# Questions tagged [automata]

Questions about mathematical devices that read an input stream symbol by symbol and use a state transition map to produce an output stream, maybe using secondary storage.

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### What are the practical examples of Semidecidable problems? Is NP problem a semidecidable problem?

I am going through a Turing machine topic. I know about decidable, semi decidable, and decidable problems. But honestly speaking, I did not get any practical examples of Semidecidable problems. Can ...
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### A language that is not context free

I working through some textbook exercises, and came across a problem that I'm struggling with. Give a CFL $L$ such that $\{x|\forall y \in \Sigma^* \space xy \in L\}$ is not a CFL. I've got the idea ...
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### what is the function of a turing machine

The main question asked me to build a certain turing machine such that given a word w over {0,1}* the turing machine accepts all such words and ends in accept state with the tape string = the word ...
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### Computational power of a Turing Machine with infinite states

Consider a turing machine with infinite states. This machine is identical to a regular machine. Only that number of states could be infinite. Does this machine has more computational power than a ...
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### Show $L =$ { w $\in (a,b) ^*$| for every u substring of w, $-5\le|u|_a−|u|_b\le5\}$ is regular

I try to show that this language is regular: $L =$ { w $\in \ (a,b) ^ *$| for every u substring of w, $-5\le|u|_a−|u|_b\le5\}$ If I build a NFA and run on it every substring of w (skip other letters ...
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### Does P = NP in Cellular Automata of Hyperbolic Spaces?

I read a few years ago in this book that NP problems are tractable in the space of cellular automata in the hyperbolic plane. What does this mean? Does P = NP ...
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### Proof that $\{0|1\}^*0\{0|1\}^n$ requires at least $2^{n+1}$ states

How can you prove that any DFA accepting the language generated by the regular expression $\{0|1\}^*0\{0|1\}^n$ requires at least $2^{n+1}$ states? I first attempted induction on $n$. But I don't ...
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### In an NFA, what if there are no transitions out of an accept state but there are symbols left in the string?

Let's say I have a string 0110 and after 011 I reach an accept state (let's call the accept state "q") in an NFA. However, there is no transition mentioned in the diagram from q for the ...
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### How can I combine 2 PDA's into 1

I need to form PDA for this language: {$a^nb^m|n=m \vee n=2m$} I know the idea of building each one separately but how do I combine them into 1 PDA? LHS: for every 'a' I push 'A' inside stack and for ...
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### Is it necessary for a Push down Automaton (PDA) to have a stack?

I am given a Finite Automaton and the question is to design an Equivalent PDA for it. This is my FA: Is this PDA correct or do I need to add a stack to it? If its right when is the stack needed?
$L_1 ,L_2$ are regular language. We form a new language $L_{12}$ as follows: $L_{12}=\left \{ w_1\cdot w_2|w_1\in L_1\wedge w_2\in L_2\wedge|w_1|=|w_2| \right \}$ In this exersice I am not given any ...