Finite automata, formal logic, and circuit complexity
Finite automata, formal logic, and circuit complexity
Handbook of formal languages, vol. 1
Stutter-invariant temporal properties are expressible without the next-time operator
Information Processing Letters
Automata, Languages, and Machines
Automata, Languages, and Machines
Varieties Of Formal Languages
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
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Motivated by open problems in language theory, logic and circuit complexity, Straubing generalized Eilenberg's variety theory, introducing the ${\mathcal C}$-varieties. As a further contribution to this theory, this paper first studies a new ${\mathcal C}$-variety of languages, lying somewhere between star-free and regular languages. Then, continuing the early works of Esik-Ito, we extend the wreath product to ${\mathcal C}$-varieties and generalize the wreath product principle, a powerful tool originally designed by Straubing for varieties. We use it to derive a characterization of the operations L→ LaA* and L → La on languages. Finally, we investigate the decidability of the operation V →V∗LI (the wreath product by locally trivial semigroups) and solve it explicitely in several non-trivial cases.