8,906 research outputs found
An Algebra of Synchronous Scheduling Interfaces
In this paper we propose an algebra of synchronous scheduling interfaces
which combines the expressiveness of Boolean algebra for logical and functional
behaviour with the min-max-plus arithmetic for quantifying the non-functional
aspects of synchronous interfaces. The interface theory arises from a
realisability interpretation of intuitionistic modal logic (also known as
Curry-Howard-Isomorphism or propositions-as-types principle). The resulting
algebra of interface types aims to provide a general setting for specifying
type-directed and compositional analyses of worst-case scheduling bounds. It
covers synchronous control flow under concurrent, multi-processing or
multi-threading execution and permits precise statements about exactness and
coverage of the analyses supporting a variety of abstractions. The paper
illustrates the expressiveness of the algebra by way of some examples taken
from network flow problems, shortest-path, task scheduling and worst-case
reaction times in synchronous programming.Comment: In Proceedings FIT 2010, arXiv:1101.426
Max-plus (A,B)-invariant spaces and control of timed discrete event systems
The concept of (A,B)-invariant subspace (or controlled invariant) of a linear
dynamical system is extended to linear systems over the max-plus semiring.
Although this extension presents several difficulties, which are similar to
those encountered in the same kind of extension to linear dynamical systems
over rings, it appears capable of providing solutions to many control problems
like in the cases of linear systems over fields or rings. Sufficient conditions
are given for computing the maximal (A,B)-invariant subspace contained in a
given space and the existence of linear state feedbacks is discussed. An
application to the study of transportation networks which evolve according to a
timetable is considered.Comment: 24 pages, 1 Postscript figure, proof of Lemma 1 and some references
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Max-plus algebra in the history of discrete event systems
This paper is a survey of the history of max-plus algebra and its role in the field of discrete event systems during the last three decades. It is based on the perspective of the authors but it covers a large variety of topics, where max-plus algebra plays a key role
The earlier the better: a theory of timed actor interfaces
Programming embedded and cyber-physical systems requires attention not only to functional behavior and correctness, but also to non-functional aspects and specifically timing and performance constraints. A structured, compositional, model-based approach based on stepwise refinement and abstraction techniques can support the development process, increase its quality and reduce development time through automation of synthesis, analysis or verification. For this purpose, we introduce in this paper a general theory of timed actor interfaces. Our theory supports a notion of refinement that is based on the principle of worst-case design that permeates the world of performance-critical systems. This is in contrast with the classical behavioral and functional refinements based on restricting or enlarging sets of behaviors. An important feature of our refinement is that it allows time-deterministic abstractions to be made of time-non-deterministic systems, improving efficiency and reducing complexity of formal analysis. We also show how our theory relates to, and can be used to reconcile a number of existing time and performance models and how their established theories can be exploited to represent and analyze interface specifications and refinement steps.\u
Consistency of adjacency spectral embedding for the mixed membership stochastic blockmodel
The mixed membership stochastic blockmodel is a statistical model for a
graph, which extends the stochastic blockmodel by allowing every node to
randomly choose a different community each time a decision of whether to form
an edge is made. Whereas spectral analysis for the stochastic blockmodel is
increasingly well established, theory for the mixed membership case is
considerably less developed. Here we show that adjacency spectral embedding
into , followed by fitting the minimum volume enclosing convex
-polytope to the principal components, leads to a consistent estimate
of a -community mixed membership stochastic blockmodel. The key is to
identify a direct correspondence between the mixed membership stochastic
blockmodel and the random dot product graph, which greatly facilitates
theoretical analysis. Specifically, a norm and central
limit theorem for the random dot product graph are exploited to respectively
show consistency and partially correct the bias of the procedure.Comment: 12 pages, 6 figure
Bounds on series-parallel slowdown
We use activity networks (task graphs) to model parallel programs and
consider series-parallel extensions of these networks. Our motivation is
two-fold: the benefits of series-parallel activity networks and the modelling
of programming constructs, such as those imposed by current parallel computing
environments. Series-parallelisation adds precedence constraints to an activity
network, usually increasing its makespan (execution time). The slowdown ratio
describes how additional constraints affect the makespan. We disprove an
existing conjecture positing a bound of two on the slowdown when workload is
not considered. Where workload is known, we conjecture that 4/3 slowdown is
always achievable, and prove our conjecture for small networks using max-plus
algebra. We analyse a polynomial-time algorithm showing that achieving 4/3
slowdown is in exp-APX. Finally, we discuss the implications of our results.Comment: 12 pages, 4 figure
The set of realizations of a max-plus linear sequence is semi-polyhedral
We show that the set of realizations of a given dimension of a max-plus
linear sequence is a finite union of polyhedral sets, which can be computed
from any realization of the sequence. This yields an (expensive) algorithm to
solve the max-plus minimal realization problem. These results are derived from
general facts on rational expressions over idempotent commutative semirings: we
show more generally that the set of values of the coefficients of a commutative
rational expression in one letter that yield a given max-plus linear sequence
is a semi-algebraic set in the max-plus sense. In particular, it is a finite
union of polyhedral sets
PRISM: a tool for automatic verification of probabilistic systems
Probabilistic model checking is an automatic formal verification technique for analysing quantitative properties of systems which exhibit stochastic behaviour. PRISM is a probabilistic model checking tool which has already been successfully deployed in a wide range of application domains, from real-time communication protocols to biological signalling pathways. The tool has recently undergone a significant amount of development. Major additions include facilities to manually explore models, Monte-Carlo discrete-event simulation techniques for approximate model analysis (including support for distributed simulation) and the ability to compute cost- and reward-based measures, e.g. "the expected energy consumption of the system before the first failure occurs". This paper presents an overview of all the main features of PRISM. More information can be found on the website: www.cs.bham.ac.uk/~dxp/prism
Local Exchangeability
Exchangeability---in which the distribution of an infinite sequence is
invariant to reorderings of its elements---implies the existence of a simple
conditional independence structure that may be leveraged in the design of
probabilistic models, efficient inference algorithms, and randomization-based
testing procedures. In practice, however, this assumption is too strong an
idealization; the distribution typically fails to be exactly invariant to
permutations and de Finetti's representation theory does not apply. Thus there
is the need for a distributional assumption that is both weak enough to hold in
practice, and strong enough to guarantee a useful underlying representation. We
introduce a relaxed notion of local exchangeability---where swapping data
associated with nearby covariates causes a bounded change in the distribution.
We prove that locally exchangeable processes correspond to independent
observations from an underlying measure-valued stochastic process. We thereby
show that de Finetti's theorem is robust to perturbation and provide further
justification for the Bayesian modelling approach. Using this probabilistic
result, we develop three novel statistical procedures for (1) estimating the
underlying process via local empirical measures, (2) testing via local
randomization, and (3) estimating the canonical premetric of local
exchangeability. These three procedures extend the applicability of previous
exchangeability-based methods without sacrificing rigorous statistical
guarantees. The paper concludes with examples of popular statistical models
that exhibit local exchangeability
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