On the Gap-Complexity of Simple RL-Automata

Analysis by reduction is a method used in linguistics for checking the correctness of sentences of natural languages. This method is modelled by restarting automata. All types of restarting automata considered in the literature up to now accept at least the deterministic context-free languages. Here we introduce and study a new type of restarting automaton, the so-called t-RL-automaton, which is an RL-automaton that is rather restricted in that it has a window of size one only, and that it works under a minimal acceptance condition. On the other hand, it is allowed to perform up to t rewrite (that is, delete) steps per cycle. Here we study the gap-complexity of these automata. The membership problem for a language that is accepted by a t-RL-automaton with a bounded number of gaps can be solved in polynomial time. On the other hand, t-RL-automata with an unbounded number of gaps accept NP-complete languages.

On the Descriptional Complexity of Simple RL-Automata

Analysis by reduction is a method used in linguistics for checking the correctness of sentences of natural languages. This method is modelled by restarting automata. Here we study a new type of restarting automaton, the so-called t-sRL-automaton, which is an RL-automaton that is rather restricted in that it has a window of size 1 only, and that it works under a minimal acceptance condition. On the other hand, it is allowed to perform up to t rewrite (that is, delete) steps per cycle. We focus on the descriptional complexity of these automata, establishing two complexity measures that are both based on the description of t-sRL-automata in terms of so-called meta-instructions. We present some hierarchy results as well as a non-recursive trade-off between deterministic 2-sRL-automata and finite-state acceptors.

Institutions, Behavior and Evolution

The three articles constituting this thesis are for reasons of content or method related to the following three fields in economics: Behavioral Economics, Evolutionary Game Theory and Formal Institutional Economics. A core element of these fields is the concept of individual preferences. Preferences are of central importance for the conceptional framework to analyze human behavior. They form the foundation for the theory of rational choice which is defined by the determination of the choice set and the selection of the most preferred alternative according to some consistency requirements. The theory of rational choice is based on a very simplified description of the problem of choice (object function and constraints). However, that choices depend on many more factors is for instance propagated by psychological theories and is supported by many empirical and experimental studies. This thesis adds to a better understanding of individual behavior to the extent that the evolution of certain characteristics of preferences and their consequences on human behavior forms the overarching theme of the dissertation. The long-term effect of evolutionary forces on a particular characteristic of importance in the theoretical, empirical and experimental economic literature, the concept of inequality aversion, is subject of the article “The evolution of inequality aversion in a simplified game of life” (Chapter 4). The contribution of the article is the overcoming of a restriction of former approaches to analyze the evolution of preferences in very simple environments. By classifying human interaction into three central economic games, the article provides a first step towards a simplified and sufficiently complete description of the interaction environment. Within such an environment the article characterizes the evolutionary stable preference distribution. One result shows, that the interaction of the aforementioned three classes can stabilize a preference of inequality aversion in the subpopulation which is favored in the problem of redistribution. The two remaining articles are concerned with social norms, which dissemination is determined by medium-run forces of cultural evolution. The article “The impact of market innovations on the evolution of social norms: the sustainability case.“ (Chapter 2) studies the interrelation between product innovations which are relevant from a sustainability perspective and an according social norm in consumption. This relation is based on a conformity bias in consumption and the attempt to avoid cognitive dissonances resulting from non-compliant consumption. Among others, it is shown that a conformity bias on the consumption side can lead to multiple equilibria on the side of norm adoption. The article “Evolution of cooperation in social dilemmas: signaling internalized norms.” (Chapter 3) studies the emergence of cooperation in social dilemmas based on the signaling of social norms. The article provides a potential explanation of cooperative behavior, which does not rely on the assumption of structured populations or on the unmotivated ability of social norms to restrict individual actions or strategy spaces. A comprehensive result of the single articles is the explanation of the phenomenon of partial norm adaption or dissemination of preferences. The plurality of the applied approaches with respect to the proximity to the rational choice approach and regarding the underlying evolutionary mechanics is a particular strength of the thesis. It shows the equality of these approaches in their potential to explain the phenomenon of cooperation in environments that provide material incentives for defective behavior. This also points to the need of a unified framework considering the biological and cultural coevolution of preference patterns.

A simple retroelement based knock-down system in Dictyostelium

Characteristics of DIRS-1 Mediated Knock-Downs __ We have previously shown that the most abundant Dictyostelium discoideum retroelement DIRS-1 is suppressed by RNAi mechanisms. Here we provide evidence that both inverted terminal repeats have strong promoter activity and that bidirectional expression apparently generates a substrate for Dicer. A cassette containing the inverted terminal repeats and a fragment of a gene of interest was sufficient to activate the RNAi response, resulting in the generation of ~21 nt siRNAs, a reduction of mRNA and protein expression of the respective endogene. Surprisingly, no transitivity was observed on the endogene. This was in contrast to previous observations, where endogenous siRNAs caused spreading on an artificial transgene. Knock-down was successful on seven target genes that we examined. In three cases a phenotypic analysis proved the efficiency of the approach. One of the target genes was apparently essential because no knock-out could be obtained; the RNAi mediated knock-down, however, resulted in a very slow growing culture indicating a still viable reduction of gene expression.