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The $\pi$-calculus is a process algebra where agents interact by sendingcommunication links to each other via noiseless communication channels. Takinginto account the reality of noisy channels, an extension of the $\pi$-calculus,called the $\pi_N$-calculus, has been introduced recently. In this paper, wepresent an early transitional semantics of the $\pi_N$-calculus, which is not adirectly translated version of the late semantics of $\pi_N$, and then extendsix kinds of behavioral equivalences consisting of reduction bisimilarity,barbed bisimilarity, barbed equivalence, barbed congruence, bisimilarity, andfull bisimilarity into the $\pi_N$-calculus. Such behavioral equivalences arecast in a hierarchy, which is helpful to verify behavioral equivalence of twoagents. In particular, we show that due to the noisy nature of channels, thecoincidence of bisimilarity and barbed equivalence, as well as the coincidenceof full bisimilarity and barbed congruence, in the $\pi$-calculus does not holdin $\pi_N$.

A hierarchy of behavioral equivalences in the $\pi$-calculus with noisy channels