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Abstract. This paper compares the expressiveness of ambient calculi against different dialects of the pi-calculus. Cardelli and Gordon encoded the asynchronous pi-calculus into their calculus of Mobile Ambients (MA). Zimmer has shown that the synchronous pi-calculus without choice can be encoded in pure (no communication) Safe Ambients. We show that pure MA without restriction has symmetric electoral systems, that is, it is possible to solve the problem of electing a leader in a symmetric network. By the work of Palamidessi, this implies that pure MA without restriction is not encodable (under certain conditions) in the picalculus with separate choice. We adapt the work of Carbone and Maffeis to show that pure MA cannot be encoded (under certain other conditions) into the pi-calculus with mixed choice (but without matching).

We define a new, output-based encoding of the λ-calculus into the asynchronous π-calculusenriched with pairing -that has its origin in mathematical logic, and show that this encoding respects one-step spine-reduction up to substitution, and that normal substitution is respected up to similarity. We will also show that it fully encodes lazy reduction of closed terms, in that term-substitution as well as each reduction step are modelled up to similarity. We then define a notion of type assignment for the π-calculus that uses the type constructor →, and show that all Curry-assignable types are preserved by the encoding.

International audienceWe compare the expressive power of process calculi by studying the problem of electing a leader in a symmetric network of processes. We consider the \pi-calculus with mixed choice, separate choice and internal mobility, value-passing CCS and Mobile Ambients, together with other ambient calculi (Safe Ambients, the Push and Pull Ambient Calculus and Boxed Ambients). We provide a unified approach for all these calculi using reduction semantics

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