Computability

About: Computability is a research topic. Over the lifetime, 2829 publications have been published within this topic receiving 85162 citations.

Computability of følner sets

Abstract: We define the notion of computability of Folner sets for finitely generated amenable groups. We prove, by an explicit description, that the Kharlampovich groups, finitely presented solvable groups with unsolvable Word Problem, have computable Folner sets. We also prove computability of Folner sets for extensions — with subrecursive distortion functions — of amenable groups with solvable Word Problem by finitely generated groups with computable Folner sets. Moreover, we obtain some known and some new upper bounds for the Folner function for these particular extensions.

Random Polynomial-Time Attacks and Dolev-Yao Models.

Abstract: For several decades two different communities have been working on the formal security of cryptographic protocols. Many efforts have been made recently to take benefit of both approaches, in brief: the comprehensiveness of computational models and the automatizability of formal methods. The purpose of this paper is to investigate an original approach to relate the two views, that is: to extend existing Dolev-Yao models to account for random polynomial-time (Las Vegas) computability. This is done first by noticing that Dolev-Yao models can be seen as transition systems, possibly infinite. We then extend these transition systems with computation times and probabilities. The extended models can account for normal Dolev-Yao transitions as well as nonstandard operations such as inverting a one-way function. Our main contribution consists of showing that under sufficient realistic assumptions the extended models are equivalent to standard Dolev-Yao models as far as security is concerned. Thus our work enlarges the scope of existing decision procedures.

Weihrauch-completeness for layerwise computability

Abstract: We introduce the notion of being Weihrauch-complete for layerwise computability and provide several natural examples related to complex oscillations, the law of the iterated logarithm and Birkhoff's theorem. We also consider hitting time operators, which share the Weihrauch degree of the former examples but fail to be layerwise computable.

Chapter 13 - The Structure of Computability in Analysis and Physical Theory: An Extension of Church's Thesis

Abstract: This chapter presents a survey of computability in analysis and physical theory. The notion of a computability structure on a Banach space is of central importance in this chapter. It accords well with the intuitive notion of computability. The definition is given in the chapter axiomatically. The axioms provide for the interaction of elementary recursion theory with the basic tenets of Banach space theory. The concept that is axiomatized is “computable sequence of elements” of the Banach space. The computability structure is characterized by three axioms. This is not surprising because the Banach space itself is defined by three properties. It is a linear space with a norm, which is complete in the norm. Under general conditions, which in practice are always satisfied, the computability structure on a Banach space is unique.