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Compositions of n tree transducers

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W. F. Ogden,

W. C. RoundsAuthors Info & Claims

STOC '72: Proceedings of the fourth annual ACM symposium on Theory of computing

Pages 198 - 206

https://doi.org/10.1145/800152.804915

Published: 01 May 1972 Publication History

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Abstract

Top-down tree transductions, introduced as models of syntax-directed translations and transformational grammars in [12] and [11], are not closed under relational composition. However, closure under relational composition is not always needed; for example, in establishing closure properties of surface sets.(Surface sets are tree-languages obtained as ranges of transductions.) One such closure property, whether the image of a surface set under a transduction is a surface set, remained open.

In this paper, we show that transductions need not preserve surface sets. In fact, we exhibit a hierarchy of tree languages obtained by successive transductions. We do not have a good proof that the hierarchy inclusions are proper, but there are strong reasons for so suspecting.

As is customary in tree automata papers, we spend some effort on notation. This time, we present a list of first-order axioms for plane (ordered) trees. The Gorn-Brainerd-Doner representation of trees as prefix-closed sets of sequences ([5],[2],[3]) really is a representation in the sense that any (well-founded) abstract tree satisfying our axioms is isomorphic to a prefix-closed set. We then adopt Rosen's notation [10] for trees in subsequent definitions. In our opinion, however, a universally acceptable notation remains to be discovered.

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Cited By

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Kovács T(2005)Inducibility of the composition of frontier-to-root tree transformationsFundamentals of Computation Theory10.1007/3-540-51498-8_27(277-286)Online publication date: 28-May-2005
https://doi.org/10.1007/3-540-51498-8_27
Kamimura TSlutzki G(2005)Parallel and two-way recognizers of directed acyclic graphsMathematical Foundations of Computer Science 197910.1007/3-540-09526-8_29(317-325)Online publication date: 26-May-2005
https://doi.org/10.1007/3-540-09526-8_29
Kamimura TSlutzki G(2005)Dags and Chomsky hierarchyAutomata, Languages and Programming10.1007/3-540-09510-1_26(331-337)Online publication date: 25-May-2005
https://doi.org/10.1007/3-540-09510-1_26
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Index Terms

Compositions of n tree transducers
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Trees
  2. Mathematical analysis
    1. Numerical analysis
      1. Computation of transforms
2. Theory of computation
  1. Formal languages and automata theory
    1. Grammars and context-free languages

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STOC '72: Proceedings of the fourth annual ACM symposium on Theory of computing

May 1972

275 pages

ISBN:9781450374576

DOI:10.1145/800152

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Published: 01 May 1972

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Kovács T(2005)Inducibility of the composition of frontier-to-root tree transformationsFundamentals of Computation Theory10.1007/3-540-51498-8_27(277-286)Online publication date: 28-May-2005
https://doi.org/10.1007/3-540-51498-8_27
Kamimura TSlutzki G(2005)Parallel and two-way recognizers of directed acyclic graphsMathematical Foundations of Computer Science 197910.1007/3-540-09526-8_29(317-325)Online publication date: 26-May-2005
https://doi.org/10.1007/3-540-09526-8_29
Kamimura TSlutzki G(2005)Dags and Chomsky hierarchyAutomata, Languages and Programming10.1007/3-540-09510-1_26(331-337)Online publication date: 25-May-2005
https://doi.org/10.1007/3-540-09510-1_26
Arnold ADauchet M(2005)Sur l'inversion des morphismes d'arbresAutomata, Languages and Programming10.1007/3-540-08860-1_3(26-35)Online publication date: 26-May-2005
https://doi.org/10.1007/3-540-08860-1_3
Dauchet MTison S(1985)Decidability of confluence for ground term rewriting systemsFundamentals of Computation Theory10.1007/BFb0028794(80-89)Online publication date: 1985
https://doi.org/10.1007/BFb0028794
Engelfriet J(1981)Three hierarchies of transducersMathematical Systems Theory10.1007/BF0178697515:1(95-125)Online publication date: Dec-1981
https://doi.org/10.1007/BF01786975
Engelfriet J(1980)SOME OPEN QUESTIONS AND RECENT RESULTS ON TREE TRANSDUCERS AND TREE LANGUAGES11Preparation of this paper was supported in part by the National Science Foundation under Grant No. MCS79-04012.Formal Language Theory10.1016/B978-0-12-115350-2.50014-2(241-286)Online publication date: 1980
https://doi.org/10.1016/B978-0-12-115350-2.50014-2
Engelfriet JRozenberg GSlutzki GLipton RBurkhard WSavitch WFriedman EAho A(1978)Tree transducers, L systems and two-way machines (Extended Abstract)Proceedings of the tenth annual ACM symposium on Theory of computing10.1145/800133.804333(66-74)Online publication date: 1-May-1978
https://dl.acm.org/doi/10.1145/800133.804333
Engelfriet J(1976)Top-down tree transducers with regular look-aheadMathematical Systems Theory10.1007/BF0168328010:1(289-303)Online publication date: Dec-1976
https://doi.org/10.1007/BF01683280
Perrault CRounds WMartin NCarlyle JHarrison M(1975)Intercalation theorems for tree transducer languagesProceedings of the seventh annual ACM symposium on Theory of computing10.1145/800116.803761(126-136)Online publication date: 5-May-1975
https://dl.acm.org/doi/10.1145/800116.803761
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A comparison of pebble tree transducers with macro tree transducers

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A comparison of pebble tree transducers with macro tree transducers

The Complexity of Compositions of Deterministic Tree Transducers

Alphabetic pushdown tree transducers

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