Divergence

In computer science, a computation is said to diverge if it does not terminate or terminates in an exceptional state. Otherwise it is said to converge. In domains where computations are expected to be infinite, such as process calculi, a computation is said to diverge if it fails to be productive (i.e. to continue producing an action within a finite amount of time). Definitions Various subfields of computer science use varying, but mathematically precise, definitions of what it means for a computation to converge or diverge. Rewriting In abstract rewriting, an abstract rewriting system is called convergent if it is both confluent and terminating. The notation t ↓ n means that t reduces to normal form n in zero or more reductions, t↓ means t reduces to some normal form in zero or more reductions, and t↑ means t does not reduce to a normal form; the latter is impossible in a terminating rewriting system.