Partial derivatives of regular expressions and finite automaton constructions

Let E be a regular expression. Our aim is to establish a theoretical relation between two well-known automata recognizing the language of E, namely the position automaton P_E constructed by Glushkov or McNaughton and Yamada, and the equation automaton E_E ...

Two classical constructions to convert a regular expression into a finite non-deterministic automaton provide complementary advantages: the notion of position of a symbol in an expression, introduced by Glushkov and McNaugthon-Yamada, leads to an ...

Functional MSO transductions, deterministic two-way transducers, as well as streaming string transducers are all equivalent models for regular functions. In this paper, we show that every regular function, either on finite words or on infinite words, ...