Ebook: Operational Semantics for Timed Systems: A Non-standard Approach to Uniform Modeling of Timed and Hybrid Systems

This monograph is dedicated to a novel approach for uniform modelling of timed and hybrid systems. Heinrich Rust presents a time model which allows for both the description of discrete time steps and continuous processes with a dense real-number time model. The proposed time model is well suited to express synchronicity of events in a real-number time model as well as strict causality by using uniform discrete time steps. Thus it integrates and reconciles two views of time that are commonly used separately in di?erent application domains. In many discrete systems time is modelled by discrete steps of uniform length, in continuous systems time is seen as a dense ?ow. Themainideatointegratethesedi?erentviewsisadiscretizationofthedense real-number time structure by using constant in?nitesimal time steps within each real-number point in time. The underlying mathematical structure of this time model is based on concepts of Non-standard Analysis as proposed by Abraham Robinson in the 1950s. The discrete modelling, i.e., the descr- tion of sequential discrete algorithms at di?erent abstraction levels, is done with Abstract State Machines along the formalisms developed by Yuri Gu- vich and temporal logic. These ingredients produce a rich formal basis for describing a large variety of systems with quantitative linear time prop- ties, by seamless integration, re?nement and embedding of continuous and discrete models into one uniform semantic framework called“Non-standard Timed Abstract State Machines”(NTASM).

This monograph is dedicated to a novel approach for uniform modeling of timed and hybrid systems. The author introduces a time model that allows for both the description of discrete time steps and continuous processes with a discrete time model with infinitesimal step widths.

The underlying mathematical structure of this time model is based on the concepts of non-standard analysis. The discrete modeling, i.e., the description of sequential discrete algorithms at different abstraction levels, is done using the abstract state machines formalism.

The presentation is well balanced between theoretical elaboration and critical discussion of the applicability of the theoretical results by means of appropriate case studies. The new temporal semantics proposed helps theoreticians as well as practitioners in gaining a better understanding of time models and in building better notations, models, and tools for the formal treatment of systems where time matters.