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Expressing First-order Pi-calculus in Higher-order CCS

In the research field of process calculi, encoding between different calculi is an effective way to compare the expressive power of them and can shed light on the essence of where the difference lies. Thomsen and Sangiorgi have worked on the higher-order calculi (higher-order CCS and higherorder pi-calculus, respectively) and the encoding to and from first-order pi-calculus. But the work is not complete, in that the encoding of first-order pi-calculus with higher-order CCS is missing. In this paper, we try to settle this part. We first review the results of related work. Then we introduce the index technique that is used to abstract from extra silent actions, which are brought about during the encoding, in correspondence of operational semantics of first-order pi-calculus processes and higher-order CCS processes encoding them. The encoding strategy (an indexed version of the encoding by Thomsen but without renaming) is then presented, where indexed wires play a crucial role. To arrive at the full abstraction property, we introduce the indexed wired processes, and the indexed wired factorization theorem is presented. Then the coincidence between the indexed wired bisimilarity and indexed context bisimilarity on indexed wired processes is obtained. After that, we prove the major result of the encoding, the full abstraction theorem, with respect to indexed ground bisimilarity (first-order pi-calculus) and indexed context bisimilarity (higher-order CCS). Finally, we make some discussions on our work and suggest some future work.