Divergence (computer science)
In computer science, a computation is said to diverge if it does not terminate or terminates in an exceptional state.:377 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).
Various subfields of computer science use varying, but mathematically precise, definitions of what it means for a computation to converge or diverge.
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.
In the calculus of communicating sequential processes, divergence is a drastic situation where a process performs an endless series of hidden actions. For example, consider the following process, defined by CSP notation:
The traces of this process are defined as:
Now, consider the following process, which conceals the tick event of the Clock process:
By definition, P is called a divergent process.
- Baader, Franz; Nipkow, Tobias (1998). Term Rewriting and All That. Cambridge University Press.
- Pierce, Benjamin C. (2002). Types and Programming Languages. MIT Press.
- J. M. R. Martin and S. A. Jassim (1997). "How to Design Deadlock-Free Networks Using CSP and Verification Tools: A Tutorial Introduction" in Proceedings of the WoTUG-20.