Thread Algebra with Multi-Level Strategies

In a previous paper, we developed an algebraic theory of threads and multi-threads based on strategic interleaving. This theory includes a number of plausible interleaving strategies on thread vectors. The strategic interleaving of a thread vector constitutes a multi-thread. Several multi-threads may exist concurrently on a single host in a network, several host behaviors may exist concurrently in a single network on the internet, etc. Strategic interleaving is also present at these other levels. In the current paper, we extend the theory developed so far with features to cover multi-level strategic interleaving. We use the resulting theory to develop a simplified formal representation schema of systems that consist of several multi-threaded programs on various hosts in different networks. We also investigate the connections of the resulting theory with the algebraic theory of processes known as ACP.