Questions tagged [infinity]
7 questions
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Are any "standard" complexity classes uncountably infinite?
(This is a somewhat fuzzy question.)
I believe that most of the "standard" complexity classes that one comes across in complexity theory are countably infinite, because they are defined in terms of decision problems that can be solved by Turing…
tparker
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Determining if an NFA accepts an infinite language in polynomial time
Can we determine in polynomial time if the language accepted by an NFA is infinite?
The case of DFA is simple, but converting an NFA to a DFA may take exponential time.
Also, I ran into this post,
Determine if an NFA accepts infinite language in…
Avi Tal
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3
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Infinitely-taped (& "headed"!) Turing Machine: "Stronger" Than Standard
Multi-taped Turing machine are equivalent to the standard single-taped variety; that much I know and can prove to a level of rigor that satisfies me; so long as there are finitely many tapes, I can think of how to simulate a model like that on a…
AnonA
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can a model of computation with infinitely many states be nontrivially decidable?
i'm trying to make a game in which the player faces an infinite (finitely specified) series of enemies and has to specify a strategy that provably defeats all of them (ie defeats enemy n in finite time for all n). i'm intending to do it by having…
Silver
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5 answers
If the set of Turing machines is countably infinite, how can a Turing machine always have a finite set of states?
I have only begun studying this subject and have only completed the first few chapters of the Elements of the Theory of Computation.
I have seen the answers (on this site and elsewhere) saying that the set of all Turing machines is countably…
Wisdom Iwueze
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Sets of problems in different models of computation and cardinality
In university, I was taught the computational model hierarchy given in the following figure: https://devopedia.org/images/article/210/7090.1571152901.jpg
Essentially, Pushdown Automata (PDA) can solve more problems (i.e. recognize more languages)…
Enk9456
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Can a program that terminates have a running time of infinity? (Or not have an upper bound)
Can we have an algorithm that takes some input and does something random to it (in such a way that the algorithm does terminate) which does not have a worst-case running time upper-bound?
A (non-)example which shows what I mean: If let's say that my…
proof-of-correctness
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