Indeterminacy in concurrent computation: Difference between revisions

Revision as of 23:38, 9 January 2016

Revision as of 08:23, 20 January 2016

Line 20:

What does the mathematical theory of Actors have to say about this? A ''closed'' system is defined to be one which does not communicate with the outside. [[Actor model theory]] provides the means to characterize all the possible computations of a closed Actor system using the Representation Theorem [Hewitt 2007] as follows:

<blockquote>

:The mathematical denotation denoted by a closed system {{mono|S}} is found by constructing increasingly better approximations from an initial behavior called {{mono|⊥_S}} using a behavior approximating function {{mono|'''progression'''_S}} to construct a denotation (meaning ) for {{mono|S}} as follows :

::<math>\mathbf{Denote}_{\mathtt{mono|'''Denote'''_S}} ≡ <math>\equiv \lim_{i \to \infty}</math> '''\mathbf{progression'''_{}_{\mathtt{S}^{}^i}}(⊥<sub>\bot_\mathtt{S})</submath>)}}

</blockquote>

In this way, the behavior of {{mono|S}} can be mathematically characterized in terms of all its possible behaviors (including those involving unbounded nondeterminism).