How vital is liveness? Verifying timing properties of reactive and hybrid systems

  • Amir Pnueli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 630)


This extended abstract discusses the importance of the notion of liveness properties and their verification. The main observation is that they provide a most useful abstraction on the qualitative (non-quantitative) level of modeling. As we construct more refined models that take real-time into account, the importance of liveness and fairness decrease, and many important properties move to the safety class.

In the talk to be presented, we propose a framework for the formal specification and verification of timed and hybrid systems. For timed systems we propose a specification language that refers to time only through age functions which measure the length of the most recent time interval in which a given formula has been continuously true.

We then consider hybrid systems, which are systems consisting of a non-trivial mixture of discrete and continuous components, such as a digital controller that controls a continuous environment. The proposed framework extends the temporal logic approach which has proven useful for the formal analysis of discrete systems such as reactive programs. The new framework consists of a semantic model for hybrid time, the notion of phase transition systems, which extends the formalism of discrete transition systems, an extended version of Statecharts for the specification of hybrid behaviors, and an extended version of temporal logic that enables reasoning about continuous change.

The talk is based on extensive collaboration with Z. Manna, T. Henzinger, O. Maler, and Y. Kesten, whose results are reported in [HMP91], [MMP92], and [KP92].


Liveness fairness justice Real-time timed transitions system hybrid systems discrete and continuous systems Statecharts 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Amir Pnueli
    • 1
  1. 1.Department of Applied MathematicsWeizmann InstituteRehovotIsrael

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