# Questions tagged [semi-decidability]

Questions about which problems are semi-decidable, also known as recognizable or recursively enumerable.

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### How to show that these two disjoint sets $A$ and $B$ exist

I came across this problem which asks to show the existence of two disjoint Turing-recognizable sets $A$ and $B$ such that no decidable set $C$ can separate them... In this case, a set $C$ is said to ...
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### Check if language is decidable

I would like to determine if the following language is decidable or not. L = { w $\in$ $\Sigma^*$ | $T(M_w)$ is recognized by a Turing machine with at most 42 states}. I know that every finite ...
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### Is the Languague which contains all TMs which write the blank symbol at firs by the given input w decidable?

Consider the problem of determining whether a Turing machine M on an input w writes the blank symbol at first. Is this decidable ?
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### Show that for every language there exists a harder language

I came across this problem that I could not figure out... For every language $A$, there is supposed to be a language $B$ such that: $$A \leq_T B$$ but: $$B \not \leq_T A$$ If it is $A \leq_TB$ and ...
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### Is $L_2:=${$<M>$|$L(M)=\overline{A_TM}$} (un-)decidable?

I have to prove that the language $L_2:=${$<M>$|$L(M)=\overline{A_TM}$} is (un-)decidable. In a previous assignment we proved that $L_1:=${$<M>$|$L(M)=A_TM$} is undecidable. I would say ...
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### Unrestricted grammar for L={wc^id^j}

What is the unrestricted grammar describing this language?
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### Decide if a string is a member of a language that represents $P$?

For some enumeration of the complexity class P (such as this as an example: How does an enumerator for machines for languages work?), for each string 𝑝 in the enumeration, does there exist some other ...
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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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### How to prove semi-decidable = verifiable?

A language L is verifiable iff there is a two-place predicate R ⊆ Σ∗ × Σ∗ such that R is computable, and such that for all x ∈ Σ∗: x ∈ L ⇔ there exists y such that R(x, y) A language is semi-...
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### Semi-decidability of the language $\overline{L_{\epsilon}}$

Firstly consider the problem: given $L_H = \{R(M)w : M \in TM_0, w\in L(M)\}$ where $R(M)$ are encoded transitions of $M \in TM_0$. Assume for contradiction $\overline{L_{H}}$ is semi-decidable, then ...
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### Definition of an immune set

I'm reading a theorem about existence of a simple set. The definition of an immune set can be found from here A set $I\subseteq \mathbb {N}$ is called immune if $I$ ...
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### Is it decidable whether a Turing machine M will reach state q on input s?

Given a turing machine $M$, one of its states $q$ and an input word $w$, will $M$ ever reach $q$ on $w$? As we are not given anything about the word length, I assume that we have a finite length word....
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### Whether language of all turing machines is decidable or undecidable or semi-decidable?

I recently came across this language: $L=\{<TM>| \text{TM accepts recursively enumerable languages}\}$ It was asked in the question to find out whether language L is decidable or undecidable. ...
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### How do I construct a NTM that accepts the language consisting of the coding of turing machines that halt on one input?

I currently have a problem with the following question: Let $L = \{ \langle M \rangle \mid \exists w: \text{$M$halts for$w$in at most$|w|^3$steps} \}$. Construct an NTM (non-deterministic Turing ...
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### Is Rice-Shapiro theorem bidirectional?

Rice-Shapiro theorem states that version A Let $\Gamma$ be a set of computably enumerable sets, and $I = \{e : W_e \in \Gamma\}$ its index set in some admissible enumeration of c.e sets. If $I$...
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### Can the complement of an unrecognizable language be a recognizable language?

I know that complement of a language that is recursively enumerable, but not recursive, is definitely not recursively enumerable (or unrecognizable). So my question is what can be said about the ...