible modeling of word relations with preserved computational efficiency.

Contribution

It defines a broad class of labelled graphs and regular expressions with set specifications, extending classic automata constructions while maintaining efficiency.

Findings

Extended automata constructions for alphabet-invariant regular expressions.

Algorithms for transducers with set specs applicable to independent language questions.

Preserved computational efficiency in generalized automata and transducer models.

Abstract

We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way---for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current software systems of formal language objects do not have a mechanism to define such objects. We define transducers in which transition labels involve what we call set specifications, some of which are alphabet invariant. In fact, we give a more broad definition of automata-type objects, called labelled graphs, where each transition label can be any string, as long as that string represents a subset of a certain monoid. Then, the behaviour of the labelled graph is a subset of that monoid. We do the same for regular expressions. We obtain extensions of a few classic algorithmic constructions on ordinary regular expressions and transducers at the broad level of labelled graphs and in such a way that the computational efficiency of the extended constructions is not sacrificed. For regular expressions with set specs we obtain the corresponding partial derivative automata. For transducers with set specs we obtain further algorithms that can be applied to questions about independent regular languages, in particular the witness version of the independent property satisfaction question.