Dynamic networks of heterogeneous timed machines

Abstract

We present an algebra of discrete timed input/output automata that may execute in the context of different clock granularities – which we call timed machines; this algebra includes a refinement operator through which a machine can be extended with new states and transitions in order to accommodate a finer clock granularity as required to interoperate with other machines, and an extension of the traditional product of timed input–output automata to the situation in which the granularities of the two machines are not the same. Over this algebra, we then define an algebra of networks of timed machines that includes operations through which networks can be modified at run time, thus offering a model for systems of interconnected components that can dynamically bind to other systems and, therefore, cannot be adjusted at design time to ensure that they operate in a timed homogeneous setting. We investigate important properties of timed machines such as consistency – in the sense that a machine can be ensured to generate a non-empty language, and feasibility – in the sense that a machine can be ensured to generate a non-empty language no matter what inputs it receives, and propose techniques for checking if timed machines are consistent or are feasible. We generalise those properties to networks of timed machines, and investigate how consistency and feasibility of networks can be proved through properties that can be checked at design time without having to compute, at run time, the product of the machines that operate on those networks, which would not be practical.

A Semantic Model for Interacting Cyber-Physical Systems

“…In [8], the authors describe an algebra of timed machines and of networks of timed machines. A timed machine is a state based description of a set of timed traces, such that every observation has a time stamp that is a multiple of a time step δ .…”

“…Like existing semantic models, such as time-data streams [4], time signal [24], or discrete clock [8], we use a dense model of time. However, we allow for arbitrary but finite interleavings of observations.…”

“…We focus in this paper on different algebraic operations on sets of timed-traces (TESs), and abstract away any underlying operational model (e.g., timed-automata). In [8], the authors explain how algebraic operations on timed machines approximate the intersection of sets of timed-traces. In our case, interaction is not restricted to input/output composition, but depends on the choice of a composability constraint on TESs and a composition function on observables.…”

“…In our case, interaction is not restricted to input/output composition, but depends on the choice of a composability constraint on TESs and a composition function on observables. The work in [8] denotes an interesting class of components (closed under insertion of silent observationr-closed) that deserves investigation.…”

A Semantic Model for Interacting Cyber-Physical Systems

“…In [17], the authors describe an algebra of timed machines and of networks of timed machines. A timed machine is a state based description of a set of timed traces, such that every observation has a time stamp that is a multiple of a time step δ .…”