Acta Informatica

, Volume 28, Issue 4, pp 351–363 | Cite as

Effective construction of the syntactic algebra of a recognizable series on trees

  • Symeon Bozapalidis


In this paper we exhibit two different effective constructions of the syntactic algebra
associated to a recognizable formal series on treesS.
The one method consists of a direct construction of
(=a copy of
) which is the subspace
with the natural algebra structure.
We first determine a basis
$$S\tau _1^{ - 1} ,...,S\tau _m^{ - 1} $$
of the subspace
$$F_S = \left\langle {{{S\tau ^{ - 1} } \mathord{\left/ {\vphantom {{S\tau ^{ - 1} } {\tau \in P_\Sigma }}} \right. \kern-\nulldelimiterspace} {\tau \in P_\Sigma }}} \right\rangle \subseteq F^{T_\Sigma } $$
and then, using the junction isomorphism
we obtain a basis for
The second method consists of considering an arbitrary surjective realization (
, φ) ofS, defining an appropriate ideal ℬ of
and then constructing the quotient algebra
; this quotient is isomorphic to
and thus independent of the choice of (


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Symeon Bozapalidis
    • 1
  1. 1.Department of MathematicsAristotle University of ThessalonikiThessalonikiGreece

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