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1answer
20 views

Are all languages generate by Turing machines countable?

Are all languages generate by Turing machines countable? I know that the set of all TMs are countable, but what about the languages that they generate?
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1answer
60 views

Prove that the set of all total functions is countable [closed]

I'm stuck on a theory/set proof question: $S$ is the set of all total functions $f : \{0, 1\} \to \mathbb{N}$ (natural numbers), prove that S is countable. I have found a sample solution ...
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0answers
19 views

Automata Theory countably and uncountably infinite [duplicate]

I'm going over some of the pre-requisite math regarding Automata theory, and finite representations. I read the following: If ∑ is a finite alphabet the set of all strings over the alphabet (∑*) is ...
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2answers
115 views

Why are pushdown automata countable? [closed]

I began a chapter in a textbook on computational theory where they begin to talk about decidable languages. The problems in this section are pretty confusing and I honestly don't know how to begin ...
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1answer
67 views

Undecidability and Countability

This question is prompted by Undecidable unary languages (also known as Tally languages) How does the countability of a language imply (un)decidability?
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2answers
247 views

Is the set of all valid C programs countable?

Is the set of all syntactically valid C programs countable or uncountable?
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1answer
144 views

Where am I wrong?: “countability” and “recursive enumerability”

I have a a few fundamental doubts in recursive enumerability and countability and below, I have written what I understand them to be with proofs. But there are contradictions at the end. What is wrong ...
2
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1answer
113 views

How to prove “The power set of a countable set must be uncountable”?

I'm not sure if this statement is correct, but my friend said so. The problem arose from this T/F question: Let $F=\{f: f$ be a primitive recursive function from $\mathbb{N}$ to $\mathbb{N}\}$, then ...
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3answers
149 views

If set of TM's is not countable?

I was reading about counting principle related to TOC. I understand that the set of TMs are countable infinity. I couldn't understand the significance of it. What is its not countable?
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2answers
475 views

Cantor's diagonal method in simple terms?

Could anyone please explain Cantor's diagonalization principle in simple terms?
3
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1answer
252 views

Does there exist any work on creating a Real Number/Probability Theory Framework in COQ?

COQ is an interactive theorem prover that uses the calculus of inductive constructions, i.e. it relies heavily on inductive types. Using those, discrete structures like natural numbers, rational ...