Abstract. We introduce PEP, the Post Embedding Problem, a variant of PCP where one compares strings with the subword relation, and PEP reg, a further variant where solutions are constrained and must belong to a given regular language. PEP reg is decidable but not primitive recursive. This entails the decidability of reachability for unidirectional systems with one reliable and one lossy channel. Keywords: Post correspondence problem; Lossy channel systems; Higman’s Lemma. 1

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 proved to be decidable. Further, the main forms of strong bisimilarity for higher-order processes (higher-order bisimilarity, context bisimilarity, normal bisimilarity, barbed congruence) coincide. They also coincide with their asynchronous versions. A sound and complete axiomatization of bisimilarity is given. Finally, bisimilarity is shown to become undecidable if at least four static (i.e., top-level) restrictions are added to the calculus.

Lossy channel systems are systems of finite state automata that communicate via unreliable unbounded fifo channels. They are an important computational model because of the role they play in the algorithmic verification of communication protocols.

Lossy channel systems (LCS's) are systems of finite state automata that communicate via unreliable unbounded fifo channels. In order to circumvent the undecidability of model checking for nondeterministic LCS's, probabilistic models have been introduced, where it can be decided whether a linear-time property holds almost surely. However, such fully probabilistic systems are not a faithful model of nondeterministic protocols.