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Questions related to computability theory, a.k.a. recursion theory

2
votes
Program 2 can be a FlooP interpreter. When started in a state in which the source code of a FlooP program is in internal memory, it will execute it. It can do this by keeping its internal memory subdi …
answered Nov 10 '21 by reinierpost
2
votes
We can't. Infinitely many different PDAs for the same DCFL exist. In 1997, Géraud Sénizergues proved that equivalence of DCFLs is decidable, and he was awarded the Gödel Prize for it. For general co …
answered Jul 14 '17 by reinierpost
4
votes
No, it is not too strong. We fundamentally conceive of computation as an activity with unlimited resources. For instance, take a very popular and simple algorithm such as long division. It takes two a …
answered Nov 20 '18 by reinierpost
1
vote
In imperative programming, state machines are quite common, and they usually look more or less like the following pseudo-code: state = INITIAL_STATE; while (token = read_an_input_token(input)) { …
answered May 9 '18 by reinierpost
2
votes
Others have provided plenty of good answers, but they don't explicitly mention one caveat that once confused me a lot: Turing completeness doesn't imply that a language can express arbitrary computabl …
answered Oct 3 '16 by reinierpost
13
votes
The Church–Turing thesis doesn't need to be taken as an article of faith; it probably makes more sense to regard it as stating a description, a definition, of what we mean by the term "computation", a …
answered Apr 5 '16 by reinierpost
1
vote
At the time Turing machines were invented, computers were women who would execute calculations on scrap paper. That is the notion of computation Turing machines express. Their tape isn't part of them …
answered Apr 23 '13 by reinierpost
1
vote
A nondeterministic machine leaves choice points open: points at which multiple continuations can be taken. Two ways to 'determinize' this: backtracking: follow the tree of possibilities in depth-firs …
answered Aug 19 '21 by reinierpost