Local safety and local liveness for distributed systems

Abstract : We introduce local safety and local liveness for distributed systems whose executions are modeled by Mazurkiewicz traces. We characterize local safety by local closure and local liveness by local density. Restricting to first-order definable properties, we prove a decomposition theorem in the spirit of the separation theorem for linear temporal logic. We then characterize local safety and local liveness by means of canonical local temporal logic formulae.