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This thesis introduces fnnlib, a C++ library for recurrent neural network simulations that I developed between October 2009 and March 2010 at Osaka University's Graduate School of Engineering. After covering the theory behind recurrent neural networks, backpropagation through time, recurrent neural networks with parametric bias, continuous-time recurrent neural networks, and echo state networks, the design of the library is explained. All of the classes as well as their interrelationships are presented along with reasons as to why certain design decisions were made. Towards the end of the thesis, a small practical example is shown. Also, fnnlib is compared to other neural network libraries.
Specifying behaviors of multi-agent systems (MASs) is a demanding task, especially when applied in safety-critical systems. In the latter systems, the specification of behaviors has to be carried out carefully in order to avoid side effects that might cause unwanted or even disastrous behaviors. Thus, formal methods based on mathematical models of the system under design are helpful. They not only allow us to formally specify the system at different levels of abstraction, but also to verify the consistency of the specified systems before implementing them. The formal specification aims a precise and unambiguous description of the behavior of MASs, whereas the verification aims at proving the satisfaction of specified requirements. A behavior of an agent can be described as discrete changes of its states with respect to external or internal actions. Whenever an action occurs, the agent moves from one state to another one. Therefore, an efficient way to model this type of discrete behaviors is to use a kind of state transition diagrams such as finite automata. One remarkable advantage of such transition diagrams is that they lend themselves formal analysis techniques using model checking. The latter is an automatic verification technique which determines whether given properties are satisfied within a model underlying a particular system. In realistic physical environments, however, it is necessary to consider continuous behaviors in addition to discrete behaviors of MASs. Examples of those type of behaviors include the movement of a soccer agent to kick off or to go to the ball, the process of putting out the fire by a fire brigade agent in a rescue scenario, or any other behaviors that depend on any timed physical law. The traditional state transition diagrams are not sufficient to combine these types of behaviors. Hybrid automata offer an elegant method to capture such types of behaviors. Hybrid automata extend regular state transition diagrams with methods that deal with those continuous actions such that the state transition diagrams are used to model the discrete changes of behaviors, while differential equations are used to model the continuous changes. The semantics of hybrid automata make them accessible to formal verification by means of model checking. The main goal of this thesis is to approach hybrid automata for specifying and verifying behaviors of MASs. However, specifying and and verifying behaviors of MASs by means of hybrid automata raises several issues that should be considered. These issues include the complexity, modularity, and the expressiveness of MASs' models. This thesis addresses these issues and provides possible solutions to tackle them.
Die Entwicklung von Algorithmen im Sinne des Algorithm Engineering geschieht zyklisch. Der entworfene Algorithmus wird theoretisch analysiert und anschließend implementiert. Nach der praktischen Evaluierung wird der Entwurf anhand der gewonnenen Kenntnisse weiter entwickelt. Formale Verifffizierung der Implementation neben der praktischen Evaluierung kann den Entwicklungsprozess verbessern. Mit der Java Modeling Language (JML) und dem KeY tool stehen eine einfache Spezififfkationssprache und ein benutzerfreundliches, automatisiertes Verififfkationstool zur Verfügung. Diese Arbeit untersucht, inwieweit das KeY tool für die Verifffizierung von komplexeren Algorithmen geeignet ist und welche Rückmeldungen für Algorithmiker aus der Verififfkation gewonnen werden können.Die Untersuchung geschieht anhand von Dijkstras Algorithmus zur Berechnung von kürzesten Wegen in einem Graphen. Es sollen eine konkrete Implementation des Standard-Algorithmus und anschließend Implementationen weiterer Varianten verifffiziert werden. Dies ahmt den Entwicklungsprozess des Algorithmus nach, um in jeder Iteration nach möglichen Rückmeldungen zu suchen. Bei der Verifffizierung der konkreten Implementation merken wir, dass es nötig ist, zuerst eine abstraktere Implementation mit einfacheren Datenstrukturen zu verififfzieren. Mit den dort gewonnenen Kenntnissen können wir dann die Verifikation der konkreten Implementation fortführen. Auch die Varianten des Algorithmus können dank der vorangehenden Verififfkationen verifiziert werden. Die Komplexität von Dijkstras Algorithmus bereitet dem KeY tool einige Schwierigkeiten bezüglich der Performanz, weswegen wir während der Verifizierung die Automatisierung etwas reduzieren müssen. Auf der anderenrn Seite zeigt sich, dass sich aus der Verifffikation einige Rückmeldungen ableiten lassen.