The framework also defines what it means for one TIOA to implement another, based on an inclusion relationship between their external behavior sets, and defines notions of simulations, which provide sufficient conditions for demonstrating implementation relationships. In particular, the framework includes a notion of external behavior for a timed I/O automaton, which captures its discrete interactions with its environment. The need to prove rigorous theoretical results about timed distributed algorithms makes it important to have a suitable mathematical foundation.Īn important feature of the TIOA framework is its support for decomposing timed system descriptions. Such algorithms arise, for example, in traditional and wireless communications, networks of mobile devices, and shared-memory multiprocessors. The TIOA framework also supports description and analysis of timed distributed algorithms - distributed algorithms whose correctness and performance depend on the relative speeds of processors, accuracy of local clocks, or communication delay bounds. Many applications involving timed systems have strong safety, reliability, and predictability requirements, which make it important to have methods for systematic design of systems and rigorous analysis of timing-dependent behavior. Timed systems are employed in a wide range of domains including communications, embedded systems, real-time operating systems, and automated control. Timed systems are systems in which desirable correctness or performance properties of the system depend on the timing of events, not just on the order of their occurrence. This monograph presents the Timed Input/Output Automaton (TIOA) modeling framework, a basic mathematical framework to support description and analysis of timed (computing) systems.

Distributed algorithms nancy lynch pdf