Analyzing the effective content of the Lebesgue density theorem played a crucial role in some recent developments in algorithmic randomness, namely, the solutions of the ML-covering and ML-cupping problems. Two new classes of reals emerged from this inquiry: the positive density points with respect to effectively closed (or Π1) sets of reals, and a proper subclass, the density-one points. Bienv...

In this article, a program block without halting instructions is called NoStopCode program block. If a program consists of two blocks, where the first block is parahalting (i.e. halt for all states) and No-StopCode, and the second block is parahalting and shiftable, it can be computed by combining the computation results of the two blocks. For a program which consists of a instruction and a blo...

The problem of diffraction by an elastic wedge has a significant history. A rather detailed survey was presented in [1], so we shall restrict ourselves to a short commentary. Up to the mid 1990s, most of the authors had been interested in the computational aspects of the problem, leaving the question of rigorous formulation aside (we mean the existence and uniqueness theorems). In the mid 1990s...

Most real world environments are non-deterministic. Automatic plan formation in non-deterministic dommns is, however, still an open problem. In this paper we present a practical algorithm for the automatic generation of solutions to planning problems in nondeterministic domains. Our approach has the following main features. First, the planner generates Universal Plans. Second, it generates plan...

This chapter is concerned with sound and complete algorithms for testing satisfiability, i.e., algorithms that are guaranteed to terminate with a correct decision on the satisfiability/unsatisfiability of the given CNF. One can distinguish between a few approaches on which complete satisfiability algorithms have been based. The first approach is based on existential quantification, where one su...

We describe a resource bounding technique called the Flow Balance Constraint (FBC) to tightly bound the amount of available resource for a set of partially ordered events with piecewise constant resource impact. We provide an efficient algorithm for calculating FBC and bound its complexity. We compare this technique with two existing resource bounding techniques, the Balance Constraint (BC) due...

Semi-hyperhypersimple c.e. sets, also known as diagonals, were introduced by Kummer. He showed that by considering an analogue of hyperhypersimplicity, one could characterize the sets which are the Halting problem relative to arbitrary computable numberings. One could also consider half of splittings of maximal or hyperhypersimple sets and get another variant of maximality and hyperhypersimplic...

In Dhar’s model of abelian distributed processors, finite automata occupy the vertices of a graph and communicate via the edges. A local commutativity condition ensures that the output of such a network does not depend on the order in which the automata process their inputs. In this paper (the first of a series) we consider the halting problem for such networks and the crticial group, an invari...

We prove a number of results in effective randomness, using methods in which Π1 classes play an essential role. Amongst many others, the results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.

We propose here a new approach for video sequence interpretation based on declarative models of activities. The aim of the video sequence interpretation is to recognize incrementaly certain situations, like states of the scene, events and scenarios, in a video stream, in order to understand what happens in the scene. The input of the activity recognition is an a priori model of the scene and hu...