# Tagged Questions

Automata Theory, including abstract machines, grammars, parsing, grammatical inference, transducers, and finite-state techniques

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### Let $LOOP_{TM}$ be descriptor language of all touring machines that won't halt for any input. Show reduction of $HALT_{TM}$ to $LOOP_{TM}$

Question from Homework that I'm having difficult to answer on: Let $LOOP_{TM} = \{\langle M\rangle \mid \text{M is a TM that does not halt on any input w}\}$ Let $LOOP_{TM}$ be descriptor ...
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### Converting an NFA to DFA

I am atttempting to convert an NFA into an equivalent DFA. I did it, but i am not sure if it is correct. If anyone can please take a look at let me know if it is correct or if there is something wrong ...
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### Finding regular expressions for which a given Turing machine halts and accepts, halts and rejects, and diverges.

Consider the Turing machine M = (Q,Σ,Γ,δ,q,F) F = {t} Q = {q,r,s,t,v,x} Σ = {a,b,c} Γ = {B,a,b,c} δ = [q,a,q,a,R] [q,b,q,b,R] [q,c,v,b,R] [q,B,r,B,L] [r,a,s,B,L] [r,b,s,B,L] [r,c,s,B,L] ...
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### Graph and language/automaton equivalence

I'm looking for a reference rather than an answer. I think I'm just not Googling the right combination of terms. I imagine that there is a class of graphs which is equivalent to some class of ...
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### Languages and their Regular Expressions - Automata

I am working on some Automata practice problems. I am working a 2 part question. Here it is: Let $\Sigma = \{a,b\}$ be an alphabet. Let $L = \left\{w \in \Sigma^* \mid n_a(w) \le 4\right\}$ ...
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### Pumping Lemma proof and the union/intersection of regular and non-regular languages

I am still learning the pumping lemma. I have a problem for which I used it. I used it on the first part (a) but I am unsure if it is correct. Parts b-d, I am not sure how to do it. I created a dfa ...
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### Using the Pumping Lemma To Prove A Language Is Not Regular

I am taking a Automata class and we just went over the Pumping Lemma. Initially, it did not make sense. I am still not fully comfortable but I have started trying to use it to prove that a language is ...
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### How to construct a DFA for truncate the rightmost symbol from a given string?

If I have a truncate operation defined which removes the rightmost symbol from a string ,for instance I have a string say aababb so it removes the rightmost symbol b and the output is aabab. so how ...
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### How can a Moore machine be converted into an equivalent Mealy machine and vice versa?

Moore machine is a finite-state machine whose output values are determined by its current state only. Mealy machine is a finite-state machine whose output values are determined both by its current ...
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### Trouble with induction on the length of a word

In the accepted solution of the question If L is regular, prove that $\sqrt{L}=\{w:ww\in L\}$ is regular the answerer made the claim that "What's left is to show that $δ ′ (q_{0}' ,w)=h$ , which can ...
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### How to construct the DFA for the following question?

Given $L=\{ab^5 w b^4 \}$ where $w=\{a,b\}^*$. I am not able to construct it, I tried it but getting problems with the transitions for input symbol a.
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### Learning finite automata from symbol set and given sample

Good day. We have a finite automaton F1, for example, . We need to get automaton F2 that accepts strings like accepted by ...
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### NFA to DFA and Regular Expression

The truth is that my teacher gave us a homework, and I wanted to ask you if I did this right. What I have to do is answer the following questions given the following NFA. Why is this an NFA? What ...
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### nth-root of continued fraction with Raney transducers

There are some algorithms for doing basic arithmetic by using regular continued fraction expansions. These algorithms are mainly due to Gosper (1972) and Raney (1973). These two approaches use ...