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Article Dans Une Revue Semigroup Forum Année : 2014

A syntactic congruence for languages of birooted trees

Résumé

The study of languages of labelled birooted trees, that is, elements of the free inverse monoid enriched by a vertex labelling, has led to the notion of quasi-recognisability. It generalises the usual notion of recognisability by replacing homomorphisms by certain prehomomorphism into finite ordered monoids, called adequate, that only preserve some products: the so-called disjoint ones. In this paper we study the underlying partial algebra setting and we define a suitable notion of a syntactic congruence such that (i) having a syntactic congruence of finite index captures MSO-definability; (ii) a certain order-bisimulation refinement of the syntactic congruence captures quasi-recognisability in the same way.
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Dates et versions

hal-00947972 , version 1 (17-02-2014)

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Achim Blumensath, David Janin. A syntactic congruence for languages of birooted trees. Semigroup Forum, 2014, 91 (3), pp.675-698. ⟨10.1007/s00233-014-9677-x⟩. ⟨hal-00947972⟩
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