On recognizable stable trace languages

We relate several models of concurrency introduced in the literature in order to extend classical Mazurkiewicz traces. These are mainly Droste's concurrent automata and Arnold's CCI sets of P-traces, studied in the framework of local trace languages. Also, a connection between these models and classical traces is presented in details through a natural notion of projection. These relationships enable us to use efficiently Arnold's result in two other frameworks. First, we give a finite distributed implementation for regular CCI sets of P-traces (or, equivalently, finite stably concurrent automata) by means of bounded labelled Petri nets. Second, we present a new, simple and constructive method to relate Stark's trace automata with Bednarczyk's asynchronous transition systems. This improves a recent result in Scott domain theory.