Modelling operating system structures by timed stream processing functions

Abstract

Some extensions of the basic formalism of stream processing functions are useful to specify complex structures such as operating systems. In this paper we give the foundations of higher order stream processing functions. These are functions which send and accept not only messages representing atomic data, but also complex elements such as functions. Some special notations are introduced for the specification and manipulation of such functions. A representation of time is outlined, which enables us to model time dependent behaviour. Finally, we demonstrate how characteristic operating system structures can be modelled by timed higher order stream processing functions.

Kahn Process Networks and a Reactive Extension

“…A timed process network model is a model which not only describes the data transformations of the network, but also the timing of such a process [11], [52]. Such a model is typically made by labeling symbols with time-stamps or tags from a particular time domain of choice (for instance non-negative integers or reals) or, more general, according to the tagged-signal model of [32], allowing for instance also partially ordered or super-dense time domains common in hardware description languages [34].…”

“…Using time information, decisions can be taken in a deterministic way, based on the time-stamps of data, for instance to describe a merge process which merges symbols in the order in which they arrive (with some provision, for instance fixed priority, when tokens arrive at the same time) [11], [52], [34]. Alternative network equations can be formulated and different fixed-point theorems (such as Kleene's or Banach's) can be used to show them to have a unique solution.…”

Algorithms and Framework for Energy Efficient Parallel Stream Computing on Many-Core Architectures

“…Channels convey streams between modules and a stream can be defined as a finite or infinite ordered list of elements a 1 , a 2 , · · · , a n where all elements, including the empty element Λ (noted ∅ by Broy and Dendorfer [16] and <> by Stephens [135]), belong to a set A. Elements can be assigned to a discrete time value from a time set T = N = {0, 1, 2, 3, · · · }, in a function a : T → A. Kahn [77] denotes such a list or function as A ω and Broy and Dendorfer [16] decompose it further into A ω = A * ∪ A ∞ where A * is the set of finite sequences of elements in A, and A ∞ is the set of infinite sequences over A. It is interesting to observe that the first references to streams were intended to model histories of loop variables and employed in the verification of operating systems [16,135].…”

“…Elements can be assigned to a discrete time value from a time set T = N = {0, 1, 2, 3, · · · }, in a function a : T → A. Kahn [77] denotes such a list or function as A ω and Broy and Dendorfer [16] decompose it further into A ω = A * ∪ A ∞ where A * is the set of finite sequences of elements in A, and A ∞ is the set of infinite sequences over A. It is interesting to observe that the first references to streams were intended to model histories of loop variables and employed in the verification of operating systems [16,135]. Consequently, channels and streams are sometimes also referred to as histories.…”

“…We refer to the survey by Stephens [135] and to Broy and Dendorfer [16] for more primitive operations over streams. An important property of a ST is that it is a function that maps an input stream to an output stream; in other words, every element in the output stream is a function of all elements of input streams consumed so far instead of just one corresponding element in each input stream.…”