Theses

See some of the topics offered at RISC for a bachelor/master/PhD thesis. This list is not comprehensive, other topics are also possible. In case there is no suitable topic for you in the list then please contact any of the RISC Faculty directly.

Open Topics

Gelenkmechanismen

Bachelor Thesis
Advisor: Josef Schicho
Gelenkmechanismen (Advisor: Josef Schicho). Man konstruiere Familien von Bennett-Mechanismen, die eine vollständige Drehung ohne Kollisionen zulassen.

Hamilton-Mechanik

Bachelor Thesis
Advisor: Josef Schicho
Hamilton-Mechanik (Advisor: Josef Schicho). Man beschreibe die Bewegung zweier fester Körper, die durch ein Drehgelenk miteinander verbunden sind, ohne Einwirkung äußerer Kräfte.
Further development and use of the unification and generalization algorithm library (Advisor: Teimuraz Kutsia). At RISC, we have been developing an open source library of unification and generalization algorithms, currently hosted at http://www.risc.jku.at/projects/stout/Unification is a process of equation solving, aiming at computing a most general common instance of the terms involved. Anti-unification is its dual process, aiming at computing a least general common generalization of the input terms (retaining their common structure as much as possible).The topics are for one or more bachelor theses: Extend the library by implementing recently developed improvements of some of the algorithms already in the library; add a new algorithm for term-graph generalization; add an algorithm for context sequence matching with regular constraints; experimental applications.Prerequisites: Programming in Java (since the library is written in Java), basic knowledge of logic, some familiarity with declarative programming and automated reasoning is a plus.
Symbolic computation and positivity of holonomic sequences (Advisor: Veronika Pillwein). Around ten years ago Stefan Gerhold and Manuel Kauers developed a symbolic method to show positivity for sequences defined by a linear recurrence relation with polynomial coefficients. More recently, in the course of a termination analysis, a variation of this method has been introduced. The goal of this thesis is to implement this new procedure in Mathematica and compare its behaviour at some practical examples with the existing implementation of the Gerhold-Kauers method.
Theorema Project: Document Processing (Advisor: Wolfgang Windsteiger). The task in this thesis is to setup an environment for preparing entire (big) mathematical documents in Theorema 2.0. This comprises the design of appropriate Mathematica stylesheets and a mechanism for translating Mathematica notebooks into nicely formatted LaTeX documents

Prerequisites: basic knowledge of the Mathematica programming language and LaTeX, interest in writing/formating mathematical documents, working in a bigger team, and structured software development.

Working area: 50% mathematics, 50% informatics.

Theorema Project: Specialized Proving Methods (Advisor: Wolfgang Windsteiger). In the frame of this thesis, specialized proving/solving tequniques for particular areas of mathematics (e.g. polynomials, vector spaces, etc.) should be studied and implemented in the frame of Theorema 2.0. Prerequisites: basic knowledge of the Mathematica programming language, interest in logic/proving, working in a bigger team, and structured software development. Working area: 80% mathematics, 20% informatics.

Finished Theses

2018

A Gateway for the Generic Conversion of Protocols for Smart Meters and IoT Applications

Ramez Elbaroudy

Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria. Master Thesis. July 2018. [pdf]
[bib]
@misc{RISC5727,
author = {Ramez Elbaroudy},
title = {{A Gateway for the Generic Conversion of Protocols for Smart Meters and IoT Applications}},
language = {english},
abstract = {In the recent years the number of Internet of things (IoT) devices have increased in a remarkable way.Due to this increase of devices many challenges have appeared. One of the most markable challenge isinteroperability challenge, where devices use different standards, protocols and conventions to exchangeinformation. This challenge has appeared because of the different devices’ specifications and the differentmanufacturers of the different types of IoT devices. The current thesis proposes a generic API that canbe used for communication with different IoT devices, which use different conventions and protocols;understanding the underlying conventions or protocols used. In this thesis, we used smart meters as theIoT devices for testing the generic API. The generic API is first described in an abstract way; then wedescribe the Java binding in order to use the API with the Java programming language. The implementedgeneric API enables developers to communicate with different IoT devices without the need of knowing thespecification of each protocol. The current thesis can be considered as an important point of extendingthe research field of interoperability of IoT devices. Furthermore, the generic API can be extended inorder to support other types of protocols and conventions.},
year = {2018},
month = {July},
translation = {0},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria},
length = {85}
}

Das Shifting-Bottleneck Verfahren für das Job-Shop Scheduling-Problem

M. Schlenkrich

JKU Linz. Bachelor Thesis. September 2018. [pdf]
[bib]
@misc{RISC5874,
author = {M. Schlenkrich},
title = {{Das Shifting-Bottleneck Verfahren für das Job-Shop Scheduling-Problem}},
language = {deutsch},
abstract = {Schedulingprobleme treten in unserer Welt in den verschiedensten Bereichen auf.Egal ob in Krankenhäusern bei der Zuteilung von Patienten zu Behandlungs-räumen, in Tischlereien und anderen Manufakturen bei der Abfolge von Ar-beitsschritten auf Maschinen oder der Nutzung von Schienentrassen im Bahn-verkehr. Das Lösen dieser Ablaufplanungsprobleme ist oftmals essentiell, umeinen reibungsfreien Arbeitsalltag garantieren zu können oder um Produktions-prozesse zu optimieren.Eine besonders häufig auftretende Variante dieser Schedulingprobleme istdas sogenannte Job-Shop Ablaufplanungsproblem, bei dem die Aufträge aufallen zur Verfügung stehenden Ressourcen in einer definierten Reihenfolge be-arbeitet werden müssen. Für große Problemdaten mit einer hohen Anzahl anAufträgen und Maschinen ist das Lösen dieser Probleme sehr aufwändig und immathematisch-wissenschaftlichen Bereich noch nicht zur Gänze erforscht.Eine Methode zur Lösung dieser Problemklasse ist die Shifting-BottleneckHeuristik. Wie der Name schon verrät, handelt es sich dabei nicht um ein exaktesVerfahren, sondern um eine Heuristik, die zwar eine zulässige Lösung liefert, diesjedoch nicht unbedingt das Optimum sein muss. In der Regel sind die Lösungendieses Verfahrens jedoch sehr gute Näherungen.Dieses Verfahren löst mehrere kleinere Hilfsprobleme und gelangt nach mIterationen zu einem Ergebnis, wobei m die Anzahl der Ressourcen bzw. Ma-schinen ist. Das Lösen dieser Hilfsprobleme geschieht zwar exakt, was Zeit undRechenaufwand kostet, diese sind jedoch um einiges einfacher zu lösen als dasGesamtproblem und somit bleibt der Aufwand in einem akzeptablen Rahmen.Die Basisversion der Shifting-Bottleneck Heuristik wurde im Rahmen dieserArbeit in Python implementiert und mit Benchmarkproblemdaten aus der Li-teratur getestet.},
year = {2018},
month = {September},
translation = {0},
institution = {JKU Linz},
length = {36}
}

2017

An Online Auction System for Selling Fiber Products

C. Ilonka

ISI Hagenberg, JKU Linz. Master Thesis. July 2017. [pdf]
[bib]
@misc{RISC5873,
author = {C. Ilonka},
title = {{An Online Auction System for Selling Fiber Products}},
language = {english},
abstract = {The thesis presents the design and development of the Lenzing Global Auction Portalproject. The Lenzing Global Auction Portal is a software system for running multiplesimultaneous online auctions. The system implements the Dutch auction model, butprovides the means to integrate different auction models as well.The system is based on the Client/Server architecture model. The server-side follows themicroservice based architecture model combined with the multi-layer architecture model.The client-side consists of two mobile-first web applications following the single-pageapplication principle.},
year = {2017},
month = {July},
translation = {0},
institution = {ISI Hagenberg, JKU Linz},
length = {60}
}

Complex Analysis Based Computer Algebra Algorithms for Proving Jacobi Theta Function Identities

Liangjie Ye

RISC and the DK program Linz. PhD Thesis. 2017. Updated version in June 2017. [pdf]
[bib]
@phdthesis{RISC5463,
author = {Liangjie Ye},
title = {{Complex Analysis Based Computer Algebra Algorithms for Proving Jacobi Theta Function Identities}},
language = {english},
year = {2017},
note = {Updated version in June 2017},
translation = {0},
school = {RISC and the DK program Linz},
length = {122}
}

2016

Axiomatic Description of Gröbner Reduction

Christoph Fuerst

RISC, JKU Linz. PhD Thesis. December 2016. [pdf]
[bib]
@phdthesis{RISC5388,
author = {Christoph Fuerst},
title = {{Axiomatic Description of Gröbner Reduction}},
language = {english},
year = {2016},
month = {December},
translation = {0},
school = {RISC, JKU Linz},
length = {154}
}

Algebraic Geometry methods in Kinematics: Mobile Pods

Matteo Gallet

Johannes Kepler University. PhD Thesis. October 2016.
[bib]
@phdthesis{RISC5393,
author = {Matteo Gallet},
title = {{Algebraic Geometry methods in Kinematics: Mobile Pods}},
language = {English},
year = {2016},
month = {October},
translation = {0},
school = {Johannes Kepler University},
length = {82}
}

Computer-Assisted Exploration of Gröbner Bases Theory in Theorema

A. Maletzky

RISC, Johannes Kepler University Linz. PhD Thesis. May 2016.
[bib]
@phdthesis{RISC5361,
author = {A. Maletzky},
title = {{Computer-Assisted Exploration of Gröbner Bases Theory in Theorema}},
language = {english},
year = {2016},
month = {May},
translation = {0},
school = {RISC, Johannes Kepler University Linz},
length = {197}
}

Formally Modeling and Analyzing Mathematical Algorithms with Software Specification Languages & Tools

Daniela Ritirc

Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria. Master Thesis. January 2016. [pdf]
[bib]
@misc{RISC5224,
author = {Daniela Ritirc},
title = {{Formally Modeling and Analyzing Mathematical Algorithms with Software Specification Languages & Tools}},
language = {english},
abstract = {In this thesis the behaviour of software specification languages and tools on mathematicalalgorithms shall be investigated. The main goal is to investigate how tools which havebeen designed for modeling and analyzing software in other application contexts can beapplied to mathematical algorithms. For this purpose, two different mathematical algorithms,namely the DPLL method and Dijkstra’s Shortest Path Algorithm are selected.Furthermore five well-known software specification languages are selected: JML, Alloy,TLA/PlusCal, VDM and Event-B. It shall be examined how far the algorithms can bemodeled and how far model checking respectively verification succeeds. The goal of thethesis is not a proper verification/check of every model with every tool but a survey ofthe potential as well as the difficulties of the usage of software specification languagesfor the analysis of mathematical algorithms.As a starting point for each algorithm a formal specification is derived and the algorithmsare supplied in pseudo-code. A Java prototype is implemented for each algorithmwhich is then specified by JML annotations. Furthermore the algorithms are modelled inTLA/PlusCal, Alloy, VDM and Event-B and for each language the appropriate analysissupported by the tool is selected (visualizing, model checking, verification).The main result of the thesis is that each tool shows some success when it is usedfor specifying and analyzing mathematical algorithms, because modeling the algorithmssucceeded in every language. In TLA, VDM and Alloy it was possible to completelymodel check the specifications. Furthermore it was possible to visualize the algorithmsin Alloy. In JML and Event-B it was possible to verify major parts of the model;},
year = {2016},
month = {January},
translation = {0},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria},
keywords = {formal methods, model checking, program verification},
length = {167}
}

Rational and Algebraic Solutions of First-Order Algebraic ODEs

N. Thieu Vo

Research Institute for Symbolic Computation. PhD Thesis. 2016. [pdf]
[bib]
@phdthesis{RISC5399,
author = {N. Thieu Vo},
title = {{Rational and Algebraic Solutions of First-Order Algebraic ODEs}},
language = {english},
year = {2016},
translation = {0},
school = {Research Institute for Symbolic Computation},
length = {93}
}

2015

Anti-Unification Algorithms: Design, Analysis, and Implementation

Alexander Baumgartner

RISC, JKU Linz. PhD Thesis. September 2015. [pdf]
[bib]
@phdthesis{RISC5180,
author = {Alexander Baumgartner},
title = {{Anti-Unification Algorithms: Design, Analysis, and Implementation}},
language = {english},
year = {2015},
month = {September},
translation = {0},
school = {RISC, JKU Linz},
length = {169}
}

Symbolic solutions of first-order algebraic differential equations

Georg Grasegger

Johannes Kepler University Linz. PhD Thesis. 06 2015. [url]
[bib]
@phdthesis{RISC5160,
author = {Georg Grasegger},
title = {{Symbolic solutions of first-order algebraic differential equations}},
language = {english},
year = {2015},
month = {06},
translation = {0},
school = {Johannes Kepler University Linz},
length = {154},
url = {http://epub.jku.at/obvulihs/content/titleinfo/753082}
}

Dual Space Algorithms for Computing Multiplicity Structure of Isolated Points

H. Rahkooy

RISC, JKU Linz. PhD Thesis. July 2015.
[bib]
@phdthesis{RISC5288,
author = {H. Rahkooy},
title = {{Dual Space Algorithms for Computing Multiplicity Structure of Isolated Points}},
language = {english},
year = {2015},
month = {July},
translation = {0},
school = {RISC, JKU Linz},
length = {69}
}

Gröbner Bases and Generalized Sylvester Matrices

Manuela Wiesinger-Widi

Johannes Kepler University Linz. PhD Thesis. 07 2015. [url]
[bib]
@phdthesis{RISC5170,
author = {Manuela Wiesinger-Widi},
title = {{Gröbner Bases and Generalized Sylvester Matrices}},
language = {english},
year = {2015},
month = {07},
translation = {0},
school = {Johannes Kepler University Linz},
length = {116},
url = {http://epub.jku.at/obvulihs/content/titleinfo/776913}
}

2014

Fast and rigorous computation of special functions to high precision

F. Johansson

RISC. PhD Thesis. 2014. [pdf]
[bib]
@phdthesis{RISC4972,
author = {F. Johansson},
title = {{Fast and rigorous computation of special functions to high precision}},
language = {english},
year = {2014},
translation = {0},
school = {RISC},
length = {0}
}

Computer Algebra and Analysis: Complex Variables Visualized

Thomas Ponweiser

RISC Institute, JKU Linz, Austria. Diploma Thesis. 2014. [pdf]
[bib]
@mastersthesis{RISC5011,
author = {Thomas Ponweiser},
title = {{Computer Algebra and Analysis: Complex Variables Visualized}},
language = {english},
year = {2014},
translation = {0},
school = {RISC Institute, JKU Linz, Austria},
length = {102}
}

2013

3-loop contributions to heavy flavor Wilson coefficients of neutral and charged current DIS

Alexander Hasselhuhn

TU Dortmund University. PhD Thesis. 2013. [url]
[bib]
@phdthesis{RISC4942,
author = {Alexander Hasselhuhn},
title = {{3-loop contributions to heavy flavor Wilson coefficients of neutral and charged current DIS}},
language = {english},
abstract = {The present thesis presents the calculation of higher order corrections to the structure functions of deep-inelastic scattering. In particular heavy quark effects in QCD corrections are determined on the 3-loop level. In the asymptotic region Q^2 >> m^2, the heavy flavor Wilson coefficients can be represented in terms of the light flavor Wilson coefficients and the massive operator matrix elements (OMEs). New contributions to the OMEs A_{gq,Q} and A_{gg,Q} are obtained. Furthermore, methods for the computer algebraic computation of ladder diagrams are given, making use of different representations of generalized hypergeometric functions and Appell functions. Here symbolic summation techniques are applied. For the calculation of graphs with two disjoint massive cycles, these methods are altered including Mellin-Barnes integrals and properties of iterated integrals. Finally, for the process of charged current deep-inelastic scattering, the complete 2-loop corrections to the heavy flavor Wilson coefficients are constructed and given in x-space and Mellin-space. The results of the thesis are necessary for the precise determination of the parton densities (PDFs) and the strong coupling constant at 3-loop precision.},
year = {2013},
translation = {0},
school = {TU Dortmund University},
length = {179},
url = {http://www.ub.tu-dortmund.de/katalog/titel/1435872}
}

Removable Singularities of Ore Operators

Maximilian Jaroschek

RISC. PhD Thesis. November 2013. [pdf]
[bib]
@phdthesis{RISC4848,
author = {Maximilian Jaroschek},
title = {{Removable Singularities of Ore Operators}},
language = {english},
year = {2013},
month = {November},
translation = {0},
school = {RISC},
length = {115}
}

Gesture-Based Browsing of Mathematics

S. El Bedewy

Internationaler Universitätslehrgang Informatics: Engineering and Management (ISI), Johannes Kepler University Linz. Master Thesis. 2013. [pdf]
[bib]
@misc{RISC4899,
author = {S. El Bedewy},
title = {{Gesture-Based Browsing of Mathematics}},
language = {english},
year = {2013},
translation = {0},
institution = {Internationaler Universitätslehrgang Informatics: Engineering and Management (ISI), Johannes Kepler University Linz},
length = {70}
}

2012

Computer Algebra Algorithms for Special Functions in Particle Physics

J. Ablinger

J. Kepler University Linz. PhD Thesis. April 2012. [pdf]
[bib]
@phdthesis{RISC4542,
author = {J. Ablinger},
title = {{Computer Algebra Algorithms for Special Functions in Particle Physics}},
language = {english},
year = {2012},
month = {April},
translation = {0},
school = {J. Kepler University Linz},
length = {233}
}

Computational Logic and Quantifier Elimination Techniques for (Semi-)automatic Static Analysis and Synthesis of Algorithms

Madalina Erascu

Research Institute for Symbolic Computation. PhD Thesis. 2012. RISC Technical Report 12-16. [pdf]
[bib]
@phdthesis{RISC4605,
author = {Madalina Erascu},
title = {{Computational Logic and Quantifier Elimination Techniques for (Semi-)automatic Static Analysis and Synthesis of Algorithms}},
language = {english},
year = {2012},
note = {RISC Technical Report 12-16},
translation = {0},
school = {Research Institute for Symbolic Computation},
length = {109}
}

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