Resource Bounded Immunity and Simplicity

Revisiting the thirty years-old notions of resource-bounded immunity and simplicity, we investigate the structural characteristics of various immunity notions: strong immunity, almost immunity, and hyperimmunity as well as their corresponding simplicity notions. We also study limited immunity and simplicity, called k-immunity and feasible k-immunity, and their simplicity notions. Finally, we propose the k-immune hypothesis as a working hypothesis that guarantees the existence of simple sets in NP.Comment: This is a complete version of the conference paper that appeared in the Proceedings of the 3rd IFIP International Conference on Theoretical Computer Science, Kluwer Academic Publishers, pp.81-95, Toulouse, France, August 23-26, 200

Immunity and Simplicity for Exact Counting and Other Counting Classes

Ko [RAIRO 24, 1990] and Bruschi [TCS 102, 1992] showed that in some relativized world, PSPACE (in fact, ParityP) contains a set that is immune to the polynomial hierarchy (PH). In this paper, we study and settle the question of (relativized) separations with immunity for PH and the counting classes PP, C_{=}P, and ParityP in all possible pairwise combinations. Our main result is that there is an oracle A relative to which C_{=}P contains a set that is immune to BPP^{ParityP}. In particular, this C_{=}P^A set is immune to PH^{A} and ParityP^{A}. Strengthening results of Tor\'{a}n [J.ACM 38, 1991] and Green [IPL 37, 1991], we also show that, in suitable relativizations, NP contains a C_{=}P-immune set, and ParityP contains a PP^{PH}-immune set. This implies the existence of a C_{=}P^{B}-simple set for some oracle B, which extends results of Balc\'{a}zar et al. [SIAM J.Comp. 14, 1985; RAIRO 22, 1988] and provides the first example of a simple set in a class not known to be contained in PH. Our proof technique requires a circuit lower bound for ``exact counting'' that is derived from Razborov's [Mat. Zametki 41, 1987] lower bound for majority.Comment: 20 page

Existence versus Exploitation: The Opacity of Backbones and Backdoors Under a Weak Assumption

Backdoors and backbones of Boolean formulas are hidden structural properties. A natural goal, already in part realized, is that solver algorithms seek to obtain substantially better performance by exploiting these structures. However, the present paper is not intended to improve the performance of SAT solvers, but rather is a cautionary paper. In particular, the theme of this paper is that there is a potential chasm between the existence of such structures in the Boolean formula and being able to effectively exploit them. This does not mean that these structures are not useful to solvers. It does mean that one must be very careful not to assume that it is computationally easy to go from the existence of a structure to being able to get one's hands on it and/or being able to exploit the structure. For example, in this paper we show that, under the assumption that P $\neq$ NP, there are easily recognizable families of Boolean formulas with strong backdoors that are easy to find, yet for which it is hard (in fact, NP-complete) to determine whether the formulas are satisfiable. We also show that, also under the assumption P $\neq$ NP, there are easily recognizable sets of Boolean formulas for which it is hard (in fact, NP-complete) to determine whether they have a large backbone

Emergence, Emergentism and Pragmatism

In this paper, I argue for the usefulness of pragmatism as a framework within which to develop the theological application of emergentist theory. I consider some philosophical issues relevant to the recent revival of interest, across various disciplines, in the concept of emergence and clarify some of the conceptual issues at stake in the attempts to formulate the philosophical position of emergentism and to apply it theologically. After highlighting some major problems arising from the main existing ways of formulating emergentism, I build on the work of Sami Pihlström, outlining a less problematic, alternative proposal. I attempt to show that the philosophical problems can be circumvented by an appeal to the pragmatist tradition, which is a useful philosophical framework within which to develop an emergentist theory fit for theological application

Complexity of certificates, heuristics, and counting types , with applications to cryptography and circuit theory

In dieser Habilitationsschrift werden Struktur und Eigenschaften von Komplexitätsklassen wie P und NP untersucht, vor allem im Hinblick auf: Zertifikatkomplexität, Einwegfunktionen, Heuristiken gegen NP-Vollständigkeit und Zählkomplexität. Zum letzten Punkt werden speziell untersucht: (a) die Komplexität von Zähleigenschaften von Schaltkreisen, (b) Separationen von Zählklassen mit Immunität und (c) die Komplexität des Zählens der Lösungen von ,,tally`` NP-Problemen

Empiricism and Philosophy

Though Quine's argument against the analytic-synthetic distinction is widely disputed, one of the major effects of his argument has been to popularise the belief that there is no sharp distinction between science and philosophy. This thesis begins by distinguishing reductive from holistic empiricism, showing why reductive empiricism is false, refuting the major objections to holistic empiricism and stating the limits on human knowledge it implies. Quine's arguments (and some arguments that have been mistakenly attributed to him) from holism against the analytic-synthetic are considered, and while many of them are found wanting one good argument is presented. Holism does not, however, imply that there is no sharp distinction between science and philosophy, and indeed implies that the distinction between scientific and philosophical disputes is perfectly sharp. The grounds upon which philosophical disputes may be resolved are then sought for and deliniated

Empiricism and Philosophy

Though Quine's argument against the analytic-synthetic distinction is widely disputed, one of the major effects of his argument has been to popularise the belief that there is no sharp distinction between science and philosophy. This thesis begins by distinguishing reductive from holistic empiricism, showing why reductive empiricism is false, refuting the major objections to holistic empiricism and stating the limits on human knowledge it implies. Quine's arguments (and some arguments that have been mistakenly attributed to him) from holism against the analytic-synthetic are considered, and while many of them are found wanting one good argument is presented. Holism does not, however, imply that there is no sharp distinction between science and philosophy, and indeed implies that the distinction between scientific and philosophical disputes is perfectly sharp. The grounds upon which philosophical disputes may be resolved are then sought for and deliniated

The Institution of Theory

Originally published in 1994. In The Institution of Theory, Murray Krieger examines, at once sympathetically and critically, the process by which theory has become institutionalized in the American academy and the consequences of theory as an academic institution. He traces the transformation of literary theory into critical theory and relates it to changes in the place of literature within questions about discourse at large. And he faces the costs as well as the gains of the recent denial of privilege to the literary. To support his view of the issues at stake in current theoretical debates, Krieger surveys both the history of American criticism and the general history of literary theory in the West. He sees divisions in each of them that foreshadow the current debates: in the first a conflict between the social and the aesthetic functions of literature, and in the second a conflict between the treatment of literature as a reflection of a culture's ideology and the treatment of literature as a subversion of that ideology. To what extent, he asks, are our debates new and to what extent are they merely refashioned versions of those we have always had