Abstract
An alphabetic cone is a family of forests stable under alphabetic tree transductions, whereas we call REC-closed each family of forests closed under the operations of union, top-catenation,a-product anda-star; the sheaves are families having both the above properties.
For a given sheaf of forests ℱ, both the families of languages (ℱ) and yield (ℱ) (of branches and yields of ℱ respectively) constitute full AFL's.
Further we show that the familyK-REC of forests supporting recognizable formal power series on trees is a sheaf and so is the family OCF of behaviors of one counter treeautomata.
On the contrary, restricted one counter forests (ROCF) constitute an alphabetic cone which fails to be a sheaf; ROCF N (restricted one counter forests over alphabets with degree ≦N) is alphabetically principal generated by the Lukasiewicz forest of rankN.
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References
Aho, A.V.: Indexed grammars: an extension of the context-free case. JACM15, 647–671 (1968)
Alexandrakis, A., Bozapalidis, S.: Weighted grammars and Kleene's theorem. Inf. Proc. Lett.24, 1–4 (1987)
Arnold, A., Dauchet, M.: Une relation d'équivalence décidable sur la classe des forêts régulières. Publ. Labo Calcul Lille52 (1975)
Arnold, A., Dauchet, M.: Transduction de forêts reconnaissables monadiques. Forêts corégulières. RAIRO Inf. Thèor.10, 5–28 (1976)
Arnold, A., Dauchet, M.: Un théorèm de Chomsky-Schützenberger pour les forêts algèbriques. Calcollo14, 161–184 (1977)
Arnold, A., Dauchet, M.: Forêts algèbriques et homomorphisme inverses. Inf. Control34 (2), 182–196 (1978)
Arnold, A., Leguy, B.: Une propriete des forets algebriques “de Greibach”. Inf. Control46 (2), 108–134 (1980)
Autebert, J.M., Boasson, L.: Transductions rationnelles. Paris: Masson 1988
Berstel, J.: Transductions and context-free languages. Stuttgart: Teubner 1978
Berstel, J., Reutenauer, C.: Recognizable formal power serieson trees. Theoret. Comput. Sci.18, 15–148 (1982)
Berstel, J., Reutenauer, C.: Rational Series and Their Languages (EATCS). Berlin, Heidelberg, New York: Springer 1988
Bozapalidis, S., Alexandrakis, A.: Représentations matricielles des séries d'arbre reconnaissable. Inf. Théor. Appl.23 (4), 449–459 (1989)
Bozapalidis, S.: Effective construction of the syntactic algebra of a recognizable series on trees. Acta Inf.28, 351–363 (1991)
Bozapalidis, S.: Alphabetic tree relations. Theoret. Comput. Sci.99, 177–211 (1992)
Engelfriet, J.: Bottom-up, top-down tree transformations: a comparison. Math. Systems Theory9, 198–231 (1975)
Gecseg, F., Steinby, M.: Tree automata. Budapest: Akademiai Kiado 1984
Ginsburg, S.: Algebraic and automata-theoretic properties of formal languages. Amsterdam, New York, Oxford: North-Holland 1975
Ginsburg, S., Greibach, S.: Abstract families of languages. In: Studies in Abstract Families of Languages. Mem. Am. Math. Soc.87, 1–32 (1969)
Guessarian, I.: Pushdown tree automata. Math. Systems Theory16, 237–263 (1983)
Maibaum, T.S.E.: A generalized approach to formal languages. J. Comput. System Sci.8, 409–439 (1974)
Rounds, W.C.: Mappings and grammars on trees. Math. Systems Theory4, 257–287 (1970)
Salomaa, A., Soittola, M.: Automata-theoretic aspects of formal power series. Berlin, Heidelberg, New York: Springer 1978
Thatcher, J.W., Wright, J.B.: Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Systems Theory2(1), 57–81 (1968)
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Bozapalidis, S., Rahonis, G. On two families of forests. Acta Informatica 31, 235–260 (1994). https://doi.org/10.1007/BF01218405
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DOI: https://doi.org/10.1007/BF01218405