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Two Complete Axiom Systems for the Algebra of Regular Events

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Arto SalomaaAuthors Info & Claims

Journal of the ACM (JACM), Volume 13, Issue 1

Pages 158 - 169

https://doi.org/10.1145/321312.321326

Published: 01 January 1966 Publication History

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Abstract

The theory of finite automata is closely linked with the theory of Kleene's regular expressions. In this paper, two formal systems for the algebraic transformation of regular expressions are developed. Both systems are consistent and complete; i.e., the set of equations derivable within the system equals the set of equations between two regular expressions denoting the same event. One of the systems is based upon the uniqueness of the solution of certain regular expression equations, whereas some facts concerning the representation theory of regular events are used in connection with the other.

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Cited By

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Grabmayer C(2024)From Compactifying Lambda-Letrec Terms to Recognizing Regular-Expression ProcessesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.408.2408(21-41)Online publication date: 1-Oct-2024
https://doi.org/10.4204/EPTCS.408.2
Różowski WSilva ASobocinski PLago UEsparza J(2024)A Completeness Theorem for Probabilistic Regular ExpressionsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662084(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662084
Keskin EMeyer Rvan der Wall S(2024)Urgency Annotations for Alternating ChoicesPrinciples of Verification: Cycling the Probabilistic Landscape10.1007/978-3-031-75778-5_17(351-373)Online publication date: 18-Nov-2024
https://doi.org/10.1007/978-3-031-75778-5_17
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Index Terms

Two Complete Axiom Systems for the Algebra of Regular Events
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Representation of mathematical objects
2. Theory of computation
  1. Formal languages and automata theory

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Published In

Journal of the ACM Volume 13, Issue 1

Jan. 1966

175 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321312

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1966

Published in JACM Volume 13, Issue 1

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Grabmayer C(2024)From Compactifying Lambda-Letrec Terms to Recognizing Regular-Expression ProcessesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.408.2408(21-41)Online publication date: 1-Oct-2024
https://doi.org/10.4204/EPTCS.408.2
Różowski WSilva ASobocinski PLago UEsparza J(2024)A Completeness Theorem for Probabilistic Regular ExpressionsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662084(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662084
Keskin EMeyer Rvan der Wall S(2024)Urgency Annotations for Alternating ChoicesPrinciples of Verification: Cycling the Probabilistic Landscape10.1007/978-3-031-75778-5_17(351-373)Online publication date: 18-Nov-2024
https://doi.org/10.1007/978-3-031-75778-5_17
Rooduijn JKozen DSilva A(2024)A Cyclic Proof System for Guarded Kleene Algebra with TestsAutomated Reasoning10.1007/978-3-031-63501-4_14(257-275)Online publication date: 2-Jul-2024
https://doi.org/10.1007/978-3-031-63501-4_14
Rodrigues NSebe MChen XRoşu G(2024)A Logical Treatment of Finite AutomataTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-031-57246-3_20(350-369)Online publication date: 4-Apr-2024
https://doi.org/10.1007/978-3-031-57246-3_20
Beier SHolzer M(2024)On Regular Expression Proof Complexity of Salomaa’s Axiom System $$F_1$$Taming the Infinities of Concurrency10.1007/978-3-031-56222-8_4(72-100)Online publication date: 20-Mar-2024
https://doi.org/10.1007/978-3-031-56222-8_4
Kappé TSchmid TSilva A(2023)A Complete Inference System for Skip-free Guarded Kleene Algebra with TestsProgramming Languages and Systems10.1007/978-3-031-30044-8_12(309-336)Online publication date: 22-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-30044-8_12
Kappé T(2023)Completeness and the Finite Model Property for Kleene Algebra, ReconsideredRelational and Algebraic Methods in Computer Science10.1007/978-3-031-28083-2_10(158-175)Online publication date: 3-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-28083-2_10
Krogmeier PLin ZMurali AMadhusudan P(2022)Synthesizing axiomatizations using logic learningProceedings of the ACM on Programming Languages10.1145/35633486:OOPSLA2(1697-1725)Online publication date: 31-Oct-2022
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Grabmayer C(2022)Milner’s Proof System for Regular Expressions Modulo Bisimilarity is CompleteProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3532430(1-13)Online publication date: 2-Aug-2022
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Regular Transducer Expressions for Regular Transformations

Finite and infinite regular thue systems

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