"Given a program P and an input data set I there is no way in general to say if P will ever finish processing the data I".
This theorem was enounced in 1936 by A. TURING and is closely related to the incompleteness theorem of GÖDEL.
It relates also to what is known as the halting problem, thus formulated by J. CASTI: "Is there a general algorithm for determining if a program will halt ?" (1990, p.346).
While the problem has some partial and specific solutions, TURING demonstrated that no general one does exist.
As observed by A. CHURCH, uncomputability reflects undecidability and non-recursivity.
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Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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