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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59 views

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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105 views

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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1answer
57 views

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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Number of queries for $NP^{NP}$

So a few days ago my lecturer told us that for every nondeterministic polynomial time oracle machine $M$, there is a nondeterministic polynomial time oracle machine $N$ that gives us $L(N^{3-SAT}) = L(...
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Confused about definition of a non-deterministic decider

Fallowing are some definitions from book "introduction to theory of computation" by sipser. a nondeterministic turing machine is a decider if all its computation branches halt on all input. ...
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Counting strongly connected components in a directed graph in $NL$

Define $K\_SCC = \{ \langle G, k \rangle \,:\, G \text{ has at least $k$ strongly connected components} \}$ I want to show that $K\_SCC \in NSPACE(\log n)$, using that $st-CONN$ and $\overline{st-CONN}...
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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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58 views

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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Proof that class of languages accepted by DPDA by empty stack is not closed under union

My first intuition was to take two languages $L_1$ and $L_2$ (symbol $d$ at the end is to fulfill prefix property): $$L_1 = \{ a^i b^i c^j d : i,j \ge 0 \} \mathrm{\ \ and\ \ } L_2 = \{ a^i b^j c^j d :...
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97 views

What does a non-deterministic guess "look like"?

I have been trying to understand the solution to the following problem: "Show that if $L_2$ and $L_3$ are Turing recognisable, then so is $L_2L_3 = \{w_1w_2 : w_1 \in L_2,w_2\in L_3\}$: which ...
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1answer
76 views

Can converting NFA to DFA change the language?

In the context of studying the conversion from an NFA to the equivalent DFA, I came across the following NFA, which accepts all strings over the alphabet $\{0,1\}$ which contain $01$: After I ...
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Minimal number of states for an NFA of all different words

Given $\Sigma =\{0,1,@\}$, I am looking at a language $L=\{u@v | u,v\in \{0,1\}^k\wedge u\neq v\}$. So $u,v$ have only $0,1$s, same length $k$, yet are different. Also, for me $k$ is a known constant. ...
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132 views

Build an FA that accepts only the words baa, ab, and abb and no other strings longer or shorter

I have been trying solve this problem for a while now for a university assignment. I'm required to build a DFA and an NFA for the above question. So far I have been able to solve the DFA but can not ...
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1answer
32 views

Converting along regular expression to NFA

I have the following regular expression for the set of all strings such that each block of five consecutive symbols contains exactly two 0's (consider the alphabet to be {0, 1}): (0+1+ϵ)4+(11100+ϵ)r(...
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321 views

Regular Expression and NFA: each block of five consecutive symbols contains at least two 0's

Consider the alphabet {0, 1}. How do I find the regular expression for the set of all strings such that each block of five consecutive symbols contains at least two 0's? Here, by block I mean a given ...
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Are there more succint algorithm for translating NFA's to DFA's?

When translating an NFA to its deterministic equivalent, we get an exponential blowup due to the powerset construction method. I tried to search but couldn't find an appropriate question regarding ...
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1answer
119 views

Polynomial time verification of Graph Isomorphism problem

Using guess and check method, for two given graphs with the same number of nodes, a NTM selects a permutation of the node set and then checks if the edges are preserved. The nondeterministic selection ...
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Constructing an NFA that is equivalent to a regular expression

I am a little stuck at attempting to give an NFA for the regular expression $0^+(10^+0)^∗$ , where the alphabet is ${0, 1}$. I have tried to construct multiple NFA's state diagram and the closest I ...
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51 views

Prove no DFA with four states can accept L={111}

Assume we have a language L={111}. Prove no DFA with four states can accept L. Can’t a DFA with 4 states accept L?
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1answer
35 views

What is the difference between deterministic and confluent?

I understand deterministic as a function for some input will always give the same output, and these inputs and outputs can be sets of values represent by a predicate. I understand confluent as ...
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1answer
79 views

Explaining NFA in words

I have an NFA, and the question I am asked is : Let 𝑎 < 𝑏 < 𝑐. Now in simple English, express the language of the NFA to explain what type of strings are accepted by it. In simple English, my ...
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62 views

Finite automaton for all words whose length $n$ satisfies $\operatorname{gcd}(n,504) \geq 6$

I have been working on the following homework question, and I just can't seem to make any progress: Construct a finite automaton having fewer than 36 states that recognizes the language $\{s \in a^* :...
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293 views

Constructing a NFA from a regular expression

I have the following regular expression $R=ab^*(\epsilon \cup c) \cup c^*a$ and I want to construct the NFA that accepts languages defined by that regular expression. I started by constructing the NFA ...
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1answer
83 views

Constructing a NFA that accept complement of language L of another NFA

if given a language $L$ recognized by NFA $N_0$ over an alphabet $\Sigma$. Is it possible to find a general way of constructing an NFA $N_1$ that accept $L^C$ such that $L^C= \{w \in \Sigma^{*} |\mid ...
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38 views

new language accepted by FA when new transitions are added to a FA?

found this question online and I am trying to solve this question. I have solved this question but I think I might be missing some cases. Could someone verify if my answers are correct? Let N = (Σ ∪ {...
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Simultaneous reachability of NFA states

Suppose I have a $n$-state non-deterministic finite automaton $F$ over alphabet $\Sigma$. Let $S(x)$ be the set of states reachable from the starting state by consuming string $x$. I am interested for ...
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1answer
70 views

this language and acceptance by queue automaton

I don't know how to prove or show that: $ L_1 = \{xx|x \in \Sigma^\ast\} $ (that can be accepted by queue automaton) If it would be possible, show by deterministic queue automaton, if not, by non-...
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1answer
64 views

PDA for the language of words $uv$ such that $|u| \geq |v|$ and $v$ contains 1

Consider the language $\{ uv : \text{$|u| \ge |v|$ and $v$ contains a 1}\}$. I am unable to understand how to accept this language using a PDA. How to check the length condition as well as check if ...
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1answer
116 views

Conversion of $\epsilon$-NFA to a DFA

So, I was watching a video about the conversion of $\epsilon$-NFA to a DFA. In the resulted DFA, she didn't write the state 4 in any successor set of the sets containing the state 3, and her ...
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116 views

Find language and regular expression

I don't know how to find the Language and the regular expression for each one. there are any special method for those kind of question?
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1answer
128 views

Building non-deterministic automata

I'm trying to make non deterministic automata for specific language . I cant understand my mistake! Rules: 1){a,b,c} 2) if I have the sequence "bb" and later in the word I have the sequence &...
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160 views

Is NP in NP/Poly?

The answer is yes, NP/poly is defined as the class of problems solvable in polynomial time by a non-deterministic Turing machine that has access to a polynomial-bounded advice function--the advice ...
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1answer
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What is the relationship between the number of transition rules for an NDTM and the resulting number of computational branches?

How can an NDTM have a growing number of branches as you feed larger and larger inputs with only finite number of transition rules specified--ie what is the relationship between the number of branches ...
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How to explain that a program that runs in NTIME(O(lg n)) is in the class P?

if a non-deterministic program executes only lg(n) decisions on each branch of the computation tree, then the problem this program solves is in P? That means, there is a deterministic algorithm that ...
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110 views

Why does converting a NDTM to a a DTM result in a higher time complexity?

I feel like I am really close to understanding the difference between P vs NP, and I think it comes down to this. The confusion stems from the fact that both P and NP problems are done in polynomial ...
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92 views

How do you create a sentential form in a given grammar?

I am given the following grammar: $$S ::= aBS| abT |a$$ $$T::= d | dT$$$$B ::= da | ϵ | S$$ I need to decide whether $aBaabda$ can be produced in the given grammar. I am unsure how the grammar can ...
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Is there a decision problem in NP whose corresponding function problem is not in #P?

I am trying to get an imagination of the class #P for my bachelor thesis. Right now I think of it as a DTM that runs every possible path to run an algorithm on some decision problem at once. But in ...
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124 views

How would I prove that nondeterministic Turing machines are undecidable?

How would I go about proving that the language: $$A_{NTM }= \{\langle N, w\rangle | N \text{ is a nondeterministic TM and } N \text{ accepts }w\}$$ is undecidable? I looked at the proof for $A_{TM}$ ...
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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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188 views

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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1answer
102 views

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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151 views

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 ...
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1answer
92 views

Is this push-down automaton non-deterministic, as JFLAP states?

There is a tool called JFLAP, which, among other things, can analyze push-down automata, and find non-determinism. In this example it is detecting non-determinism in state ...
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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 ...

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