School of Computing

How to stop time stopping

H. Bowman and R. Gomez

Formal Aspects of Computing, 18(4):182-196, December 2006.

Abstract

Zeno-timelocks constitute a challenge for the formal verification of timed automata: they are difficult to detect, and the verification of most properties (e.g., safety) is only correct for timelock-free models. Some time ago, Tripakis proposed a syntactic check on the structure of timed automata: If a certain condition (called strong non-zenoness) is met by all the loops in a given automaton, then zeno-timelocks are guaranteed not to occur. Checking for strong non-zenoness is efficient, and compositional (if all components in a network of automata are strongly non-zeno, then the network is free from zeno-timelocks).

Strong non-zenoness, however, is sufficient-only: There exist non-zeno specifications which are not strongly non-zeno. A TCTL formula is known that represents a sufficient-and-necessary condition for non-zenoness; unfortunately, this formula requires a demanding model-checking algorithm, and not all model-checkers are able to express it. In addition, this algorithm provides only limited diagnostic information.

Here we propose a number of alternative solutions. First, we show that the compositional application of strong non-zenoness can be weakened: Some networks can be guaranteed to be free from Zeno-timelocks, even if not every component is strongly non-zeno. Secondly, we present new syntactic, sufficient-only conditions that complement strong non-zenoness. Finally, we describe a sufficient-and-necessary condition that only requires a simple form of reachability analysis. Furthermore, our conditions identify the cause of zeno-timelocks directly on the model, in the form of unsafe loops. We also comment on a tool that we have developed, which implements the syntactic checks on Uppaal models. The tool is also able to derive, from those unsafe loops in a given automaton (in general, an Uppaal model representing a product automaton of a given network), the reachability formulas that characterise the occurrence of zeno-timelocks. A modified version of the CSMA/CD protocol is used as a case-study.

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Bibtex Record

@article{2433,
author = {H. Bowman and R. Gomez},
title = {How to stop time stopping},
month = {December},
year = {2006},
pages = {182-196},
keywords = {determinacy analysis, Craig interpolants},
note = {},
doi = {},
url = {http://www.cs.kent.ac.uk/pubs/2006/2433},
    publisher = {Springer London},
    publication_type = {article},
    submission_id = {559_1159267150},
    journal = {Formal Aspects of Computing},
    volume = {18},
    number = {4},
}

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