Abstract
A fundamental result about formal languages states:
Theorem 1
A regular language is first-order definable if and only if its syntactic monoid contains no nontrivial groups.
Rest assured, we will explain in the next section exactly what the various terms in the statement mean!
Publisher
Association for Computing Machinery (ACM)
Reference30 articles.
1. ∑11-Formulae on finite structures
2. Regular languages in NC1
3. Jean Berstel Alain Lascoux and Dominique Perrin (Eds.). 2009. Marcel-Paul Schützenberger Oeuvres Complètes. http://igm.univ-mlv.fr/~berstel/Schutzenberger/Oeuvres-Completes/oeuvrescompletes.html Jean Berstel Alain Lascoux and Dominique Perrin (Eds.). 2009. Marcel-Paul Schützenberger Oeuvres Complètes. http://igm.univ-mlv.fr/~berstel/Schutzenberger/Oeuvres-Completes/oeuvrescompletes.html
4. Weak Second-Order Arithmetic and Finite Automata
5. Unbounded fan-in circuits and associative functions