terminationbased

Terminationbased is a term used to describe approaches, methods, or results that center on termination guarantees as a primary property. The word is a compound notations choice rather than a fixed industry standard, but it appears in discussions of program analysis, formal verification, and related areas to signal a focus on whether and how a process halts.

In computer science, a terminationbased perspective often accompanies or precedes correctness claims. For a function, procedure, or search procedure, practitioners seek proof or evidence that all possible execution paths terminate, sometimes before asserting full functional correctness. Termination analysis is thus a core component of many automated verifiers, static analyzers, and proof systems, helping to bound resources and ensure decidability of further analysis.

Common techniques in terminationbased work include the use of well-founded orders, structural recursion, size-change arguments, and resource or measure functions (such as decreases in a chosen metric). In term rewriting and functional programming, termination-based methods aim to prove strong normalization or total termination, ensuring that every evaluation sequence is finite.

The concept is closely related to, yet distinct from, total correctness, which combines partial correctness with termination. While safety, liveness, and soundness address other properties, terminationbased approaches specifically foreground guarantees about halting behavior. Limitations include the difficulty of proving termination for all inputs in complex systems and the possibility that some useful models resist termination proofs.

See also: termination analysis, total correctness, well-foundedness, termination proof, strong normalization, size-change termination.