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

Research output: Contribution to conference › Paper › peer-review

3 Citations (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.

Original language	English
Pages	23-29
Number of pages	7
DOIs	https://doi.org/10.1145/345542.345568
Publication status	Published - 2000
Externally published	Yes
Event	Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000) - St Andrews, UK Duration: 7 Aug 2000 → 9 Aug 2000

Conference

Conference	Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC 2000)
City	St Andrews, UK
Period	07.08.2000 → 09.08.2000

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10.1145/345542.345568

Cite this

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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

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

Y2 - 7 August 2000 through 9 August 2000

ER -

Algorithms for near-rings of non-linear transformations

Abstract

Conference

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