A Pumping Lemma for Output Languages of Attributed Tree Transducers

An attributed tree transducer is a formal model for studying properties of attribute grammars. In this paper we introduce and prove a pumping lemma for output languages of noncircular, producing, and visiting attributed tree transducers. We apply this pumping lemma to gain two results: (1) there is no noncircular, producing, and visiting attributed tree transducer which computes the set of all monadic trees with exponential height as output and (2) there is a hierarchy of noncircular, producing, and visiting attributed tree transducers with respect to their number of attributes.

[1]  Heiko Vogler,et al.  Synthesized and inherited functions - a new computational model for syntax-directed semantics , 1994 .

[2]  Stephen Scheinberg,et al.  Note on the Boolean Properties of Context Free Languages , 1960, Inf. Control..

[3]  Alfred V. Aho,et al.  Translations on a Context-Free Grammar , 1971, Inf. Control..

[4]  Giora Slutzki,et al.  Ogden's Lemma for Monterminal Bounded Languages , 1986, RAIRO Theor. Informatics Appl..

[5]  Zoltán Fülöp.  On attributed tree transducers , 1981, Acta Cybern..

[6]  David S. Wise.  A Strong Pumping Lemma for Context-Free Languages , 1976, Theor. Comput. Sci..

[7]  Joost Engelfriet,et al.  Tree transducers, L systems and two-way machines (Extended Abstract) , 1978, J. Comput. Syst. Sci..

[8]  Armin Kühnemann,et al.  A Pumping Lemma for Output Languages of Macro Tree Transducers , 1995, CAAP.

[9]  Arnaldo Moura,et al.  A Generalization of Ogden's Lemma , 1982, JACM.

[10]  G. Rozenberg,et al.  Pumping Lemmas for Regular Sets , 1981, SIAM J. Comput..

[11]  James W. Thatcher,et al.  Generalized Sequential Machine Maps , 1970, J. Comput. Syst. Sci..

[12]  Gregor von Bochmann,et al.  Semantic evaluation from left to right , 1976, CACM.

[13]  Zoltán Ésik,et al.  Decidability results concerning tree transducers I , 1980, Acta Cybern..

[14]  Sabine Kuske.  A Maximum Path Length Pumping Lemma for Edge-Replacement Languages , 1993, FCT.

[15]  S. Yu,et al.  A Pumping Lemma for Deterministic Context-Free Languages , 1989, Inf. Process. Lett..

[16]  Sándor Vágvölgyi,et al.  Attributed Tree Transducers Cannot Induce all Deterministic Bottom-Up Tree Transformations , 1995, Inf. Comput..

[17]  Giora Slutzki,et al.  A generalized Ogden's lema for linear conteext-free languages , 1986, Bull. EATCS.

[18]  Friedhelm Hinz.  Erzeugung von Bildsprachen durch Chomsky-Grammatiken: Entscheidbarkeits- und Komplexitätsfragen , 1990 .

[19]  J. Meigs,et al.  WHO Technical Report , 1954, The Yale Journal of Biology and Medicine.

[20]  C. Raymond Perrault.  Intercalation Lemmas for Tree Transducer Languages , 1976, J. Comput. Syst. Sci..

[21]  Hans-Jörg Kreowski.  A Pumping Lemma for Context-Free Graph Languages , 1978, Graph-Grammars and Their Application to Computer Science and Biology.

[22]  Joost Engelfriet,et al.  Macro Tree Transducers , 1985, J. Comput. Syst. Sci..

[23]  Annegret Habel,et al.  Hyperedge Replacement: Grammars and Languages , 1992, Lecture Notes in Computer Science.