Hierarchies of hyper-AFLs

For a full semi-AFL K, B(K) is defined as the family of languages generated by all K-extended basic macro grammars, while H(K) B(K) is the smallest full hyper-AFL containing K; a full basic-AFL is a full AFL K such that B(K) = K (hence every full basic-AFL is a full hyper-AFL). For any full semi-AFL K, K is a full basic-AFL if and only if B(K) is substitution closed if and only if H(K) is a full basic-AFL. If K is not a full basic-AFL, then the smallest full basic-AFL containing K is the union of an infinite hierarchy of full hyper-AFLs. If K is a full principal basic-AFL (such as INDEX, the family of indexed languages), then the largest full AFL properly contained in K is a full basic-AFL. There is a full basic-AFL lying properly in between the smallest full basic-AFL and the largest full basic-AFL in INDEX

Three hierarchies of transducers

Composition of top-down tree transducers yields a proper hierarchy of transductions and of output languages. The same is true for ETOL systems (viewed as transducers) and for two-way generalized sequential machines

Extended macro grammars and stack controlled machines

K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semi-AFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type D, the stack controlled machine type corresponding to D is introduced, denoted S(D), and the checking-stack controlled machine type CS(D). The data structure of this machine is a stack which controls a pushdown of data structures from D. If D accepts K, then S(D) accepts B(K) and CS(D) accepts LB(K). Thus the classes B(K) are characterized by stack controlled machines and the classes LB(K), i.e., the full hyper-AFLs, by checking-stack controlled machines. A full basic-AFL is a full AFL K such that B(K)C K. Every full basic-AFL is a full hyper-AFL, but not vice versa. The class of OI macro languages (i.e., indexed languages, i.e., nested stack automaton languages) is a full basic-AFL, properly containing the smallest full basic-AFL. The latter is generated by the ultrabasic macro grammars and accepted by the nested stack automata with bounded depth of nesting (and properly contains the stack languages, the ETOL languages, i.e., the smallest full hyper-AFL, and the basic macro languages). The full basic-AFLs are characterized by bounded nested stack controlled machines

Tree transducers, L systems, and two-way machines

A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results

Theoretische Informatica

Deze notitie beschrijft in het kort wat theoretische informatica is en hoe dit door de groep Theoretische Invormatica van de Universiteit Twente wordt bedreven in onderwijs en onderzoek

Engi maðr skapar sik sjálfr: Individual agency and the communal creation of outsiders in Íslendingasögur outlaw narratives

This thesis examines how Íslendingasögur out¬law narratives engage with socio-political concepts of community and the individual. It demonstrates that the sagas discussed share key anxieties over the deep structural problems in society, which are shown to restrict the individual agency of their protagonists, a restriction that motivates the transgressive behaviour of these individuals. The thesis suggests that these texts force their audiences to consider how each of their protagonists, despite his desire to live on his own terms, has his life and fate primarily defined—or indeed created—by the other members of his community. The introductory chapter details important trends in literary-critical scholarship about Íslendingasögur outlaw narratives, particularly trends that have caused problems for analysis of the texts’ socio-political dimensions. Chapter two reviews the usefulness of interpreting Gísli Súrsson as a primarily anachronistic figure within his contemporary society; it argues that such an interpretation overly downplays how the society of Gísla saga is shown to be defined by conflicting systems of communal expectation, which underlie Gísli’s approach to vengeance. Chapter three discusses how Grettis saga shows that various social constructs, including outlawry, are used reductively by Grettir’s society to frame him as a figure of Otherness; it demonstrates that the text implies that society’s use of these constructs to create outsiders is a fundamentally problematic method for dealing with difficult individuals. Chapter four demonstrates how Harðar saga juxtaposes the extra-legal Hólmverjar with normative Icelandic society in order to highlight fundamental structural problems that affect both communities in their capacity to provide stable environments for their individual members. Chapter five discusses Fóstbrœðra saga’s treatment of sworn-brotherhood as a symbolically extra-legal community; it also shows how Þormóðr uses his status as an outsider to subvert familiar notions of normativity and Otherness, thereby gaining advantages in his dealings with society

The word problem and combinatorial methods for groups and semigroups

The subject matter of this thesis is combinatorial semigroup theory. It includes material, in no particular order, from combinatorial and geometric group theory, formal language theory, theoretical computer science, the history of mathematics, formal logic, model theory, graph theory, and decidability theory. In Chapter 1, we will give an overview of the mathematical background required to state the results of the remaining chapters. The only originality therein lies in the exposition of special monoids presented in §1.3, which uni.es the approaches by several authors. In Chapter 2, we introduce some general algebraic and language-theoretic constructions which will be useful in subsequent chapters. As a corollary of these general methods, we recover and generalise a recent result by Brough, Cain & Pfei.er that the class of monoids with context-free word problem is closed under taking free products. In Chapter 3, we study language-theoretic and algebraic properties of special monoids, and completely classify this theory in terms of the group of units. As a result, we generalise the Muller-Schupp theorem to special monoids, and answer a question posed by Zhang in 1992. In Chapter 4, we give a similar treatment to weakly compressible monoids, and characterise their language-theoretic properties. As a corollary, we deduce many new results for one-relation monoids, including solving the rational subset membership problem for many such monoids. We also prove, among many other results, that it is decidable whether a one-relation monoid containing a non-trivial idempotent has context-free word problem. In Chapter 5, we study context-free graphs, and connect the algebraic theory of special monoids with the geometric behaviour of their Cayley graphs. This generalises the geometric aspects of the Muller-Schupp theorem for groups to special monoids. We study the growth rate of special monoids, and prove that a special monoid of intermediate growth is a group

Distribution and characterization of bacterial communities in diverse Antarctic ecosystems by high-troughput sequencing

Geological events and historical climate changes have eliminated or reduced most life in Antarctica to mainly microbial organisms in relatively simple communities. Due to its exceptional location, millennia long isolations and extreme climatic conditions, the continent offers a spectacular and unique background for fundamental scientific research and the testing of hypotheses. Notwithstanding the fact that Antarctica is still considered by many to be one of the last pristine environments on Earth, it is not only threatened by climate change, which particularly has severe effects on parts of West and Maritime Antarctica, but also by an ever increasing number of tourists and even scientists themselves. Studies on Antarctic biota are relatively scarce, and despite the fact that bacteria are fundamental to the Antarctic ecosystems, only a minority of the studies focus on these organisms. This results in a lacuna in the knowledge about the diversity, distribution and functioning of and the relationships between these organisms under the extreme Antarctic conditions. The recent advent of High-throughput sequencing (HTS) applications enables to sequence millions of DNA-fragments in a very short time, allowing us to visualise bacterial communities at a very high resolution, without the necessity for prior isolation of the organisms. In this PhD-study, we have applied some of these new technologies in order to investigate the bacterial diversity of different habitats throughout the Antarctic. In a first study (Chapter 2), we have compared the results obtained by pyrosequencing and compared these with the results of a previous isolation campaign. As expected, a much larger diversity of bacteria were found with pyrosequencing. While five bacterial phyla were recovered by cultivation, this was the case for 22 phyla with the NGS-approach, and a large amount of unknown diversity was evident. At the same time, it became clear that also the part of the 16S rRNA gene that was sequenced had an impact on the perceived diversity, with the V1-V2 fragments resulting in ~50% more OTUs than the V3-V2 fragments and only a limited amount of overlap in the genera recovered was noticed. In contrast, more chimeric sequences were identified in the V3-V2 amplicons. Notwithstanding the fact that pyrosequencing yielded a higher diversity, there was very little overlap with the cultivation approach, with only about 4 % of the OTUs recovered by cultivation found with pyrosequencing. In contrast, we also noticed that some singleton pyrosequencing OTUs where easily grown on growth media, and hence were not errors in the pyrosequencing data. This study thus showed that several factors could have a large impact on the perceived diversity, and that complementary techniques are necessary to discover the total bacterial diversity. In a second study (Chapter 3), we have examined the effects of both different bedrock types (granite and gneiss) and the presence of macrobiota (mosses, lichens and algae) on the composition of bacterial communities in high-altitude inland soils of different regions if the western Sør Rondane Mountains (Queen Maud Land, East Antarctica), near the Belgian Princess Elisabeth research station. We have used the at present most used HTS-platform, Illumina’s MiSeq, which allows sequencing longer gene fragments and yields more sequences compared to pyrosequencing. We combined this with the ARISA genetic fingerprinting technique. We demonstrated that organic carbon was the most significant parameter in structuring bacterial communities, followed by pH, electric conductivity, bedrock type and moisture content, while spatial distance was of less importance. Diversity showed a positive correlation with moisture content. Acidobacteria and Actinobacteria dominated dry gneiss derived mineral soils, while Proteobacteria, Cyanobacteria, Armatimonadetes and candidate phylum FBP were dominant in samples with a high organic carbon content. A large part of the unexplained variation is probably caused by the absence of data about important nutrients in our dataset (nitrogen and phosphorous), together with microclimatic and topographic differences between sample locations, and noise and stochasticity. In a last study we again used the Illumina MiSeq platform to perform a pan-continental charting of benthic and littoral microbial mats. In total, 138 samples from lakes in eight Antarctic regions and two Sub-Antarctic islands were analysed. We found a significant trend of increasing biodiversity with decreasing latitude from 85° to 54° S, although this than again decreased until 45° S. The mean annual temperature appeared to have a highly significant effect on community structure between Sub-Antarctica and Antarctica, while, besides the geographical distance, electric conductivity, and to a lesser extent pH, was important in explaining differences between samples on the Antarctic continent. In this study, too, a very high unknown diversity was observed. Particularly Cyanobacteria and Alphaproteobacteria dominated freshwater microbial mats, while Bacteroidetes and the alphaproteobacterial Rhodobacteraceae family dominated saline lakes. The Sub-Antarctic Marion Island was highly deviant with very low species richness, dominated by Janthinobacterium (Betaproteobacteria). In conclusion this thesis supports the hypothesis that for Bacteria in the Antarctic Region, too, distinct biogeographic patterns exist and that the environment exerts large selective pressures on community structure and composition, complemented by biotic factors. There is a high amount of heterogeneity at both local and continental scale due to both spatial distance and local differences in environmental variables such as electric conductivity, pH, moisture content, organic carbon and microclimate. Although we only were able sample a fraction of the continent, it is expected that similar patterns hold across the entire continent. However, additional sampling and in depth (metagenomics) sequencing linked to extensive environmental data, combined with phylogenetic analysis is needed to resolve important questions such as within and inter-continental dispersal, functioning and correlation of observed patterns to environmental data