Summary
A new technique for proving timing properties for timing-based algorithms is described; it is an extension of the mapping techniques previously used in proofs of safety properties for asynchronous concurrent systems. The key to the method is a way of representing a system with timing constraints as an automaton whose state includes predictive timing information. Timing assumptions and timing requirements for the system are both represented in this way. A multi-valued mapping from the “assumptions automaton” to the “requirements automaton” is then used to show that the given system satisfies the requirements. One type of mapping is based on a collection of “progress functions” providing measures of progress toward timing goals. The technique is illustrated with two examples, a simple resource manager and a two-process race system.
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Nancy A. Lynch received the B.S. degree in mathematics from Brooklyn College, Brooklyn, NY, in 1968, and the Ph.D. degree in mathematics from the Massachusetts Institute of Technology, Cambridge, MA, in 1972. She is presently a professor of computer science and electrical engineering at Massachusetts Institute of Technology. She has also been on the computer science faculty at Georgia Institute of Technology and on the mathematics faculty at Tufts University and the University of Southern California. Her research interests are in distributed and real-time computing and theoretical computer science. In particular, she has worked on formal models and verification methods, on algorithm design and analysis, and on impossibility results. She also likes to hike and ski.
Hagit Attiya received the B.Sc. degree in Mathematics and Computer Science from the Hebrew University of Jerusalem, in 1981, the M.Sc. and Ph.D. degrees in Computer Science from the Hebrew University of Jerusalem, in 1983 and 1987, respectively. She is presently a senior lecturer at the department of Computer Science at the Technion, Israel Institute of Technology. Prior to this, she has been a post-doctoral research associate at the Laboratory for Computer Science at M.I.T. Her general research interests are distributed computation and theoretical computer science. More specific interests include fault-tolerance, timing-based and asynchronous algorithms.
This work was supported by ONR contracts N00014-85-K-0168 and N00014-91-J-1046, by NSF grants CCR-8611442 and CCR-8915206, and by DARPA contracts N00014-87-K-0825 and N00014-89-J-1988
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Lynch, N.A., Attiya, H. Using mappings to prove timing properties. Distrib Comput 6, 121–139 (1992). https://doi.org/10.1007/BF02252683
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DOI: https://doi.org/10.1007/BF02252683