Timed I/O automata: a mathematical framework for modeling and analyzing real-time systems

We describe the timed input/output automata (TIOA) framework, a general mathematical framework for modeling and analyzing real-time systems. It is based on timed I/O automata, which engage in both discrete transitions and continuous trajectories. The framework includes a notion of external behavior, and notions of composition and abstraction. We define safety and liveness properties for timed I/O automata, and a notion of receptiveness, and prove basic results about all of these notions. The TIOA framework is defined as a special case of the new hybrid I/O automata (HIOA) modeling framework for hybrid systems. Specifically, a TIOA is an HIOA with no external variables; thus, TIOAs communicate via shared discrete actions only, and do not interact continuously. This restriction is consistent with previous real-time system models, and gives rise to some simplifications in the theory (compared to HIOA). The resulting model is expressive enough to describe complex timing behavior, and to express the important ideas of previous timed automata frameworks.

1. Introduction

This paper describes the Timed Input/Output Automata (TIOA) framework, a general mathematical framework for modeling and analyzing real-time systems. Designers of real-time systems can use this framework to describe complex systems and decompose them into manageable pieces. In particular, they can use TIOA to describe their systems at multiple levels of abstraction, and to decompose their systems into more primitive, interacting components. Designers can use TIOA to prove safety, liveness, and performance properties of real-time systems. Since TIOA is purely mathematical, such proofs are generally done by hand. However, TIOA is a natural basis for computer support tools, which will be developed in the future. The TIOA framework is general enough to express previous results from other frameworks, such as [24], [23], [5], [22], [21], [29].