Automata, Languages, and Machines
Automata, Languages, and Machines
Syntactic Semiring of a Language
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
On Logical Descriptions of Regular Languages
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Extended temporal logic on finite words and wreath product of monoids with distinguished generators
DLT'02 Proceedings of the 6th international conference on Developments in language theory
A Robust Class of Regular Languages
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Equations Defining the Polynomial Closure of a Lattice of Regular Languages
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Bitopological duality for distributive lattices and heyting algebras
Mathematical Structures in Computer Science
A topological approach to recognition
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Theme and variations on the concatenation product
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Boolean algebras of regular languages
DLT'11 Proceedings of the 15th international conference on Developments in language theory
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Lattices of logical fragments over words
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Learning in the limit with lattice-structured hypothesis spaces
Theoretical Computer Science
Regular ideal languages and their boolean combinations
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
Algebra-coalgebra duality in brzozowski's minimization algorithm
ACM Transactions on Computational Logic (TOCL)
Varieties and Covarieties of Languages (Extended Abstract)
Electronic Notes in Theoretical Computer Science (ENTCS)
Iterated periodicity over finite aperiodic semigroups
European Journal of Combinatorics
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This paper presents a new result in the equational theory of regular languages, which emerged from lively discussions between the authors about Stone and Priestley duality. Let us call lattice of languagesa class of regular languages closed under finite intersection and finite union. The main results of this paper (Theorems 5.2 and 6.1) can be summarized in a nutshell as follows:A set of regular languages is a lattice of languages if and only if it can be defined by a set of profinite equations.The product on profinite words is the dual of the residuation operations on regular languages.In their more general form, our equations are of the form u茂戮驴v, where uand vare profinite words. The first result not only subsumes Eilenberg-Reiterman's theory of varieties and their subsequent extensions, but it shows for instance that any class of regular languages defined by a fragment of logic closed under conjunctions and disjunctions (first order, monadic second order, temporal, etc.) admits an equational description. In particular, the celebrated McNaughton-Schützenberger characterisation of first order definable languages by the aperiodicity condition x茂戮驴= x茂戮驴+ 1, far from being an isolated statement, now appears as an elegant instance of a very general result.