  We develop a new algebraic framework to reason about languages of
Mazurkiewicz traces. This framework supports true concurrency and provides a
non-trivial generalization of the wreath product operation to the trace
setting. A novel local wreath product principle has been established. The new
framework is crucially used to propose a decomposition result for recognizable
trace languages, which is an analogue of the Krohn-Rhodes theorem. We prove
this decomposition result in the special case of acyclic architectures and
apply it to extend Kamp's theorem to this setting. We also introduce and
analyze distributed automata-theoretic operations called local and global
cascade products. Finally, we show that aperiodic trace languages can be
characterized using global cascade products of localized and distributed
two-state reset automata.
