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This course covers advanced methods using binary relations for graphs, modelling, algorithm development and program semantics. It presents the mathematical foundations and tools for relational programming, modelling and visualisation.
TopicsIn this course we explore binary relations and their application in modelling. We will covera selection of topics from the following, non-exclusive list:• foundations - relations - orders - lattices• applications - graphs: transitive closure, reachability, matchings, cycles, confluence - modelling: two-person games, social choice, preference - algorithm development: relational specification, program transformation - program semantics: verication, preconditions, fixpoints, computation models• tools - relational programming and modelling languages: Alloy, RelView - counterexample generators: Mace4, Nitpick - automated theorem provers: Isabelle, Prover9
After completing the course you will:know relations, basic relational operations and their properties,understand the matrix and graph representations of relations,be able to perform specific modelling tasks using relations,be able to formally reason about relations,be able to use tools for programming, modelling or reasoning with relations,be aware of program semantics,be aware of the abstraction provided by relations.
Subject to the approval of the Head of Department
Walter Guttmann
There will be two assignments each worth 25% of the final grade and an exam worth 50% of the final grade. Read notices and documents posted to the COSC432 area on Learn. The exam is open book.
Lectures will be based on G. Schmidt, T. Strohlein: Relations and graphs, Springer, 1993. R. Bird, O. de Moor: Algebra of programming, Prentice Hall, 1997. C. Brink, W. Kahl, G. Schmidt: Relational methods in computer science, Springer, 1997. R. Berghammer: Ordnungen, Verbande und Relationen mit Anwendungen, Vieweg, 2008. G. Schmidt: Relational mathematics, Cambridge University Press, 2010. D. Jackson: Software abstractions, MIT Press, 2012.Notes will be provided and you are not expected to buy these books.
Course Information on Learn
The Computer Science department's grading policy states that in order to pass a course you must meet two requirements:1. You must achieve an average grade of at least 50% over all assessment items.2. You must achieve an average mark of at least 45% on invigilated assessment items.If you satisfy both these criteria, your grade will be determined by the following University- wide scale for converting marks to grades: an average mark of 50% is sufficient for a C- grade, an average mark of 55% earns a C grade, 60% earns a B- grade and so forth. However if you do not satisfy both the passing criteria you will be given either a D or E grade depending on marks. Marks are sometimes scaled to achieve consistency between courses from year to year. AegrotatsIf factors beyond your control (such as illness or family bereavement) prevent you from completing some item of course work (including laboratory sessions), or prevent you from giving your best, then you may be eligible for aegrotat, impaired performance consideration or an extension on the assessment. Details of these may be found in the University Calendar. Supporting evidence, such as a medical certificate, is normally required. If in doubt, talk to your lecturer.
Domestic fee $881.00
International Postgraduate fees
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see Computer Science and Software Engineering .