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The benchmark for computation is typically given as Turing computability; theability for a computation to be performed by a Turing Machine. Many languagesexploit (indirect) encodings of Turing Machines to demonstrate their ability tosupport arbitrary computation. However, these encodings are usually bysimulating the entire Turing Machine within the language, or by encoding alanguage that does an encoding or simulation itself. This second category istypical for process calculi that show an encoding of lambda-calculus (oftenwith restrictions) that in turn simulates a Turing Machine. Such approacheslead to indirect encodings of Turing Machines that are complex, unclear, andonly weakly equivalent after computation. This paper presents an approach toencoding Turing Machines into intensional process calculi that is faithful,reduction preserving, and structurally equivalent. The encoding is demonstratedin a simple asymmetric concurrent pattern calculus before generalised tosimplify infinite terms, and to show encodings into Concurrent Pattern Calculusand Psi Calculi.

An Intensional Concurrent Faithful Encoding of Turing Machines