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

The Quantitative Structure of Exponential Time

Department of Computer Science Iowa State University Ames, Iowa 50010 Recent results on the internal, measure-theoretic structure of the exponential time complexity classes linear polynomial E = DTIME(2 ) and E = DTIME(2 ) 2 are surveyed. The measure structure of these classes is seen to interact in informative ways with bi-immunity, complexity cores, polynomial-time many-one reducibility, circuit-size complexity, Kolmogorov complexity, and the density of hard languages. Possible implications for the structure of NP are also discussed

A Note on genericity and bi-immunity

Generic sets have all properties (from among a suitably chosen class) that can be enforced by finite extension arguments. In particular, p-generic set are known to be P-bi-immune. We try to clarify the precise relationship between genericity and bi-immunity by proposing an extended notion of bi-immunity that exactly characterizes the p-generic setsPostprint (published version

A Note on genericity and bi-immunity

Generic sets have all properties (from among a suitably chosen class) that can be enforced by finite extension arguments. In particular, p-generic set are known to be P-bi-immune. We try to clarify the precise relationship between genericity and bi-immunity by proposing an extended notion of bi-immunity that exactly characterizes the p-generic set

A Note on genericity and bi-immunity

Generic sets have all properties (from among a suitably chosen class) that can be enforced by finite extension arguments. In particular, p-generic set are known to be P-bi-immune. We try to clarify the precise relationship between genericity and bi-immunity by proposing an extended notion of bi-immunity that exactly characterizes the p-generic set

A Note on Genericity and Bi-Immunity

Generic sets have all properties (from among a suitably chosen class) that can be enforced by finite extension arguments. In particular, p-generic sets are known to be P-bi-immune. We try to clarify the precise relationship between genericity and bi-immunity by proposing an extended notion of bi-immunity that exactly characterizes the p-generic sets. 1 Introduction and definitions The notion of genericity is playing a central role in several research areas of Structural Complexity. Many open problems relating relativization did only yield to genericity as a tool. There are many specific forms of genericity. We focus here on n c -generic sets, introduced in [1] and [2], which can be shown to exist in the class E corresponding to deterministic exponential time. Such n c -generic sets are, intuitively, those that enjoy all n c -decidable properties that can be enforced by finite extension arguments. We give some additional explanation of this; in the following all sets are subsets..