# Questions tagged [semi-decidability]

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### Semidecidable Turing Machine for L={a,b}*

I have a language L={a,b}* over the alphabet {a,b}. How do I build a Turing Machine that semidecides but does not decide this language? Me and my classmates tried using the macro language to solve ...
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### Is this language Recursively Enumerable or Not RE?

$L = \{\langle M, k\rangle : M\;\text{is a Turing Machine and } |\{w \in L(M) : w \in a^*b^*\}| \geq k \}$ My Interpretation of language is that $L$ is a language which contains Turing machine ...
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### How can I show that a language is Turing-recognizable and decidable?

I was wondering how I can show that the language $\{a^n b^n c^n \mid n \geq 0 \}$ is Turing-recognizable. Also, if it is Turing-decidable?
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### Efficient algorithm to determine if a lambda calculus term is equivalent to one without a given free variable

Consider the following problem: given a lambda calculus term $t$ and free variable $v$ determine whether $\phi(t,v)$, where $\phi(t,v) := \exists t'. t' \equiv t \land v \notin FV(t')$. This problem ...
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### How To Show That B is Semi-Decidable Given A

I am preparing for my Computational Theory final and ran into this exact problem : B={ x | there exists a prefix of x that is in A}. Show that B is semi-decidable. In other words, you need to ...
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### Need help understanding what co-recursively enumerable means

Lets say I have a set: $L = \{\langle G \rangle | L(G) = \Sigma^{\star}\}$ and the question asks if it is co-RE. I know that if something is co-RE, it halts on every input not in L but may or may not ...
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### Proof that total computable functions are not enumerable

In an answer to this question, a sketch of the proof that total computable functions are not enumerable is made: Because of diagonalization. If $(f_e:e \in N)$ was a computable enumeration of all ...
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### Determining if given languages are regular or recursively enumerable

I came across following problem: Suppose $L_1$ and $L_2$ are two languages, $M$ is a Turing machine $L_1 =\{M|M$ accepts at most 2016 strings$\}$ $L_2=\{M|M$ accepts at least 2016 strings$\}$ ...
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### When does an extendible 1:1 p.c. function have a 1:1 computable extension?

A partial computable function $\varphi_e$, defined on a c.e. set $W_e$, is called extendible if there exists some computable function $f$ which extends $\varphi_e$, i.e. $\varphi_e(W_e) = f(W_e)$. My ...
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### Why is the intersection of these two Languages Recursively Enumerable, not Recursive?

I am only several days exposed to computational theory, so my understanding is quite slim: in a question, it says that for a regular language L1 and a recursively enumerable but not recursive language ...
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### If Q1 and Q2 are countably enumerable, then is Q1\Q2 countably enumerable?

If Q1 and Q2 are countably enumerable, then is Q1\Q2 countably enumerable? I am reading a text where they claim that this is not the case and ask the reader to come up with a counter example. Can ...
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### Closure of Turing-recognizable languages under homomorphism

I've proven that the Turing-recognizable languages are closed under concatenation and I need to show that they are closed under homomorphism. But what's really the difference? Doesn't closure under ...
### Show that $L = L_\phi \cup L_{\{\sum^*\}} \notin RE$ with Rice theorem
Show that $L = L_\phi \cup L_{\{\sum^*\}} \notin RE$ with Rice theorem. Well I did show that with reduction, by using $HP'$. Simply by creating a function from $f(\langle M \rangle, x) = (M')$ Thus,...