On the Mother of All Automata: The Position Automaton

Abstract

We contribute new relations to the taxonomy of different conversions from regular expressions to equivalent finite automata. In particular, we are interested in ordinary transformations that construct automata such as, the follow automaton, the partial derivative automaton, the prefix automaton, the automata based on pointed expressions recently introduced and studied, and last but not least the position, or Glushkov automaton ($\mathcal {A}_{{{\mathrm{POS}}}}$), and their double reversed construction counterparts. We deepen the understanding of these constructions and show that with the artefacts used to construct the Glushkov automaton one is able to capture most of them. As a byproduct we define a dual version $\mathcal {A}_{{{\mathrm{\overleftarrow{{{\mathrm{POS}}}}}}}}$ of the position automaton which plays a similar role as $\mathcal {A}_{{{\mathrm{POS}}}}$ but now for the reverse expression. It turns out that although the conversion of regular expressions and reversal of regular expressions to finite automata seems quite similar, there are significant differences.

S. Broda, E. Maia, N. Moreira, R. Reis—Partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020.