# Questions tagged [decidability]

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### 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 ...
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-...
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 ...
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 ...
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 (...
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 ...
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 ...
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 ...
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 ...
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?
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 ...
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 ...