## First-order definable languages (2008)

Venue: | Logic and Automata: History and Perspectives, Texts in Logic and Games |

Citations: | 9 - 2 self |

### BibTeX

@INPROCEEDINGS{Diekert08first-orderdefinable,

author = {Volker Diekert and Paul Gastin},

title = {First-order definable languages},

booktitle = {Logic and Automata: History and Perspectives, Texts in Logic and Games},

year = {2008},

pages = {261--306},

publisher = {Amsterdam University Press}

}

### OpenURL

### Abstract

We give an essentially self-contained presentation of some principal results for first-order definable languages over finite and infinite words. We introduce the notion of a counter-free Büchi automaton; and we relate counter-freeness to aperiodicity and to the notion of very weak alternation. We also show that aperiodicity of a regular ∞-language can be decided in polynomial space, if the language is specified by some Büchi automaton. 1