500 research outputs found
Bisimulation equivalence of differential-algebraic systems
In this paper, the notion of bisimulation relation for linear input-state-output systems is extended to general linear differential-algebraic (DAE) systems. Geometric control theory is used to derive a linear-algebraic characterisation of bisimulation relations, and an algorithm for computing the maximal bisimulation relation between two linear DAE systems. The general definition is specialised to the case where the matrix pencil sE - A is regular. Furthermore, by developing a one-sided version of bisimulation, characterisations of simulation and abstraction are obtained
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
Equivalence of hybrid dynamical systems
A common theme in theoretical computer science (in particular, the theory of distributed processes and computer-aided verification) and in systems and control theory is to charac-terize systems which are ‘externally equivalent’. The intuitive idea is that we only want to distinguish between two systems if the distinction can be detected by an external syste
Achievable bisimilar behaviour of abstract state systems
Given a plant system and a desired system, we study conditions for which there exists a controller that interconnected with the plant, yields a system that is bisimilar to the desired system. Some sufficient and some necessary conditions are provided in the general case of (non-deterministic) abstract state systems and stronger results are obtained for the special classes of autonomous abstract state systems, finite abstract state systems, and non-deterministic linear dynamical systems
Bisimilar control affine systems
The notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation. These equivalences are in turn used to simplify verification and synthesis for these models as well as to enable compositional reasoning. In systems theory, a similar notion is also of interest in order to develop modular verification and design tools for purely continuous or hybrid control systems. In this paper, we introduce two notions of bisimulation for nonlinear systems. We present differential-algebraic characterizations of these notions and show that bisimilar systems of different dimensions are obtained by factoring out certain invariant distributions. Furthermore, we also show that all bisimilar systems of different dimension are of this form
Behavioural hybrid process calculus
Process algebra is a theoretical framework for the modelling and analysis of the behaviour of concurrent discrete event systems that has been developed within computer science in past quarter century. It has generated a deeper nderstanding of the nature of concepts such as observable behaviour in the presence of nondeterminism, system composition by interconnection of concurrent component systems, and notions of behavioural equivalence of such systems. It has contributed fundamental concepts such as bisimulation, and has been successfully used in a wide range of problems and practical applications in concurrent systems. We believe that the basic tenets of process algebra are highly compatible with the behavioural approach to dynamical systems. In our contribution we present an extension of classical process algebra that is suitable for the modelling and analysis of continuous and hybrid dynamical systems. It provides a natural framework for the concurrent composition of such systems, and can deal with nondeterministic behaviour that may arise from the occurrence of internal switching events. Standard process algebraic techniques lead to the characterisation of the observable behaviour of such systems as equivalence classes under some suitably adapted notion of bisimulation
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
Process Algebras
Process Algebras are mathematically rigorous languages with well defined semantics that permit describing and verifying properties of concurrent communicating systems.
They can be seen as models of processes, regarded as agents that act and interact continuously with other similar agents and with their common environment. The agents may be real-world objects (even people), or they may be artifacts, embodied perhaps in computer hardware or software systems.
Many different approaches (operational, denotational, algebraic) are taken for describing the meaning of processes. However, the operational approach is the reference one. By relying on the so called Structural Operational Semantics (SOS), labelled transition systems are built and composed by using the different operators of the many different process algebras. Behavioral equivalences are used to abstract from unwanted details and identify those systems that react similarly to external
experiments
Presenting Distributive Laws
Distributive laws of a monad T over a functor F are categorical tools for
specifying algebra-coalgebra interaction. They proved to be important for
solving systems of corecursive equations, for the specification of well-behaved
structural operational semantics and, more recently, also for enhancements of
the bisimulation proof method. If T is a free monad, then such distributive
laws correspond to simple natural transformations. However, when T is not free
it can be rather difficult to prove the defining axioms of a distributive law.
In this paper we describe how to obtain a distributive law for a monad with an
equational presentation from a distributive law for the underlying free monad.
We apply this result to show the equivalence between two different
representations of context-free languages
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