Symbolic model checking for distributed real-time systems

Abstract

In this paper, we examine the symbolic model checking problem for distributed real-time systems where time is represented by the real numbers and multiple clocks are allowed. A symbolic model checking algorithm is proposed. This algorithm handles timing constraints that are written in inequalities whose two sides refer to readings of the same local clock. The timing inequalities are used as triggers for transitions in Multiclock Continuously Timed Automaton (MCTA), a variation of the Timed Safety Automaton [11] which we propose as the specification language for distributed real-time systems. We also propose MTCTL, an extension of TCTL by the introduction of multiple local clocks, for specifying system behavior to be verified.

There are three major contributions of this paper. First, we give a symbolic model checking algorithm for Timed Safety Automata and TCTL which naturally makes use of the BDD approach of Bryant[4] and Burch et al[5], and avoids the complications in [11]. Second, we propose a unified approach for checking both real-time and state properties by treating inequalities as propositions that are governed by some axioms. This is not only a more elegant way to represent the finite structure of the state space, but is also more suitable for symbolic manipulation. Third, we introduce MTCTL and MCTA together as a new tool for specifying and reasoning about distributed real-time system behavior that allows for different granularities for local clocks and clock jitters.

Supported in part by a research grant from the Office of Naval Research under ONR contract number N00014-89-J-1472.