Questions tagged [decidability]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
-1
votes
1answer
27 views

Does Turing machine move left on particular input?

We know that RE language is the collection of unrestricted grammar which is known as type-0 grammar that's why emptiness, finiteness of every RE languages is undecidable. My question is how I check ...
0
votes
1answer
53 views

Why is it undecidable to check the emptiness and finiteness of a context-sensitive grammar?

Context-sensitive languages have context-sensitive grammars, and context-free languages have context-free grammars. Using context-free grammars, we can decide the finiteness and emptiness of context-...
-1
votes
0answers
21 views

TM decidable or undecidable problem?

Question: Explain why the following problems are decidable or undecidable (Using rice's theorem where possible). Does the language accepted by a Turing machine contain an even-length word? Holds a ...
0
votes
0answers
30 views

Why linear bounded automata emptiness and finiteness isn't decidable? [duplicate]

We know that linear bounded automata has tape size based on input size which is limited. Context-sensitive languages are accepted by LBA. My question is that if LBA has limited tape size why it's ...
-1
votes
0answers
32 views

halting turing machine which never hang(HTM)$<$ Recursive [closed]

We know that TM with no write option have less power than standard turing machine. My teacher said that: $1.$halting turing machine which never hang(HTM)$<$ Recursive $2.$linear-bounded automaton (...
0
votes
1answer
136 views

Why REC languages is undecidable under emptiness and finiteness?

Membership problem of Recursive languages are decidable. My approach: Let $L$ be a recursive language and $M$ be the Turing Machine that accepts it. For string $w,$ if $w ∈ L,$ then $M$ halts in ...
0
votes
0answers
42 views

Whether $L(G)=L(R)$ is decidable for DCFL and CFL?

Let $G_1$ be the context free grammar and $R$ be regular language. Now I have to check whether $L(G_1)=L(R)$ is decidable or not? My approach $\overline{L(G_1)}=\overline{L(R)}$. Now $L(G_1)$ not ...
0
votes
1answer
76 views

Rice theorem could apply except RE language?

You know that Rice theorem is applicable to check decidability of RE language. Also we know that all regular, deterministic context free, context free, recursive languages are RE languages. $Q_1:$ So ...
0
votes
2answers
100 views

Regularity of CFG and DCFL

I read that it is undecidable whether, given a CFG $G$, $L(G)$ is regular. And there exists no algorithm that, given a CFG $G$ such that $L(G)$ is regular, outputs a DFA that accepts $L(G)$. My ...
0
votes
1answer
28 views

Why finiteness problem of CFL is decidable?

We know that every $CFL$ has infinite configuration space. Due to this equality problem is undecidable. But why finiteness property is decidable inspite having infinite configuration space?
0
votes
1answer
74 views

Reduction from undecidability, decidability to decididabilty

If given any two language both $L_1$ and $L_2$ are decidable then why both $L_1\leq_m^\mathsf{}L_2$ and $L_2\leq_m^\mathsf{}L_1$ are false. Please provide easy explanation with any counterexample ...
0
votes
0answers
28 views

Is this language in RE?

Given the following language: $$L=\left \{ <M> | \exists L \in R \quad s.t \quad L(M)\subseteq L \right \}$$ I need to determine it's compuation class(R or RE). I used Rice Theorem as follows to ...
0
votes
0answers
15 views

Loop in control flow graph of a program versus checking whether program goes into infinite loop or not

Which of these is true or false. 1)If Control Flow graph(CFG) doesn't contain any loop, the program will never go into infinite loop. 2)If CFG contains loop, the program may or may not go into ...
-1
votes
1answer
46 views

How to determine whether this language is regular?

I've encountered this question recently: Given $\Sigma=\{\sigma_1, \sigma_2, ..., \sigma_n\}$ and $n\ge 2$, determine whether the following language is regular or not: $$ L_1=\{w\in\Sigma^*|for \ 1 \...
0
votes
1answer
28 views

Prove decidable

L={⟨M⟩: M is a DFA and for each string in L(M) the number of 1s is more than or equal to the number of 0s } T = "On input where M is encoded DFA" ...
0
votes
0answers
23 views

The role of diagonalization - asymmetry between TM and Recursion Theory

This might be a slightly strange or irrelevant question. My apologies if it is. I'll try to formulate it the best I can. First, here is an hypothesis: diagonalization is syatematically used to prove ...
2
votes
1answer
41 views

Effectively decidable vs. noneffectively (or ineffectively) decidable

The introduction of https://www.sciencedirect.com/science/article/pii/0001870882900482 starts with the following sentence: The word problem for commutative semigroups is effectively decidable. I ...
1
vote
2answers
59 views

Prove that { $\langle M \rangle$ : $M$ is a TM and $L(M)$ is decidable} is undecidable

So I want to prove that $$ \big\{\langle M \rangle : \text{ M is a TM and } L(M) \text{ is decidable} \big\}$$ is undecidable. To do so I want to reduce it from$\ \overline{A_{TM}}$ with a function ...
1
vote
1answer
31 views

Decidability of $\{⟨G⟩ \mid \text{$G$ is CFG and $L(G) ⊈ \Sigma^+$}\}$

I want to prove that the following language is decidable: $$\mathit{SEQ}_{\mathit{CFG}} = \{⟨G⟩ \mid \text{$G$ is CFG and $L(G) ⊈ L$}\}, \text{ where } L = \Sigma^* - \{\epsilon\}$$ So, I think about ...