From Two-Way Transducers to Regular Function Expressions

Nicolas Baudru (1, 2) , Pierre-Alain Reynier (1, 2)

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
2 MOVE - Modélisation et Vérification

Transducers constitute a fundamental extension of automata. The class of regular word functions has recently emerged as an important class of word-to-word functions, characterized by means of (functional, or unambiguous, or deterministic) two-way transducers, copyless streaming string transducers, and MSO-definable graph transformations. A fundamental result in language theory is Kleene’s Theorem, relating finite state automata and regular expressions. In [3], the authors introduced a set of regular function expressions and proved a similar result for regular word functions, by showing the equivalence with copyless streaming string transducers. In this paper, we propose a direct, simplified and effective translation from unambiguous two-way transducers to regular function expressions extending the Brzozowski and McCluskey algorithm. In addition, we identify a subset of regular function expressions characterizing the (strict) subclass of functional sweeping transducers.

Domaines: Informatique [cs]; Théorie et langage formel [cs.FL]

Nicolas Baudru, Pierre-Alain Reynier. From Two-Way Transducers to Regular Function Expressions. 22nd International Conference on Developments in Language Theory (DLT 2018), Sep 2018, Tokyo, Japan. pp.96-108, ⟨10.1007/978-3-319-98654-8_8⟩. ⟨hal-02003430⟩