Hiermit versichere ich, daa ich die Arbeit selbstt andig verfaat und keine anderen als die angegebenen Quellen und Hilfsmittel benutzt sowie Zitate kenntlich gemacht habe. I have many people to thank and acknowledge. Especially I would like to thank my advisor, Eric Rosen, for all the time he spent in supporting my thesis work.

Real time systems are widely used systems in now days. Most of these systems work in fault prone environment. The job running in these systems should be finished on its deadline as timing constraints which requires some energy to finishing it. If there is any fault occurring in the system then it may not be possible that the job running will finish on its deadline and will give the desired resu...

We consider extensions of xed-point logic by means of generalized quantiiers in the context of descriptive complexity. By the well-known theorem of Immerman and Vardi, xed-point logic captures PTime over linearly ordered structures. It fails, however , to express even most fundamental structural properties, like simple cardinality properties, in the absence of order. In the present investigatio...

The classical logical antinomy known as Richard-Berry paradox is combined with plausible assumptions about the size i.e. the descriptional complexity, of Turing machines formalizing certain sentences, to show that formalization of language leads to contradiction.

We quickly review labelled Markov processes (LMP) and provide a counterexample showing that in general measurable spaces, event bisimilarity and state bisimilarity differ in LMP. This shows that the logic in Desharnais [3] does not characterize state bisimulation in non-analytic measurable spaces. Furthermore we show that, under current foundations of Mathematics, such logical characterization ...

The paper examines the concept of hairpin-free words motivated from the biocomputing and bioinformatics fields. Hairpin (-free) DNA structures have numerous applications to DNA computing and molecular genetics in general. A word is called hairpin-free if it cannot be written in the form xvyθ(v)z, with certain additional conditions, for an involution θ (a function θ with the property that θ equa...

We propose a framework for modelling and solving search problems using logic, and describe a project whose goal is to produce practically effective, general purpose tools for representing and solving search problems based on this framework. The mathematical foundation lies in the areas of finite model theory and descriptive complexity, which provide us with many classical results, as well as po...

Traditional image-based localisation methods do not work when the robot is moving in an environment whose appearance is changing in time. We propose an extension to the classical image-based localisation that uses a Distributed Vision System (DVS) and can work also in highly dynamic environments. The DVS is composed of omnidirectional cameras installed in the environment and can communicate wit...

One of the fundamental results of descriptive complexity theory, due to Immerman [12] and Vardi [17], says that a class of ordered finite structures is definable in fixed-point logic if, and only if, it is computable in polynomial time. Much effort has been spent on the problem of capturing polynomial time, that is, describing all polynomial time computable classes of not necessarily ordered fi...