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.