48 research outputs found

    Finite-State Genericity : on the Diagonalization Strength of Finite Automata

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    Algorithmische Generizit¨atskonzepte spielen eine wichtige Rolle in der Berechenbarkeitsund Komplexit¨atstheorie. Diese Begriffe stehen in engem Zusammenhang mit grundlegenden Diagonalisierungstechniken, und sie wurden zur Erzielung starker Trennungen von Komplexit¨atsklassen verwendet. Da f¨ur jedes Generizit¨atskonzept die zugeh¨origen generischen Mengen eine co-magere Klasse bilden, ist die Analyse generischer Mengen ein wichtiges Hifsmittel f¨ur eine quantitative Analyse struktureller Ph¨anomene. Typischerweise werden Generizit¨atskonzepte mit Hilfe von Erweiterungsfunktionen definiert, wobei die St¨arke eines Konzepts von der Komplexit¨at der zugelassenen Erwiterungsfunktionen abh¨angt. Hierbei erweisen sich die sog. schwachen Generizit¨atskonzepte, bei denen nur totale Erweiterungsfunktionen ber¨ucksichtigt werden, meist als wesentlich schw¨acher als die vergleichbaren allgemeinen Konzepte, bei denen auch partielle Funktionen zugelassen sind. Weiter sind die sog. beschr¨ankten Generizit¨atskonzepte – basierend auf Erweiterungen konstanter L¨ange – besonders interessant, da hier die Klassen der zugeh¨origen generischen Mengen nicht nur co-mager sind sondern zus¨atzlich Maß 1 haben. Generische Mengen diesen Typs sind daher typisch sowohl im topologischen wie im maßtheoretischen Sinn. In dieser Dissertation initiieren wir die Untersuchung von Generizit¨at im Bereich der Theorie der Formalen Sprachen: Wir f¨uhren finite-state-Generizit¨atskonzepte ein und verwenden diese, um die Diagonalisierungsst¨arke endlicher Automaten zu erforschen. Wir konzentrieren uns hierbei auf die beschr¨ankte finite-state-Generizit¨at und Spezialf ¨alle hiervon, die wir durch die Beschr¨ankung auf totale Erweiterungsfunktionen bzw. auf Erweiterungen konstanter L¨ange erhalten. Wir geben eine rein kombinatorische Charakterisierung der beschr¨ankt finite-state-generischen Mengen: Diese sind gerade die Mengen, deren charakteristische Folge saturiert ist, d.h. jedes Bin¨arwort als Teilwort enth¨alt. Mit Hilfe dieser Charakterisierung bestimmen wir die Komplexit¨at der beschr¨ankt finitestate- generischen Mengen und zeigen, dass solch eine generische Menge nicht regul¨ar sein kann es aber kontext-freie Sprachen mit dieser Generizit¨atseigenschaft gibt. Die von uns betrachteten unbeschr¨ankten finite-state-Generizit¨atskonzepte basieren auf Moore-Funktionen und auf Verallgemeinerungen dieser Funktionen. Auch hier vergleichen wir die St¨arke der verschiedenen korrespondierenden Generizit¨atskonzepte und er¨ortern die Frage, inwieweit diese Konzepte m¨achtiger als die beschr¨ankte finite-state-Generizit ¨at sind. Unsere Untersuchungen der finite-state-Generizit¨at beruhen zum Teil auf neuen Ergebnissen ¨uber Bi-Immunit¨at in der Chomsky-Hierarchie, einer neuen Chomsky-Hierarchie f¨ur unendliche Folgen und einer gr¨undlichen Untersuchung der saturierten Folgen. Diese Ergebnisse – die von unabh¨angigem Interesse sind – werden im ersten Teil der Dissertation vorgestellt. Sie k¨onnen unabh¨angig von dem Hauptteil der Arbeit gelesen werden

    The architecture and acuity of critical systems thinking

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    This thesis looks at two critical urges in Critical Systems Thinking that both complement and critique each other. Firstly, there is an urge to construct in a critical manner. Secondly, there is an urge to be critical about such constructions. They complement and critique each other in the manner in which the second urge requires the first urge in order to understand what it means when one begins to create by construction, and also in which the first urge requires the second in order to understand the privileged position that construction is given in epistemology. These two urges give two stages.Construction relates to four clear conditions that develop from an Architectural study. This study offers two definitions of Architecture : structural longevity and relational modification. Consequently, a Structure and Process are established (first two stages) which together content an Architecture of Critical Systems Thinking (third stage). This Architecture is then applied to Systems Thinking through a study of five Systems Thinkers, this application offers an Architecture as commensurability (fourth stage). The Architecture is thereby offered as author.De-construction relates to four clear conditions that develop from the Architecture of Critical Systems Thinking. Each condition questions the Architectural authority to construct. The Process (reversed to complement and critique) questions the Structural consistency of the Architecture (first). A Structure of Acuity develops that maintains meaning where the Architecture neutralised meaning (second). A Contentless Acuity follows (third), thereby allowing the contentlessness of paradigm (in)commensurability to be discussed as an application of the Acuity of Critical Systems Thinking. The Acuity is thereby offered as reader.To balance these two urges is to read with authority

    Acta Cybernetica : Volume 18. Number 1.

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    Metaphors of travel and writing: deconstruction of the "at-home" and the promise of the other

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    The purpose of the thesis is to consider travel relations with regard to their onto-phenomenological and semantic of possibility and to raise the question of a possible ethics of travel. In turning the notion of travel back upon its signifying conditions, a connection is established with the notion of metaphor. The metaphysical polarity between proper and metaphorical meaning is furthered onto a problematic of the couple Oikos (house, home in Greek and generally everything that constitutes a sense of the-at-home) and travel with the purpose of complicating their mutual determination and to deconstructively challenge the derivational and recuperative logic that permeates their intra-metaphysical designation. The reconsideration of the conceptual presuppositions of “travel” is carried out through the critique of what is called its hermeneutic premise, formulated here largely drawing on Paul Ricoeur. It is maintained that “travel” in its Western European conceputalisation participates in the traditions of the metaphysics if presence and logocentrism and it is on this level that deconstructive thinking takes effect. Questions related to the theme of travel, such as space, time, boundary, itinerary, event, encounter, as well as to travel writing, such as generic delimination, representation, constative reference and performative engagement, testimonial value, and the antinomy of fact and fiction, are addressed and relocated through the preoccupation with their phenomenological and tropological motifs and in particular with their generalised metaphorical and allegorical conditions, as these are designated by Jacques Derrida and Paul de Man, respectively. The association of the notion of travel with metaphor, and, by extension, that between Oikos and properness, will show that senses of home and away, rather than being pregiven, emerge from a scriptural condition - a structural of difference and deferral- that interrupts their reductive, totalising, monistic formulations as well as dialectical conceptualisations

    The deep extent of mental autonomy

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    The central aim of this thesis is to argue that the autonomous nature of mentalistic explanation presents a stronger constraint on what counts as a satisfactory statement of the relation between the mental and the physical than can be acknowledged within the metaphysical framework of non-reductive physicalism. Although the chief merit of non-reductive physicalism appears to be its ability to respect the irreducibility of mental concepts to physical concepts, whilst respecting the primacy of the physical ontology, I claim that its commitment to the principles of physicalism prevents that framework from being able to accommodate what I will refer to as the deeper extent of the autonomous nature of mentalistic explanation. The deeper extent of the autonomous nature of mentalistic explanation manifests itself in the fact that the work carried out by mentalistic explanations is completely separate from the work carried out by physicalistic explanations. I claim that the deeper extent of the autonomous nature of mentalistic explanation cannot be recognised within a metaphysical framework which claims to recognise the primacy of the physical ontology because recopsing deep autonomy requires giving up the assumption that the mental must be related to the physical in the manner appropriate to discharging such metaphysical principles. I defend the claim that we can recognise the deeper extent of the autonomous nature of mentalistic explanation if we take our successful explanatory practices as the starting point of our investigation, and only then revert to the question of how best to articulate the relation between the mental and the physical. My claim is that there is an intrinsic connection between the nature of the mental and the nature of human relationships, and I therefore suggest that the autonomous nature of mentalistic explanation ought to be understood in connection with the autonomous nature of human relationships. The basic ideas in this thesis are derived by combining features of Wittgenstein’s rule following considerations with features of John MacMurray’s approach to human relationships. On the basis of this combination, I argue for the more specific claim that there is an intrinsic connection between what it means to say that an individual has the capacity to think and what it means to say that he has the capacity to be involved in various types of human relationships. This connection is then used to develop a non-causal account of human action to challenge the physicalist ’s causal account, which will be used to support the claim that mentalistic explanations are autonomous with respect to physicalistic explanations in the deeper sense. I conclude by arguing that the considerations which put us in position to recognise the deeper extent of the autonomous nature of mentalistic explanation ought to constrain our statement of the relation between the mental and the physical, and I suggest that this statement should be consistent with the way in which mentalistic and physicalistic explanations carry out their work in our explanatory practices. I claim that individuals are subject to mentalistic explanations in so far as they have a life to live in the world with other people, and that individuals are subject to physicalistic explanations in so far as human beings are creatures whose life has a natural biological dimension. But rather than identifying the mental with the physical, and thereby compromise the deeper extent of the autonomous nature of mentalistic explanation, I suggest that this relation might be understood in terms of the fact that the mental is embedded in the dimension of human life which is constituted by the involvement of individuals in various types of relationshps with each other, and that the dimension of human life in which physicalistic explanations are operative is presupposed as the causal background which must be in place if individuals are to have such a life to live in the world

    Part I:

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