951 research outputs found
Refining ideal behaviours
This paper provides some mathematical properties of behaviours of systems, where the individual elements of a behaviour are modeled by ideals of a suitable partial order. It is well-known that the associated ideal completion provides a simple way of constructing algebraic cpos. An ideal can be viewed as a set of consistent finite or compact approximations of an object which itself may even be infinite.
We introduce a special way of characterising behaviours through sets of relevant approximations
Performance modelling and the representation of large scale distributed system functions
This thesis presents a resource based approach to model generation for performance characterization and correctness checking of large scale telecommunications networks. A notion called the timed automaton is proposed and then developed to encapsulate behaviours of networking equipment, system control policies and non-deterministic user behaviours. The states of pooled network resources and the behaviours of resource consumers are represented as continually varying geometric patterns; these patterns form part of the data operated upon by the timed automata. Such a representation technique allows for great flexibility regarding the level of abstraction that can be chosen in the modelling of telecommunications systems. None the less, the notion of system functions is proposed to serve as a constraining framework for specifying bounded behaviours and features of telecommunications systems. Operational concepts are developed for the timed automata; these concepts are based on limit preserving relations. Relations over system states represent the evolution of system properties observable at various locations within the network under study. The declarative nature of such permutative state relations provides a direct framework for generating highly expressive models suitable for carrying out optimization experiments. The usefulness of the developed procedure is demonstrated by tackling a large scale case study, in particular the problem of congestion avoidance in networks; it is shown that there can be global coupling among local behaviours within a telecommunications network. The uncovering of such a phenomenon through a function oriented simulation is a contribution to the area of network modelling. The direct and faithful way of deriving performance metrics for loss in networks from resource utilization patterns is also a new contribution to the work area
Stream processors and comodels
In 2009, Hancock, Pattinson and Ghani gave a coalgebraic characterisation of
stream processors drawing on ideas of
Brouwerian constructivism. Their stream processors have an intensional
character; in this paper, we give a corresponding coalgebraic characterisation
of extensional stream processors, i.e., the set of continuous functions
. Our account sites both our result and that of
op. cit. within the apparatus of comodels for algebraic effects originating
with Power-Shkaravska. Within this apparatus, the distinction between
intensional and extensional equivalence for stream processors arises in the
same way as the the distinction between bisimulation and trace equivalence for
labelled transition systems and probabilistic generative systems.Comment: 24 pages; v4: final accepted versio
Algebra, coalgebra, and minimization in polynomial differential equations
We consider reasoning and minimization in systems of polynomial ordinary
differential equations (ode's). The ring of multivariate polynomials is
employed as a syntax for denoting system behaviours. We endow this set with a
transition system structure based on the concept of Lie-derivative, thus
inducing a notion of L-bisimulation. We prove that two states (variables) are
L-bisimilar if and only if they correspond to the same solution in the ode's
system. We then characterize L-bisimilarity algebraically, in terms of certain
ideals in the polynomial ring that are invariant under Lie-derivation. This
characterization allows us to develop a complete algorithm, based on building
an ascending chain of ideals, for computing the largest L-bisimulation
containing all valid identities that are instances of a user-specified
template. A specific largest L-bisimulation can be used to build a reduced
system of ode's, equivalent to the original one, but minimal among all those
obtainable by linear aggregation of the original equations. A computationally
less demanding approximate reduction and linearization technique is also
proposed.Comment: 27 pages, extended and revised version of FOSSACS 2017 pape
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