The tag has no usage guidance.

learn more… | top users | synonyms

-3
votes
1answer
62 views

Is every countably infinite language recursive?

We'll say the alphabet for the languages is finite, say {0,1}.
1
vote
2answers
63 views

Can a regular language have uncountably many strings?

Obviously it can have a countably infinite number of strings. (Take the language descibed by the regular expression 0* as an example.) But can a RL have uncountably many strings? I'm leaning toward no,...
1
vote
3answers
92 views

Is there a non-recursive and uncountable language L?

Does there exist a non-recursive language, L, such that the cardinality of L is uncountable? I would really like an explanation as to why this question is true or false because at the moment, I have ...
4
votes
3answers
71 views

Showing that the number of primitive-recursion programs for each function is countably-infinite

Problem Statement Prove that if a function $f$ is primitive recursive, then there are countably infinite number of primitive recursive definitions of $f$ Yes, this is a homework question. My ...
0
votes
2answers
122 views

Countability of a binary tree

Problem: We'll define a binary tree as a tree where the degree of every internal node is exactly 3. Show that the set of all binary trees is countable. My attempt: A set is countable if it is ...
1
vote
2answers
236 views

Number of finite strings over a countably infinite alphabet

If the alphabet is countably infinite, then is the number of finite-length strings over this alphabet countably or uncountably infinite?
2
votes
1answer
483 views

Can a recursive language be uncountable?

Does there exist a recursive language $L$ whose cardinality is uncountable? I would like to have an explanation whether Turing Machine can encode uncountable languages and whether we can use this to ...
1
vote
1answer
51 views

Is the union of finite and infinite sequences over alphabet of length 1 countable?

Is the union of finite and countably infinite sequence over alphabet $\Sigma=\{1\}$, countably infinite as well? I understand this is similar a question to the one of finite and countably infinite ...
1
vote
1answer
68 views

Countability union of all finite and countably infinite sequences over finite alphabet

Is the set of all finite and countably infinite sequences over $\{0,1\}$ countable? From my analysis, I think it is countable. I think of this as the set of all strings from a finite alphabet $\Sigma=...
-1
votes
1answer
111 views

Deciding Countability of Languages

Suppose we have given $\Sigma=\{a,b\}$, Which one of the following set is not countable (a) Set of all languages over $\Sigma$ (b) Set of all regular languages over $\Sigma$ (c) Set of ...
1
vote
1answer
78 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?
0
votes
1answer
87 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 ...
1
vote
2answers
190 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 ...
2
votes
1answer
104 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?
1
vote
2answers
564 views

Is the set of all valid C programs countable?

Is the set of all syntactically valid C programs countable or uncountable?
2
votes
1answer
424 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
votes
1answer
183 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 $...
-2
votes
3answers
206 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?
3
votes
2answers
766 views

Cantor's diagonal method in simple terms?

Could anyone please explain Cantor's diagonalization principle in simple terms?
6
votes
1answer
578 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 ...