Movingpermanent

Movingpermanent is a term used in theoretical computer science and formal methods to describe a class of state-transition behaviors in which a property, once established, becomes permanent across all future states. The concept emphasizes the distinction between temporary or transient properties and those that stabilize over time.

Formally, consider a transition system (S, →) with a predicate P ⊆ S. A system exhibits movingpermanent with respect to P if, for every initial state s0 ∈ S, there exists an index t such that for all n ≥ t, the state s_n reachable along the execution satisfies P. In other words, every execution eventually enters the closed set P and remains there indefinitely. This captures the idea of eventual invariance: after some stabilization time, the property cannot be left.

Example: In a fault-tolerant controller, once a fault is detected and the controller switches to a safe mode, the state “mode is safe” becomes permanent. After a stabilization period, further inputs do not revert the system from the safe mode.

Applications and implications: Movingpermanent is used in the analysis of stabilization properties, model checking for eventual invariants, and the design of safety-critical protocols where eventual invariance is required. It relates to invariants, persistence properties, and liveness, situating itself among broader concepts of safety and stabilization in distributed and reactive systems.

Notes: The term is not universally standardized and may be used informally in different texts. See also invariants, persistence, liveness, safety, and stabilization.