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 propose two possible semantics for the output operation: the former,
that we call {\em ordered}, defines the output as an operation that returns
when the message has reached the shared data space; the latter, that we call
{\em unordered}, returns just after sending the message to the tuple
space.
We compare the expressive power of the language under both the
interpretations sketched above, using Turing equivalence as
a yardstick.
In the ordered case, we show that the language is Turing powerful
by providing the encoding of any Random Access Machine in our
process algebra.
Quite amazingly, when turning to the unordered semantics, the
language is no longer Turing powerful: this is shown by reducing
termination of processes to deadlock detection on P/T nets,
which is known to be a decidable property.