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Regular Expressions for Languages over Infinite Alphabets

Authors:

Michael Kaminski,

Tony TanAuthors Info & Claims

Fundamenta Informaticae, Volume 69, Issue 3

Pages 301 - 318

Published: 01 August 2005 Publication History

Abstract

In this paper we introduce a notion of a regular expression over infinite alphabets and show that a language is definable by an infinite alphabet regular expression if and only if it is accepted by finite-state unification based automaton - a model of computation that is tightly related to other models of automata over infinite alphabets.

References

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{2} Autebert, J.-M., Beauquir, J., Boasson, L.: Langages des Alphabets Infinis, Discrete Applied Mathematics, 2, 1980, 1-20.

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{4} Bielecki, M., Hidders, J., Paredaens, J., Tyszkiewicz, J., den Bussch, J. V.: Navigating with a browser, Proceedings of the 29th International Colloquium on Automata, Languages and Programming - ICALP 2002 (P. Widmayer, F. Triguero, R. Morales, M. Hennessy, S. Eidenbenz, R. Conejo, Eds.), Springer, Berlin, 2002, 764-775, Lecture Notes in Computer Science 2380.

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{5} Bolling, B., Leucker, M., Noll, T.: Regular MSA Languages, Technical report, Department of Computer Science, Aachen University of Technology, 2001.

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{6} Itd, J.: Automates a pile sur des alphabets infinis, Proceedings of the Symposium of Theoretical Aspects of Computer Science, Springer-Verlag, Berlin, 1984, 260-273, Lecture Notes in Computer Science 166.

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{7} Kaminski, M., Francez, N.: Finite-Memory Automata, Proceedings of the 31th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, 683-688.

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{8} Kaminski, M., Francez, N.: Finite-memory automata, Theoretical Computer Science A, 138, 1994, 329-363.

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{10} Lewis, H., Papadimitriou, C.: Elements of the Theory of Computation, Prentice-Hall, Inc., Englewood Cliffs, NJ, USA, 1981.

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{11} Neven, F., Schwentick, T., Vianu, V.: Towards Regular Languages over Infinite Alphabets, Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science (J. Sgall, A. Pultr, P. Kolman, Eds.), Springer, Berlin, 2001, 560-572, Lecture Notes in Computer Science 2136.

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{12} Neven, F., Schwentick, T., Vianu, V.: Finite State Machines for Strings over Infinite Alphabets, ACM Transactions on Computational Logic, 5, 2004, 403-435.

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{13} Otto, F.: Classes of regular and context-free languages over countably infinite alphabets, Discrete Applied Mathematics, 12, 1985, 41-56.

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{16} Shemesh, Y., Francez, N.: Finite-State Unification Automata and Relational Languages, Information and Computation, 114, 1994, 192-213.

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Cited By

Banerjee AChatterjee KGuha S(2023)Set Augmented Finite Automata over Infinite AlphabetsDevelopments in Language Theory10.1007/978-3-031-33264-7_4(36-50)Online publication date: 12-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-33264-7_4
Schröder LKozen DMilius SWiβmann T(2017)Nominal Automata with Name BindingProceedings of the 20th International Conference on Foundations of Software Science and Computation Structures - Volume 1020310.1007/978-3-662-54458-7_8(124-142)Online publication date: 22-Apr-2017
https://dl.acm.org/doi/10.1007/978-3-662-54458-7_8
Libkin LVrgoč DDeutsch A(2012)Regular path queries on graphs with dataProceedings of the 15th International Conference on Database Theory10.1145/2274576.2274585(74-85)Online publication date: 26-Mar-2012
https://dl.acm.org/doi/10.1145/2274576.2274585
Show More Cited By

Index Terms

Regular Expressions for Languages over Infinite Alphabets
1. Theory of computation
  1. Formal languages and automata theory
    1. Grammars and context-free languages

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Fundamenta Informaticae

Fundamenta Informaticae Volume 69, Issue 3

February 2006

106 pages

ISSN:0169-2968

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IOS Press

Netherlands

Publication History

Published: 01 August 2005

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Cited By

Banerjee AChatterjee KGuha S(2023)Set Augmented Finite Automata over Infinite AlphabetsDevelopments in Language Theory10.1007/978-3-031-33264-7_4(36-50)Online publication date: 12-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-33264-7_4
Schröder LKozen DMilius SWiβmann T(2017)Nominal Automata with Name BindingProceedings of the 20th International Conference on Foundations of Software Science and Computation Structures - Volume 1020310.1007/978-3-662-54458-7_8(124-142)Online publication date: 22-Apr-2017
https://dl.acm.org/doi/10.1007/978-3-662-54458-7_8
Libkin LVrgoč DDeutsch A(2012)Regular path queries on graphs with dataProceedings of the 15th International Conference on Database Theory10.1145/2274576.2274585(74-85)Online publication date: 26-Mar-2012
https://dl.acm.org/doi/10.1145/2274576.2274585
Libkin LVrgoč D(2012)Regular expressions for data wordsProceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning10.1007/978-3-642-28717-6_22(274-288)Online publication date: 11-Mar-2012
https://dl.acm.org/doi/10.1007/978-3-642-28717-6_22
Kara ASchwentick TTan T(2012)Feasible automata for two-variable logic with successor on data wordsProceedings of the 6th international conference on Language and Automata Theory and Applications10.1007/978-3-642-28332-1_30(351-362)Online publication date: 5-Mar-2012
https://dl.acm.org/doi/10.1007/978-3-642-28332-1_30
Kaminski MTan T(2008)Tree automata over infinite alphabetsPillars of computer science10.5555/1805839.1805860(386-423)Online publication date: 1-Jan-2008
https://dl.acm.org/doi/10.5555/1805839.1805860
Segoufin L(2007)Static analysis of XML processing with data valuesACM SIGMOD Record10.1145/1276301.127630836:1(31-38)Online publication date: 1-Mar-2007
https://dl.acm.org/doi/10.1145/1276301.1276308
Segoufin L(2006)Automata and logics for words and trees over an infinite alphabetProceedings of the 20th international conference on Computer Science Logic10.1007/11874683_3(41-57)Online publication date: 25-Sep-2006
https://dl.acm.org/doi/10.1007/11874683_3

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