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

On the existence of complete disjoint NP-pairs

Disjoint NP-pairs are an interesting model of computation with important applications in cryptography and proof complexity. The question whether there exists a complete disjoint NP-pair was posed by Razborov in 1994 and is one of the most important problems in the field. In this paper we prove that there exists a many-one hard disjoint NP-pair which is computed with access to a very weak oracle (a tally NP-oracle). In addition, we exhibit candidates for complete NP-pairs and apply our results to a recent line of research on the construction of hard tautologies from pseudorandom generators

Immunity and Pseudorandomness of Context-Free Languages

We discuss the computational complexity of context-free languages, concentrating on two well-known structural properties---immunity and pseudorandomness. An infinite language is REG-immune (resp., CFL-immune) if it contains no infinite subset that is a regular (resp., context-free) language. We prove that (i) there is a context-free REG-immune language outside REG/n and (ii) there is a REG-bi-immune language that can be computed deterministically using logarithmic space. We also show that (iii) there is a CFL-simple set, where a CFL-simple language is an infinite context-free language whose complement is CFL-immune. Similar to the REG-immunity, a REG-primeimmune language has no polynomially dense subsets that are also regular. We further prove that (iv) there is a context-free language that is REG/n-bi-primeimmune. Concerning pseudorandomness of context-free languages, we show that (v) CFL contains REG/n-pseudorandom languages. Finally, we prove that (vi) against REG/n, there exists an almost 1-1 pseudorandom generator computable in nondeterministic pushdown automata equipped with a write-only output tape and (vii) against REG, there is no almost 1-1 weakly pseudorandom generator computable deterministically in linear time by a single-tape Turing machine.Comment: A4, 23 pages, 10 pt. A complete revision of the initial version that was posted in February 200

Levelable Sets and the Algebraic Structure of Parameterizations

Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing instead on the parameterizations that make a given set fixed-parameter tractable, we circumvent these difficulties. We isolate parameterizations as independent measures of complexity and study their underlying algebraic structure. Thus we are able to compare parameterizations, which establishes a hierarchy of complexity that is much stronger than that present in typical parameterized algorithms races. Among other results, we find that no practically fixed-parameter tractable sets have optimal parameterizations

Dynamics of adaptive immunity against phage in bacterial populations

The CRISPR (clustered regularly interspaced short palindromic repeats) mechanism allows bacteria to adaptively defend against phages by acquiring short genomic sequences (spacers) that target specific sequences in the viral genome. We propose a population dynamical model where immunity can be both acquired and lost. The model predicts regimes where bacterial and phage populations can co-exist, others where the populations exhibit damped oscillations, and still others where one population is driven to extinction. Our model considers two key parameters: (1) ease of acquisition and (2) spacer effectiveness in conferring immunity. Analytical calculations and numerical simulations show that if spacers differ mainly in ease of acquisition, or if the probability of acquiring them is sufficiently high, bacteria develop a diverse population of spacers. On the other hand, if spacers differ mainly in their effectiveness, their final distribution will be highly peaked, akin to a "winner-take-all" scenario, leading to a specialized spacer distribution. Bacteria can interpolate between these limiting behaviors by actively tuning their overall acquisition probability.Comment: 17 pages, 4 Figures and Supplementary Material

Sovereign debt, volatility, and insurance

External debt increases the vulnerability of indebted emerging market economies to macroeconomic volatility and financial crises. Capital account reversals often lead sovereign debt repayment crises that are only resolved after prolonged and difficult debt restructuring. Foreign indebtedness exacerbates domestic financial distress in crisis, increasing both the incidence and severity of emerging market crises. These outcomes contrast with the presumption that access to international capital markets should help countries to smooth domestic consumption and investment against macroeconomic shocks. This paper uses models of sovereign to reconsider the role of sovereign debt renegotiation for international risk sharing and presents an approach for analyzing contractual innovations for implementing contingent debt repayments. The financial innovations that might allow risk-sharing rather than risk-inducing capital flows go beyond contractual changes that ease debt renegotiation by separating contingent payments from bonds.Debts, External ; Financial crises ; Insurance

Sovereign Debt, Volatility and Insurance

External debt increases the vulnerability of indebted emerging market economies to macroeconomic volatility and financial crises. Capital account reversals often lead to sovereign debt repayment crises that are only resolved after prolonged and difficult debt restructuring. Foreign indebtedness exacerbates domestic financial distress in crisis, increasing both the incidence and severity of emerging market crises. These outcomes contrast with the presumption that access to international capital markets should help countries to smooth domestic consumption and investment against macroeconomic shocks. This paper uses models of sovereign to reconsider the role of sovereign debt renegotiation for international risk sharing and presents an approach for analyzing contractual innovations for implementing contingent debt repayments. The financial innovations that might allow risk-sharing rather than risk-inducing capital flows go beyond contractual changes that ease debt renegotiation by separating contingent payments from bonds.