Algorithms for near-rings of non-linear transformations

Franz Binder; Erhard Aichinger; Jurgen Ecker; Christof Nobauer; Peter Mayr

doi:10.1145/345542.345568

Algorithms for near-rings of non-linear transformations

Franz Binder^*
, Erhard Aichinger
, Jurgen Ecker
, Christof Nobauer
, Peter Mayr

^*Korrespondierende/r Autor/-in für diese Arbeit

Publikation: Konferenzbeitrag › Papier › Begutachtung

3 Zitate (Scopus)

Abstract

In this note we present some algorithms to deal with near-rings, the appropriate algebraic structure to study non-linear functions. This is similar the role of rings in the theory of linear functions or that of groups for permutations. In particular, we give efficient algorithms that deal with big near-rings that are given by a small set of generators. In this context, generating involves composition as well as point-wise addition. In the extreme case, one transformation of a group of order n can generate a set of up to nⁿ transformations.

Originalsprache	Englisch
Seiten	23-29
Seitenumfang	7
DOIs	https://doi.org/10.1145/345542.345568
Publikationsstatus	Veröffentlicht - 2000
Extern publiziert	Ja
Veranstaltung	Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000) - St Andrews, UK Dauer: 7 Aug. 2000 → 9 Aug. 2000

Konferenz

Konferenz	Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000)
Ort	St Andrews, UK
Zeitraum	07.08.2000 → 09.08.2000

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10.1145/345542.345568

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AU - Binder, Franz

AU - Aichinger, Erhard

AU - Ecker, Jurgen

AU - Nobauer, Christof

AU - Mayr, Peter

PY - 2000

Y1 - 2000

N2 - In this note we present some algorithms to deal with near-rings, the appropriate algebraic structure to study non-linear functions. This is similar the role of rings in the theory of linear functions or that of groups for permutations. In particular, we give efficient algorithms that deal with big near-rings that are given by a small set of generators. In this context, generating involves composition as well as point-wise addition. In the extreme case, one transformation of a group of order n can generate a set of up to nn transformations.

AB - In this note we present some algorithms to deal with near-rings, the appropriate algebraic structure to study non-linear functions. This is similar the role of rings in the theory of linear functions or that of groups for permutations. In particular, we give efficient algorithms that deal with big near-rings that are given by a small set of generators. In this context, generating involves composition as well as point-wise addition. In the extreme case, one transformation of a group of order n can generate a set of up to nn transformations.

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DO - 10.1145/345542.345568

M3 - Paper

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T2 - Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000)

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Algorithms for near-rings of non-linear transformations

Abstract

Konferenz

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