The pure untyped Lambda Calculus augmented with an (erratic) choice operator is considered as an idealised non-deterministic functional language. Both the \may" and the \must" modalities of convergence are of interest to us. Following Abramsky's work on domain theory in logical form, we identify the deno-tational type that captures our computational situation: = P ! ] ? ] where P?] is the Plotk...

We test Lüth and Ghani’s proposal [11, 12, 13] to use coproducts of monads as a basis for modularity by applying their ideas to Varacca’s work [20] on combining non-determinism and probabilistic choice. In particular, we discuss i) the coproduct of non-determinism and probabilistic choice; ii) how monad compositions based upon distributivity possess a universal property; and iii) Capretta’s [4]...

In this paper, we show that the non-deterministic choice “+”, which was proposed as a primitive operator in Synchronization Tree Logic (STL for short) can be defined essentially by conjunction and disjunction in the μ-calculus (μM for short). This is obtained by extending the μcalculus with the non-deterministic choice “+” (denoted by μM) and then showing that μM can be translated into μM. Furt...

In this paper we attempt to shed light on the concept of an agent’s knowledge after a non-deterministic action is executed. We start by making a comparison between notions of non-deterministic choice, and between notions of sequential composition, of settings with dynamic and/or epistemic character; namely Propositional Dynamic Logic (PDL), Dynamic Epistemic Logic (DEL), and the more recent log...

1 The dynamics of quasicrystals, the dynamics of Kähler action, symbolic dynamics, and the dynamics of self-organization 1 1.1 The non-determinism for the dynamics of quasicrystals contra non-determinism of Kähler action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The dynamics of quasicrystals as a model for fundamental dynamics or high level symbolic...

One of the unusual challenges faced by peer-to-peer algorithms as opposed to classical distributed algorithms is that these have to compute with data non-determinism where there is no guarantee that data from a particular node will be delivered in time or delivered at all. Each distributed component not only has to work in such environment, but also has to decide how long to wait for peers to r...

This paper is an extension of a previous work where two nondeterminism analyses were presented. One of them was efficient but not very powerful and the other one was more powerful but very expensive. Here, we develop an intermediate analysis in both aspects, efficiency and power. The improvement in efficiency is obtained by speeding up the fixpoint calculation by means of a widening operator, a...

Non-deterministic programs can represent specifications, and non-determinism arises naturally in concurrent programming languages. In this dissertation, λ-calculi exhibiting erratic nondeterminism are studied in order to identify definitions and techniques that may be applicable to higher-order programming languages for specification or concurrency. The non-deterministic λ-calculi arise as frag...

It has recently been shown that cut-free deep inference systems exhibit an exponential speed-up over cut-free sequent systems, in terms of proof size. While this is good for proof complexity, there remains the problem of typically high proof search non-determinism induced by the deep inference methodology: the higher the depth of inference, the higher the non-determinism. In this work we improv...