Autonomicity and the absence of free variables for behaviors over finite rings

Margreta Kuijper; Raquel Pinto; Jan Willem Polderman; Paula Rocha

Autonomicity and the absence of free variables for behaviors over finite rings

Margreta Kuijper
, Raquel Pinto
, Jan Willem Polderman
, Paula Rocha

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

The equivalence between autonomicity and the absence of free variables is a well-known result for linear, shift-invariant and complete behaviors over a field. However, this no longer holds for a behavior that does not satisfy one of those properties. In this paper we consider linear, shift-invariant and complete behaviors over $\mathbb{Z}_{p^r}$ and study under which conditions such behaviors are autonomous and/or have no free variables.

Original language	English
Title of host publication	Proceedings of the Portuguese Conference on Automatic Control 2006
Place of Publication	Lisbon
Publisher	Portuguese Association of Automatic Control
Pages	-
Number of pages	5
ISBN (Print)	978-972-97025-2-5
Publication status	Published - Jul 2006
Event	7th Portuguese Conference on Automatic Control, CONTROLO 2006 - Instituto Superior Técnico, Lisbon, Portugal Duration: 11 Jul 2006 → 13 Jul 2006 Conference number: 7

Conference

Conference	7th Portuguese Conference on Automatic Control, CONTROLO 2006
Abbreviated title	CONTROLO
Country/Territory	Portugal
City	Lisbon
Period	11/07/06 → 13/07/06

Keywords

Finite ring
Autonomicity
Free variables

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Kuijper2006autonomityFinal published version, 334 KB

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title = "Autonomicity and the absence of free variables for behaviors over finite rings",

abstract = "The equivalence between autonomicity and the absence of free variables is a well-known result for linear, shift-invariant and complete behaviors over a field. However, this no longer holds for a behavior that does not satisfy one of those properties. In this paper we consider linear, shift-invariant and complete behaviors over \$\textbackslash{}mathbb\{Z\}\_\{p\textasciicircum{}r\}\$ and study under which conditions such behaviors are autonomous and/or have no free variables.",

keywords = "Finite ring, Autonomicity, Free variables",

author = "Margreta Kuijper and Raquel Pinto and Polderman, \{Jan Willem\} and Paula Rocha",

year = "2006",

month = jul,

language = "English",

isbn = "978-972-97025-2-5",

pages = "--",

booktitle = "Proceedings of the Portuguese Conference on Automatic Control 2006",

publisher = "Portuguese Association of Automatic Control",

note = "7th Portuguese Conference on Automatic Control, CONTROLO 2006, CONTROLO ; Conference date: 11-07-2006 Through 13-07-2006",

}

Autonomicity and the absence of free variables for behaviors over finite rings. / Kuijper, Margreta; Pinto, Raquel; Polderman, Jan Willem et al.
Proceedings of the Portuguese Conference on Automatic Control 2006. Lisbon: Portuguese Association of Automatic Control, 2006. p. -.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Autonomicity and the absence of free variables for behaviors over finite rings

AU - Kuijper, Margreta

AU - Pinto, Raquel

AU - Polderman, Jan Willem

AU - Rocha, Paula

N1 - Conference code: 7

PY - 2006/7

Y1 - 2006/7

N2 - The equivalence between autonomicity and the absence of free variables is a well-known result for linear, shift-invariant and complete behaviors over a field. However, this no longer holds for a behavior that does not satisfy one of those properties. In this paper we consider linear, shift-invariant and complete behaviors over $\mathbb{Z}_{p^r}$ and study under which conditions such behaviors are autonomous and/or have no free variables.

AB - The equivalence between autonomicity and the absence of free variables is a well-known result for linear, shift-invariant and complete behaviors over a field. However, this no longer holds for a behavior that does not satisfy one of those properties. In this paper we consider linear, shift-invariant and complete behaviors over $\mathbb{Z}_{p^r}$ and study under which conditions such behaviors are autonomous and/or have no free variables.

KW - Finite ring

KW - Autonomicity

KW - Free variables

M3 - Conference contribution

SN - 978-972-97025-2-5

SP - -

BT - Proceedings of the Portuguese Conference on Automatic Control 2006

PB - Portuguese Association of Automatic Control

CY - Lisbon

T2 - 7th Portuguese Conference on Automatic Control, CONTROLO 2006

Y2 - 11 July 2006 through 13 July 2006

ER -

Autonomicity and the absence of free variables for behaviors over finite rings

Abstract

Conference

Keywords

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