Future path-components in directed topology

The global states of complex systems often form pospaces, topological spaces equipped with compatible partial orders reflecting causal relationships between the states. The calculation of tractable invariants on such pospaces can reveal critical system behavior unseen by ordinary invariants on the underlying spaces, thereby sometimes cirumventing the state space problem bedevilling static analysis. We introduce a practical technique for calculating future path-components, algebraic invariants on pospaces of states and hence tractable descriptions of the qualitative behavior of concurrent processes.