Processsatisfies

Processsatisfies is a term used in formal methods and model checking to describe the relationship between a process and a formal specification. Informally, a process P processsatisfies a specification S when every behavior of P conforms to the requirements stated in S. In notation, this is often written as P ⊨ S or P ⊨ φ for a property φ. The notion arises from semantic theories of computation where properties are expressed in temporal logic, automata, or other formal languages.

Formalization varies by modeling framework. In a transition-system model, P ⊨ φ means all traces or all maximal runs of P satisfy φ. In process calculi such as CSP or CCS, satisfaction is defined with respect to a chosen semantic model (such as traces, failures, or bisimulation), and a process that cannot exhibit any behavior violating φ is said to satisfy φ. There are often distinctions between strong satisfaction (requiring all internal steps to align with the specification) and weak satisfaction (allowing certain internal steps to be ignored).

Variants and properties. Satisfaction can be about safety properties (something bad never happens) or liveness properties (something good eventually happens), and may be evaluated under composition, abstraction, or refinement. In practice, processsatisfies is central to proving that an implementation meets its design contract, enabling modular reasoning and automated verification.

Applications. It underpins model checking, theorem proving, runtime verification, and contract-based design. Related concepts include refinement, correctness, and the distinction between satisfied specifications and violated ones.