Relational morphisms and operations on recognizable sets
New applications of the wreath product of forest algebras
We give several new applications of the wreath product of forest algebras to the study of logics on trees. These include new simplified proofs of necessary conditions for definability in and first-order logic with the ancestor relation; a sequence of identities satisfied by all forest languages definable in ; and new examples of languages outside along with an application to the question of what properties are definable in both and
Some results on -varieties
In an earlier paper, the second author generalized Eilenberg’s variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman’s theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form , where are distinct letters. Next, we generalize the notions...
Some results on -varieties
In an earlier paper, the second author generalized Eilenberg's variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman's theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form , where are distinct letters. Next,...
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