Issue Theoret. Informatics Appl. Volume 39, Number 3, July-September 2005 Foundations of Software Science and Computer Structures (FOSSACS'04) Page(s) 587 - 618 DOI 10.1051/ita:2005030

Theoret. Informatics Appl. 39, 587-618 (2005)
DOI: 10.1051/ita:2005030

Bisimulation on speed: Lower time bounds

Gerald Lüttgen¹ and Walter Vogler<sup>2

1</sup>  Department of Computer Science, The University of York, York YO10 5DD, UK; gerald.luettgen@cs.york.ac.uk
²  Institut für Informatik, Universität Augsburg, 86135 Augsburg, Germany; walter.vogler@informatik.uni-augsburg.de

Abstract
More than a decade ago, Moller and Tofts published their seminal work on relating processes, which are annotated with lower time bounds, with respect to speed. Their paper has left open many questions regarding the semantic theory for the suggested bisimulation-based faster-than preorder, the MT-preorder, which have not been addressed since. The encountered difficulties concern a general compositionality result, a complete axiom system for finite processes, a convincing intuitive justification of the MT-preorder, and the abstraction from internal computation. This article solves these difficulties by developing and employing a novel commutation lemma relating the sequencing of action and clock transitions in discrete-time process algebra. Most importantly, it is proved that the MT-preorder is fully-abstract with respect to a natural amortized preorder that uses a simple bookkeeping mechanism for deciding whether one process is faster than another. Together these results reveal the intuitive roots of the MT-preorder as a faster-than relation, while testifying to its semantic elegance. This lifts some of the barriers that have so far hampered progress in semantic theories for comparing the speed of processes.

Mathematics Subject Classification. 68Q85

Key words: Asynchronous systems -- timed process algebra -- lower time bounds -- faster-than relation -- Moller-Tofts preorder -- bisimulation.


© EDP Sciences 2005

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