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ALL (complexity)

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This is an old revision of this page, as edited by ABBAABABABABA (talk | contribs) at 00:26, 28 August 2023 (Added clarification on the applicability on space-complexity problems and a note on the undecidability of some of the problems in the ALL class.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

In computability and complexity theory, ALL is the class of all decision problems.

Relations to other classes

ALL contains all of the complex classes of decision problems, including RE and co-RE.

While ALL contains all decision problems, it does not necessarily cover space complexities such as PSPACE and EXPSPACE because it merely covers the problems enclosed in those classes, not the class itself.

Because there are decision problems that may or may not be undecidable due to the halting problem and the set of all Turing Machine's being higher than the amount of languages possible to process, it is impossible to solve all of these decision problems, but they are countably infinite