title: An algorithmic approach to OpenFlow ruleset transformation

authors: Sanger, Richard

abstract: In an ideal development cycle for an OpenFlow application, a developer designs a pipeline to suit their application's needs and installs rules to that pipeline. Their application will run on any OpenFlow switch, whether software or hardware based. A network operator deploying this application would assess their network's requirements and purchase OpenFlow hardware to meet these requirements; such as bandwidth, port density, and flow table size. In reality, this level of interoperability does not exist as many OpenFlow switches are built on a fixed-function pipeline. Fixed-function pipelines limit the matches and actions available to rules depending on the table, but in doing so make more efficient use of expensive hardware resources such as TCAM.

This thesis investigates improving OpenFlow device interoperability by developing a method to rewrite existing rulesets to new complex fixed-function pipelines. Additionally, this thesis developed the tools to assess and verify the interoperability and equivalence of OpenFlow rulesets and pipelines. 

This thesis developed a library and tools for working with descriptions of fixed-function pipelines, specifically, the Table Type Pattern description. This library provides a method to check if an existing ruleset is compatible with a new pipeline. Additionally, this thesis designed and implemented a pragmatic approach to compare if the forwarding behaviour of two OpenFlow 1.3 rulesets is equivalent. Equivalence checking provides a tool to verify that an OpenFlow application rewritten to program a new pipeline maintains the correct forwarding behaviour.

Finally, this thesis investigates the problem of algorithmically rewriting an existing OpenFlow ruleset, programmed by an existing application, to fit a different fixed-function pipeline. Solving this problem allows an OpenFlow application to be written once and run on any OpenFlow switch. This research aimed to solve this problem in a comprehensive manner that did not rely on the target pipeline supporting features such as OpenFlow metadata. This thesis developed and implemented a general method to convert an OpenFlow 1.3 to a complex constrained fixed-function.

text: An algorithmic approach to OpenFlow ruleset transformation In an ideal development cycle for an OpenFlow application, a developer designs a pipeline to suit their application's needs and installs rules to that pipeline. Their application will run on any OpenFlow switch, whether software or hardware based. A network operator deploying this application would assess their network's requirements and purchase OpenFlow hardware to meet these requirements; such as bandwidth, port density, and flow table size. In reality, this level of interoperability does not exist as many OpenFlow switches are built on a fixed-function pipeline. Fixed-function pipelines limit the matches and actions available to rules depending on the table, but in doing so make more efficient use of expensive hardware resources such as TCAM.

This thesis investigates improving OpenFlow device interoperability by developing a method to rewrite existing rulesets to new complex fixed-function pipelines. Additionally, this thesis developed the tools to assess and verify the interoperability and equivalence of OpenFlow rulesets and pipelines. 

This thesis developed a library and tools for working with descriptions of fixed-function pipelines, specifically, the Table Type Pattern description. This library provides a method to check if an existing ruleset is compatible with a new pipeline. Additionally, this thesis designed and implemented a pragmatic approach to compare if the forwarding behaviour of two OpenFlow 1.3 rulesets is equivalent. Equivalence checking provides a tool to verify that an OpenFlow application rewritten to program a new pipeline maintains the correct forwarding behaviour.

Finally, this thesis investigates the problem of algorithmically rewriting an existing OpenFlow ruleset, programmed by an existing application, to fit a different fixed-function pipeline. Solving this problem allows an OpenFlow application to be written once and run on any OpenFlow switch. This research aimed to solve this problem in a comprehensive manner that did not rely on the target pipeline supporting features such as OpenFlow metadata. This thesis developed and implemented a general method to convert an OpenFlow 1.3 to a complex constrained fixed-function.

year: 2020

title: A projection-based solution to the SP(2N) state labeling problem

authors: Gould, M.D.

subjects: Mathematics

abstract: A projection-based solution to the symplectic group state labeling problem is presented. The approach yields a nonorthogonal Gel'fand–Tsetlin basis for the irreducible representations of Sp(2n). A method for evaluating the corresponding overlap coefficients is discussed. The action of the Sp(2n) generators, in the basis obtained, is determined and some matrix element formulas are derived. The results obtained are comparable to the matrix element formulas for O(n) and U(n).

text: A projection-based solution to the SP(2N) state labeling problem A projection-based solution to the symplectic group state labeling problem is presented. The approach yields a nonorthogonal Gel'fand–Tsetlin basis for the irreducible representations of Sp(2n). A method for evaluating the corresponding overlap coefficients is discussed. The action of the Sp(2n) generators, in the basis obtained, is determined and some matrix element formulas are derived. The results obtained are comparable to the matrix element formulas for O(n) and U(n).

year: 1985-07

title: Ko ētehi waiata tangi o Pare Hauraki

authors: Ngāpō, Korohere

subjects: Waiata tangi

abstract: Inā hiahia ai te tangata kia mōhio ngā momo mōteatea o Pare Hauraki i ngā wā o mua me huri atu rātou ki ngā wāhi kohinga waiata pērā i Ngā Mōteatea a Ngata. Ka mutu kua tuhia tēnei pitopito kōrero hei tautoko atu i te hui waiata tawhito i whakatūria i Te Whare Wānanga o Waikato i te 2008. He tirohanga tēnei tuhinga ki te momo o ngā waiata e rua kāore i āta waiatahia, i āta rangona i runga i ngā marae o Hauraki ā mohoa nei. Ka mutu mā te waihape atu anō ki tētehi waiata i titoa e Pua ki Tawhiti mō tōna tungāne tae noa atu ki te waiata tangi i titoa e Wetea rāua ko Tūkehu, tēnā pea, ka ara ake anō te whakaaro me hoki anō ngā iwi o Pare Hauraki ki te waiata atu anō i ēnei waiata.

text: Ko ētehi waiata tangi o Pare Hauraki Inā hiahia ai te tangata kia mōhio ngā momo mōteatea o Pare Hauraki i ngā wā o mua me huri atu rātou ki ngā wāhi kohinga waiata pērā i Ngā Mōteatea a Ngata. Ka mutu kua tuhia tēnei pitopito kōrero hei tautoko atu i te hui waiata tawhito i whakatūria i Te Whare Wānanga o Waikato i te 2008. He tirohanga tēnei tuhinga ki te momo o ngā waiata e rua kāore i āta waiatahia, i āta rangona i runga i ngā marae o Hauraki ā mohoa nei. Ka mutu mā te waihape atu anō ki tētehi waiata i titoa e Pua ki Tawhiti mō tōna tungāne tae noa atu ki te waiata tangi i titoa e Wetea rāua ko Tūkehu, tēnā pea, ka ara ake anō te whakaaro me hoki anō ngā iwi o Pare Hauraki ki te waiata atu anō i ēnei waiata.

year: 2011