Search

We consider the individual points on a Martin-L��f random path of Brownian motion. We show (1) that Khintchine's law of the iterated logarithm holds at almost all points; and (2) there exist points (besides the trivial example of the origin) having effective dimension $, The conference version was published as: The law of the iterated logarithm for algorithmically random paths of Brownian motion, Logical Foundations of Computer Science, Lecture Notes in Computer Science 4514 (2007), 310--317

In this paper we discuss some of the challenges and approaches for providing safety assurance for modern weapon systems via software-based safety kernels. We argue that software-centric approaches for designing and verifying safety kernels are flawed. We claim that the design and verification of safety kernels for complex event-driven real-time systems is a matter of physics and dynamical system analysis of system design. We describe an approach for rapidly prototyping safety kernels (and plants and controllers) using an agent-based safety-kernel architecture. The approach utilizes multiagent modeling and hybrid automata.

Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define Polyteam Semantics in which formulae are evaluated over a family of teams. We begin by defining a novel polyteam variant of dependence atoms and give a finite axiomatization for the associated implication problem. We relate polyteam semantics to team semantics and investigate in which cases logics over the former can be simulated by logics over the latter. We also characterize the expressive power of poly-dependence logic by properties of polyteams that are downwards closed and definable in existential second-order logic ($\textsf{ESO}$). The analogous result is shown to hold for poly-independence logic and all $\textsf{ESO}$-definable properties. We also relate poly-inclusion logic to greatest fixed point logic.