finite set of messages ${\mathit{Msg}}$ and a finite-state transition system ${\mathcal{A}}_p=(S_p,{\iota}_p,\Delta_p)$ for each process $p$, with finite set of states $S_p$, initial state ${\iota}_p \in S_p$, and transition relation $\Delta_p \subseteq S_p \times {\mathit{Act}_{p}({\mathit{Msg}})} \times S_p$. Moreover, we have an acceptance condition ${\mathit{Acc}}\subseteq \prod_{p \in {P}} S_p$.

Given a transition $t = (s,{\alpha},s') \in \Delta_p$, we let ${\mathit{source}}(t) = s$ and ${\mathit{target}}(t) = s'$ denote the source and target states of $t$. In addition, if ${\alpha}= {\langlea\rangle}$, then $t$ is an *internal transition* and we let ${\mathit{label}}(t) = a$. If ${\alpha}= {\langlea,!_{q}{m}\rangle}$, then $t$ is a *send transition* and we let ${\mathit{label}}(t) = a$, ${\mathit{msg}}(t) = {m}$, and ${\mathit{receiver}}(t) = q$. Finally, if ${\alpha}= {\langlea,?_{q}{m}\rangle}$, then $t$ is a *receive transition* with ${\mathit{label}}(t) = a$, ${\mathit{msg}}(t) = {m}$, and ${\mathit{sender}}(t) = q$.

A *run* $\rho$ of ${\mathcal{A}}$ on an MSC $M = (E,{\rightarrow},{\lhd},{\mathit{loc}},\lambda) \in {\mathbb{MSC}({P},\Sigma)}$ is a mapping associating with each event $e \in E_p$ a transition $\rho(e) \in \Delta_p$, and satisfying the following conditions:

1.  for all events $e \in E$, we have ${\mathit{label}}(\rho(e)) = \lambda(e)$,

2.  for all ${\rightarrow}$-minimal events $e \in E$, we have ${\mathit{source}}(\rho(e))={\iota}_{p}$, where $p = {\mathit{loc}}(e)$,

3.  for all process edges $(e,f) \in {{\rightarrow}}$, 