title: Existence of constants in regular splicing languages.
abstract: In spite of wide investigations of finite splicing systems in formal language theory, basic questions, such as their characterization, remain unsolved. It has been conjectured that a necessary condition for a regular languageLto be a splicing language is thatLmust have a constant in the Schutzenberger sense. We prove this longstanding conjecture to be true. The result is based on properties of strongly connected components of the minimal deterministic finite state automaton for a regular splicing language. Using constants of the corresponding languages, we also provide properties of transitive automata and pathautomata.
authors.affiliation: Dipartimento di Informatica Sistemistica e Comunicazione, Univ. degli Studi di Milano-Bicocca, Viale Sarca 336, 20126 Milano, Italy.
authors.forename: Paola
authors.initials: P
authors.lastname: Bonizzoni
authors.affiliation: Department of Mathematics and Statistics, University of South Florida, Tampa, FL, USA.
authors.forename: Nataša
authors.initials: N
authors.lastname: Jonoska