On the Turing equivalence of Linda coordination primitives

We introduce a process algebra containing the coordination primitives of Linda (asynchronous communication via a shared data space, read operation, non-blocking test operators on the shared space). We compare two possible semantics for the output operation: the former, we call ordered, defines the output as an operation that returns when the message has reached the shared data space; the latter, we call unordered, returns just after sending the message to the tuple space. The process algebra under the ordered semantics is Turing powerful, as we are able to program any Random Access Machine. The main result of the paper is that the process algebra under the unordered semantics is not Turing powerful. This result is achieved by resorting to a net semantics in terms of contextual nets (P/T nets with inhibitor and read arcs), and showing that there exists a deadlock-preserving simulation of such nets by finite P/T nets, a formalism where termination is decidable.