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In higher-order process calculi the values exchanged in communications may contain processes. A core calculus of higher-order concurrency is studied; it has only the operators necessary to express higher-order communications: input prefix, process output, and parallel composition. By exhibiting a nearly deterministic encoding of Minsky machines, the calculus is shown to be Turing complete and therefore its termination problem is undecidable. Strong bisimilarity, however, is shown to bedoi:10.1109/lics.2008.8 dblp:conf/lics/LanesePSS08 fatcat:c2736otrnjfixftiu2ns65q6r4