We give a labeled characterization of barbed congruence in asynchronous pi-calculus, which, unlike previous characterizations, does not use the matching construct. In absence of matching the observer cannot directly distinguish two names. In asynchronous pi-calculus the fact that two names are indistinguishable can be modeled by means of Honda and Yoshida's notion of equator. Our labeled characterization is based on such a notion. As an application of our theory we provide a fully abstract encoding with respect to barbed congruence of external mobility (communication of free names) in terms of internal mobility (communication of private names).
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