19,467 research outputs found
Process algebra modelling styles for biomolecular processes
We investigate how biomolecular processes are modelled in process algebras, focussing on chemical reactions. We consider various modelling styles and how design decisions made in the definition of the process algebra have an impact on how a modelling style can be applied. Our goal is to highlight the often implicit choices that modellers make in choosing a formalism, and illustrate, through the use of examples, how this can affect expressability as well as the type and complexity of the analysis that can be performed
Network algebra for synchronous dataflow
We develop an algebraic theory of synchronous dataflow networks. First, a
basic algebraic theory of networks, called BNA (Basic Network Algebra), is
introduced. This theory captures the basic algebraic properties of networks.
For synchronous dataflow networks, it is subsequently extended with additional
constants for the branching connections that occur between the cells of
synchronous dataflow networks and axioms for these additional constants. We
also give two models of the resulting theory, the one based on stream
transformers and the other based on processes as considered in process algebra.Comment: 24 page
StocHy: automated verification and synthesis of stochastic processes
StocHy is a software tool for the quantitative analysis of discrete-time
stochastic hybrid systems (SHS). StocHy accepts a high-level description of
stochastic models and constructs an equivalent SHS model. The tool allows to
(i) simulate the SHS evolution over a given time horizon; and to automatically
construct formal abstractions of the SHS. Abstractions are then employed for
(ii) formal verification or (iii) control (policy, strategy) synthesis. StocHy
allows for modular modelling, and has separate simulation, verification and
synthesis engines, which are implemented as independent libraries. This allows
for libraries to be easily used and for extensions to be easily built. The tool
is implemented in C++ and employs manipulations based on vector calculus, the
use of sparse matrices, the symbolic construction of probabilistic kernels, and
multi-threading. Experiments show StocHy's markedly improved performance when
compared to existing abstraction-based approaches: in particular, StocHy beats
state-of-the-art tools in terms of precision (abstraction error) and
computational effort, and finally attains scalability to large-sized models (12
continuous dimensions). StocHy is available at www.gitlab.com/natchi92/StocHy
A Combinatorial Bit Bang Leading to Quaternions
This paper describes in detail how (discrete) quaternions - ie. the abstract
structure of 3-D space - emerge from, first, the Void, and thence from
primitive combinatorial structures, using only the exclusion and co-occurrence
of otherwise unspecified events. We show how this computational view
supplements and provides an interpretation for the mathematical structures, and
derive quark structure. The build-up is emergently hierarchical, compatible
with both quantum mechanics and relativity, and can be extended upwards to the
macroscopic. The mathematics is that of Clifford algebras emplaced in the
homology-cohomology structure pioneered by Kron. Interestingly, the ideas
presented here were originally developed by the author to resolve fundamental
limitations of existing AI paradigms. As such, the approach can be used for
learning, planning, vision, NLP, pattern recognition; and as well, for
modelling, simulation, and implementation of complex systems, eg. biological.Comment: 23 pages, 4 figure
Abstractions of Stochastic Hybrid Systems
In this paper we define a stochastic bisimulation concept for a very general class of stochastic hybrid systems, which subsumes most classes of stochastic hybrid systems. The definition of this bisimulation builds on the concept of zigzag morphism defined for strong Markov processes.
The main result is that this stochastic bisimulation is indeed an equivalence relation. The secondary result is that this bisimulation relation for the stochastic hybrid system models used in this paper implies the same
kind of bisimulation for their continuous parts and respectively for their jumping structures
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
Discrete Simulation of Behavioural Hybrid Process Calculus
Hybrid systems combine continuous-time and discrete behaviours. Simulation is one of the tools to obtain insight in dynamical systems behaviour. Simulation results provide information on performance of system and are helpful in detecting potential weaknesses and errors. Moreover, the results are handy in choosing adequate control strategies and parameters. In our contribution we report a work in progress, a technique for simulation of Behavioural Hybrid Process Calculus, an extension of process algebra that is suitable for the modelling and analysis of hybrid systems
When are Stochastic Transition Systems Tameable?
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of
decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness
allows one to lift most good properties from finite Markov chains to
denumerable ones, and therefore to adapt existing verification algorithms to
infinite-state models. Decisive Markov chains however do not encompass
stochastic real-time systems, and general stochastic transition systems (STSs
for short) are needed. In this article, we provide a framework to perform both
the qualitative and the quantitative analysis of STSs. First, we define various
notions of decisiveness (inherited from [1]), notions of fairness and of
attractors for STSs, and make explicit the relationships between them. Then, we
define a notion of abstraction, together with natural concepts of soundness and
completeness, and we give general transfer properties, which will be central to
several verification algorithms on STSs. We further design a generic
construction which will be useful for the analysis of {\omega}-regular
properties, when a finite attractor exists, either in the system (if it is
denumerable), or in a sound denumerable abstraction of the system. We next
provide algorithms for qualitative model-checking, and generic approximation
procedures for quantitative model-checking. Finally, we instantiate our
framework with stochastic timed automata (STA), generalized semi-Markov
processes (GSMPs) and stochastic time Petri nets (STPNs), three models
combining dense-time and probabilities. This allows us to derive decidability
and approximability results for the verification of these models. Some of these
results were known from the literature, but our generic approach permits to
view them in a unified framework, and to obtain them with less effort. We also
derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page
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