# Volume 1, Issue 3

2005

### 1. Probabilistic Algorithmic Knowledge

The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the information provided by a randomized knowledge algorithm when its answers have some probability of being incorrect. We formalize this information in terms of evidence; a randomized knowledge algorithm returning Yes'' to a query about a fact \phi provides evidence for \phi being true. Finally, we discuss the extent to which this evidence can be used as a basis for decisions.

### 2. Security Policies as Membranes in Systems for Global Computing

We propose a simple global computing framework, whose main concern is code migration. Systems are structured in sites, and each site is divided into two parts: a computing body, and a membrane, which regulates the interactions between the computing body and the external environment. More precisely, membranes are filters which control access to the associated site, and they also rely on the well-established notion of trust between sites. We develop a basic theory to express and enforce security policies via membranes. Initially, these only control the actions incoming agents intend to perform locally. We then adapt the basic theory to encompass more sophisticated policies, where the number of actions an agent wants to perform, and also their order, are considered.

### 3. Almost periodic functions, constructively

The almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr's fundamental theorem for almost periodic functions which we then generalize to almost periodic functions on general topological groups.

### 4. Modularizing the Elimination of r=0 in Kleene Algebra

Given a universal Horn formula of Kleene algebra with hypotheses of the form r = 0, it is already known that we can efficiently construct an equation which is valid if and only if the Horn formula is valid. This is an example of <i>elimination of hypotheses</i>, which is useful because the equational theory of Kleene algebra is decidable while the universal Horn theory is not. We show that hypotheses of the form r = 0 can still be eliminated in the presence of other hypotheses. This lets us extend any technique for eliminating hypotheses to include hypotheses of the form r = 0.