# Questions tagged [nondeterminism]

Questions about automata, formal grammars or other computation-models that specifically relate to the use of nondeterminism. Not to be confused with randomness or ambiguity!

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### Show that {xy : x ∈ {a}*, y ∈ {b}*, |x| = |y|} is a not a regular language

I have been asked as an exercise how to prove that this is not a regular language. first I tried to use the pumping lemma, but I got stucked. Th erxercise hust said to prove thata this isn't a regular ...
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### My proof for equivalence of DFA and NFA

I came up with this proof for the following theorem: If $L$ is a language produced by an nfa, then there exists a dfa $M$ where $L(M) = L$. Is it correct? If it's not, what are the flaws of my proof,...
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### Is the language "substrings of a regular language that are over half the length of the superstring" regular?

We say $x$ is a majority substring of $y$ if $y \in \Sigma^* x \Sigma^*$ and $|x| \geq \frac 12|y|$. If $B$ is a regular language, is the set of majority substrings of $B$ regular? I was provided the ...
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### Computation branches on NTM

I would like to run the following string $w=011101$ on the following NTM and figure out the respective computation branches and whether it accepts or rejects that string. $\text{Start: }(q_0) 011101$ ...
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### Can a non-deterministic finite automaton die out before reading the entire string?

I am new to automata theory and have a problem that I want to solve. We have to design an NFA that starts with "ab". I have the solution and it is given by: However, my problem is: If the ...
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### Converting non-deterministic TM to deterministic TM using poly time SAT solver

Suppose there exist deterministic turing machine $M$ that could solve SAT in polynomial time. How can we construct a deterministic TM $N$ ,by using SAT solver $M$, that take as input a non-...
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### Showing NP is closed under intersection

I was solving the following question: Show that $L_1 \cap L_2 \in \mathrm{NP}$ for $L_1,L_2 \in \mathrm{NP}$. I came a cross this solution on the internet which is: $M$: On input $w$ — Run $M_1$ ...
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### Efficient algorithm to find a rejecting input of an NFA

I cannot think of a PTIME algorithm to find a rejecting input of an NFA. While it is possible to efficiently find a rejecting input for a DFA, converting an NFA to DFA is too expensive. The algorithm ...
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### Is there distinction between $(C/poly)\cap(coC/poly)$ and $(C\cap coC)/poly$?

Let $C$ be an uniform complexity class for example $NL$ or $NP$. Is there distinction between $(C/poly)\cap(coC/poly)$ and $(C\cap coC)/poly$?
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### Generalization of automaton - Sipser example 1.33

I am trying to construct a nfa that generalizes Example 1.33 found in the book Introduction to the Theory of Computation by Sipser, but I am quite sure that my transition function is wrong. I'd like ...
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### How are useless states created NFA to DFA

So I understand how to convert an NFA to a DFA, however my question is, on a conceptual level, how and why are useless states created, and how can you (if there is a way) convert an NFA to a DFA ...
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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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### Is it incorrect too say that this function problem cannot be in $FNP$?

Decision Problem: Is $2^k$ + $M$ NOT a prime? $K$ and $M$ are our inputs represented as integers. Function Variant: Output the result of $2^k$ + $m$ We can consider, $M$ = $0$. Proof that calculating ...
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### Formal definition of non deterministic PDA

How would you convert the following formal definition of deterministic pushdown automata into non deterministic ? Deterministic PDAs In general terms, a deterministic PDA is one in which there is at ...
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### Nondeterministic Turing Machine for $L^*$

If $T$ is a Turing Machine that accept a language $L$, I want to define a Turing Machine $T'$ such that accepts the language $L^*$. An approach: $T'$ is a nondeterministic Turing Machine which has ...
### Can an $NDTM$ simultaneously perform a set of operations on all strings of a given length?
Can an $NDTM$ perform a set of operations on all strings of a given length $b$, at the same time? Aka can it operate on all strings of a given length by doing something like: spawn $2^b$ branches then ...