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Transformations and translations from the point of view of generalized finite automata theory

Author:

James W. ThatcherAuthors Info & Claims

STOC '69: Proceedings of the first annual ACM symposium on Theory of computing

Pages 129 - 142

https://doi.org/10.1145/800169.805427

Published: 05 May 1969 Publication History

Abstract

The objective of this work is to expand the study of generalized finite automata theory by introducing generalized finite state mappings (finite state mappings of trees). In the process, we hope to provide an algebraic framework in which to study formalizations of transformations (in the sense that linguists use the term) and translations of natural and artificial languages. The concepts, “syntax directed translation” [2,18,19, 22, 29] and “transformation” [11, 25] can be formulated quite neatly within this framework.

Sections 2 and 3 present basic concepts of generalized finite automata theory and its relationship to context-free languages. We provide some general notation for transformations in Section 4 and in the following four sections, two basic kinds of transformations will be introduced and certain fundamental properties proved.

In Section 9, these definitions will be related to others in the literature and several areas for further investigation will be indicated.

References

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Aho, A. V., "Indexed grammars — An extension of the context-free grammars," J ACM 15 (1968) 647-671.

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Aho, A. V., and J. D. Ullman, "Automation analogs of syntax directed translation schemata," Proc. 9th Ann. Symp. on Switching and Automata Theory, October 1968.

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Bar-Hillel, Y., M. Perles, and E. Shamir, "On formal properties of phrase structure grammars," Z. Phonetik, Sprach. Kummunikations-forsch 14 (1961) 143-172.

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Brainerd, W. S., "Tree generating systems and tree automata," Ph. D. dissertation, Purdue University, June 1967.

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Brainerd, W. S., "Minimalization of tree automata," submitted for publication.

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Chomsky, N., "On the notion of 'rule of grammar," Structure of Language and Its Mathematical Aspects (Proc. Symposia Appl. Math., Vol. XII, pp. 6-24) American Mathematical Society, Providence, Rhode Island, 1961.

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Doner, J., "Tree acceptors and some of their applications," submitted for publication (1965).

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Fischer, Michael J., "Grammars with macro-like productions," Proc. 9th Ann. Symp. on Switching and Automata Theory, October 1968.

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Ginsburg, S., The Mathematical Theory of Context-Free Languages, McGrawHill, New York, 1966.

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Irons, E. T., "A syntax directed compiler for ALGOL 60," C ACM 4 (1961) 51-55.

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Peters, S., and R. W. Ritchie, "On the generative power of transformational grammars," unpublished manuscript, 1967.

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Petrone, L., "Syntax directed mappings of context-free languages," Proc. 9th Ann. Symp. on Switching and Automata Theory, October 1968.

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Rabin, M. O., "Mathematical theory of automata," Mathematical Aspects of Computer Science (Proc. Symposia Appl. Math., Vol. XIX, pp. 153-175), American Mathematical Society, Providence, Rhode Island, 1967.

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Rounds, W. C., "Trees, transducers and transformations," Ph.D. dissertation, Stanford University (August 1968).

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Thatcher, J. W., "Characterizing derivation trees of context-free grammars through a generalization of finite automata theory," J. Comp. System, Sci. 1 (1967) 317-322.

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Thatcher, J. W., and J.B. Wright, "Generalized finite automata theory with an application to a decision problem of second-order logic" Math. Systems Theory 2 (1968) 57-81.

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Thatcher, J. W., "Two approaches to generalized nondeterministic finite-state transformations," forthcoming, 1969.

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Younger, D. H., "Recognition and parsing of context-free languages in time n3," Information and Control 10 (1967) 189-208.

Cited By

Godoy GGiménez O(2013)The HOM problem is decidableJournal of the ACM10.1145/2508028.250160060:4(1-44)Online publication date: 4-Sep-2013
https://dl.acm.org/doi/10.1145/2508028.2501600
Bahr PDay LCarette JWillcock J(2013)Programming macro tree transducersProceedings of the 9th ACM SIGPLAN workshop on Generic programming10.1145/2502488.2502489(61-72)Online publication date: 28-Sep-2013
https://dl.acm.org/doi/10.1145/2502488.2502489
Creus CGascon AGodoy GRamos L(2012)The HOM Problem is EXPTIME-CompleteProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.36(255-264)Online publication date: 25-Jun-2012
https://dl.acm.org/doi/10.1109/LICS.2012.36
Show More Cited By

Index Terms

Transformations and translations from the point of view of generalized finite automata theory
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Representation of mathematical objects
2. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
      1. Rewrite systems
    2. Grammars and context-free languages

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cover image ACM Conferences

STOC '69: Proceedings of the first annual ACM symposium on Theory of computing

May 1969

267 pages

ISBN:9781450374781

DOI:10.1145/800169

Copyright © 1969 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 05 May 1969

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Cited By

Godoy GGiménez O(2013)The HOM problem is decidableJournal of the ACM10.1145/2508028.250160060:4(1-44)Online publication date: 4-Sep-2013
https://dl.acm.org/doi/10.1145/2508028.2501600
Bahr PDay LCarette JWillcock J(2013)Programming macro tree transducersProceedings of the 9th ACM SIGPLAN workshop on Generic programming10.1145/2502488.2502489(61-72)Online publication date: 28-Sep-2013
https://dl.acm.org/doi/10.1145/2502488.2502489
Creus CGascon AGodoy GRamos L(2012)The HOM Problem is EXPTIME-CompleteProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.36(255-264)Online publication date: 25-Jun-2012
https://dl.acm.org/doi/10.1109/LICS.2012.36
King-Sun Fu Bhargava B(1973)Tree Systems for Syntactic Pattern RecognitionIEEE Transactions on Computers10.1109/T-C.1973.22365422:12(1087-1099)Online publication date: 1-Dec-1973
https://dl.acm.org/doi/10.1109/T-C.1973.223654
Rosen BFischer PFabian RUllman JKarp R(1970)Tree-manipulating systems and Church-Rosser TheoremsProceedings of the second annual ACM symposium on Theory of computing10.1145/800161.805157(117-127)Online publication date: 4-May-1970
https://dl.acm.org/doi/10.1145/800161.805157
Rounds WFischer PFabian RUllman JKarp R(1970)Tree-oriented proofs of some theorems on context-free and indexed languagesProceedings of the second annual ACM symposium on Theory of computing10.1145/800161.805156(109-116)Online publication date: 4-May-1970
https://dl.acm.org/doi/10.1145/800161.805156
Rounds W(1970)Mappings and grammars on treesMathematical Systems Theory10.1007/BF016957694:3(257-287)Online publication date: Sep-1970
https://doi.org/10.1007/BF01695769
Brainerd W(1969)Semi-thue systems and representations of treesProceedings of the 10th Annual Symposium on Switching and Automata Theory (swat 1969)10.1109/SWAT.1969.19(240-244)Online publication date: 15-Oct-1969
https://dl.acm.org/doi/10.1109/SWAT.1969.19

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