Structural and Computational Existence Results for Multidimensional Subshifts

Symbolic dynamics is a branch of mathematics that studies the structure of infinite sequences of symbols, or in the multidimensional case, infinite grids of symbols. Classes of such sequences and grids defined by collections of forbidden patterns are called subshifts, and subshifts of finite type are defined by finitely many forbidden patterns. The simplest examples of multidimensional subshifts are sets of Wang tilings, infinite arrangements of square tiles with colored edges, where adjacent edges must have the same color. Multidimensional symbolic dynamics has strong connections to computability theory, since most of the basic properties of subshifts cannot be recognized by computer programs, but are instead characterized by some higher-level notion of computability. This dissertation focuses on the structure of multidimensional subshifts, and the ways in which it relates to their computational properties. In the first part, we study the subpattern posets and Cantor-Bendixson ranks of countable subshifts of finite type, which can be seen as measures of their structural complexity. We show, by explicitly constructing subshifts with the desired properties, that both notions are essentially restricted only by computability conditions. In the second part of the dissertation, we study different methods of defining (classes of ) multidimensional subshifts, and how they relate to each other and existing methods. We present definitions that use monadic second-order logic, a more restricted kind of logical quantification called quantifier extension, and multi-headed finite state machines. Two of the definitions give rise to hierarchies of subshift classes, which are a priori infinite, but which we show to collapse into finitely many levels. The quantifier extension provides insight to the somewhat mysterious class of multidimensional sofic subshifts, since we prove a characterization for the class of subshifts that can extend a sofic subshift into a nonsofic one.

Investigating the Existence of Business-IT Alignment Trap in Finnish IT Organizations

The overall purpose of this master's thesis is to investigate the existence of business-IT alignment trap in Finnish IT organizations. The alignment trap refers to the inability of IT investments to deliver the expected business benefits. The basis for this investigation is due to the previous knowledge that high level of IT alignment practice with very low efficacy in an organization can lead to alignment trap. The theory which was established on the dimensions of IT-alignment and efficacy of IT as a whole with considerations for cost reduction and revenue growth benefits. This study explored the same dimensions with the previous study but identified additional benefit (profitability). The study was conducted using the Finnish IT barometer data from different IT organizations. A quantitative research method was used in conducting this study which was built on positivist philosophical stance. The empirical data is based on survey data, an excerpt from the Finnish IT barometer data that captured the annual survey results of IT significance to Finnish organizations as evaluated by business and IT professionals. The survey data comprised of 249 respondents and their responses were categorized into high and low IT intensive which form the basis of the statistical analysis conducted. Overall, five analyses were conducted using the variables of cost reductions, revenue growth and profitability in the 2x2 matrix dimensions of IT alignment and efficacy of IT, grouped into alignment trap, maintenance zone, well-oiled IT and IT-enabled growth. The empirical results, revealed a partial existence of alignment trap in Finnish IT organizations. This is due to a very minute number of organizations that were ensnared in the alignment trap zone on the analyses conducted. Although they recorded considerable high performances in terms of revenue growth rate with IT spending below the average companies, their profitability was considered very low. Generally it was observed that Finnish IT organizations with high efficacy of IT practices had good performances, while those with low efficacy of IT experienced low performances, especially in the aspect of profitability, regardless of the degree of IT alignment. The study proposes that organizations should improve on practices that enhance effectiveness of IT more in order for them to realize the full benefits of IT and to avoid alignment trap.