FZustand

FZustand is a term used in German-language formal methods to denote a state that satisfies a property represented by a predicate F. The idea is to tag certain states of a model as belonging to a distinguished class defined by F, such as a safety or completion condition. In a system with states Q, the FZustand set is typically defined as Z_F = { q ∈ Q | F(q) is true }.

Formal characterization and usage: FZustand relies on a Boolean predicate F that assigns true or false to each state. Analyzing Z_F allows verification tasks to focus on states where the desired condition holds, for example when checking reachability, safety, or liveness properties. In model checking or program analysis, one may examine whether reachable states intersect Z_F, or whether all executions eventually reach a state in Z_F.

Relationship to other terms: The concept is related to, but not identical with, the general notion of a final state or terminal state. In some texts, Finalzustand or Final state is used to denote a terminal state with no outgoing transitions, while FZustand emphasizes a property-based classification rather than terminality. The term FZustand is thus somewhat context-dependent and can vary in definition across domains.

Examples: In a simple workflow model, F might express “the transaction is completed.” The corresponding FZustand set would consist of states representing completed executions, and verification might check that every path leads to a state in Z_F.

See also: Zustand, Finalzustand, Automata theory, Model checking, Formal verification.