# Questions tagged [finite-automata]

Questions about finite automata, an elementary automaton model with finite memory. It is equivalent to regular languages and the basis for many more complex models.

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### PDA Explanation

{a^2i.b^3i | i ≥ 0 } How would I draw this? I just started learning about pda's and I'm not sure where to start. I've looked at youtube videos explaining pda's but I'm still not understanding how to ...
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### Read regular Expression from NFA

Good evening everyone! Can someone help me with the following task? So we have this NFA: I was supposed to create a regular expression out of it. Now the solution says: $a^{+}b^{+}(c|ca^{*}b^{+})^{*}$...
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### What is the the pumping length for the regular expression (0+0001)((1111)*+(00)*)

I have this assignment question to find the pumping length of a regular language (L). The regular expression for the L is given as $(0+0001)((1111)^*+(00)^*)$ What is the length of the longest string ...
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### How to use DFA/NFA to prove the language {$0^n 𝑥1^𝑛$ | x ∈ Σ*, n ≥ 1} is regular?

I'm trying to prove the language L = {$0^n 𝑥1^𝑛$ | x ∈ Σ*, n ≥ 1} is regular, but don't know how to present it in a DFA/NFA. I'm thinking to have n+1 states in a NFA, with the start state as the ...
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### minimum number of states in cross product of two minimum DFAs

If FA1 and FA2 are 2 DFAs with minimum number of states. I want to find cross product DFA (FA1XFA2). Will the cross product DFA obtained from 2 minimum DFAs also have minimum number of states(num of ...
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### How to prove that concatenating a language A and A* is commutative?

Suppose we have a language $A$. I want to prove that $AA^*$ is commutative. I know that this expression equals $A^+$, but I'm not sure how to go about a proof yet. This is my attempt so far. If $A$ is ...
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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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### Building an NFA where where proceeding part of string has same or more 1's

Having trouble figuring out a NFA for the following language, the objective is to use only 3 states: $L = {\{1^ky : y \in \{0,1\}^* }\text{ and y contains atleast k 1's, for k} \ge 1 \}$ I have got to ...
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### Expert explanation of state elimination methods [duplicate]

I'm so sorry if this question is too general, but I need to understand the general process of the "State elimination method". In other words, what is the general idea, and what is the ...
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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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### Understand the DFA: accepting or not accepting “aa” or “bb”

I want to discuss the strings accepted by couple of DFAs: DFA in Figure 1 has 3 final states. It looks like that it accepts both the substrings "aa" (q0q3q0q1) or "bb". So this is ...
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### Sufficient condition for $xy^*z \subseteq L$ for a DFA with $n$ states

In chapter 2 of the New Turing Omnibus, the author considers an unknown finite automata with 6 states. Through trial and error, it is deduced that the words 0101, 0100101, 0100100101 are accepted. It ...
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### PDA for a language where the second part is not the reverse of the first part

I came across an exercise for constructing a PDA for the following language: $$L = \{ncm \mid n,m\in\{a,b\}^* \text{ and } n \ne m^R\}.$$ Where $L \subseteq ({a,b,c})^*$ So $n$ and $m$ are both a ...
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### Construct a DFA recognizing a language $L$ that has exactly $I(L)$ states

Let $L$ be a language, and consider the following relation $\equiv_L$ on strings: $s_1 \equiv_L s_2$ if and only if, for every string $w$, we have that $s_1w \in L \Leftrightarrow s_2w \in L$. This is ...
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### Clarification on an Hopcroft book DFA minimization example

At page 156 there is an example on how to find the distinguishable states for the following automaton: The following table shows the distinguishable states: By applying the given definition for ...
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### Check if a NFA accepts a string of non-prime length

Given a nondeterministic finite automaton $A$, give an algorithm that checks whether the language $L(A)$ decided by $A$ contains a string whose length is a composite (i.e. not prime) number. My ...
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### What language does this deterministic finite automaton accept?

Been mulling over this one for hours, my initial thought was { w ε {a,b}* | w is empty, or ends with either ab or ba} but that's clearly wrong as neither aba nor bab are accepted by the automaton. If ...
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### Extracting regex submatch boundaries without backtracking

I'm attempting to develop from scratch a simple regex engine. I would like for my engine to have the ability to report, "The regex matched on a substring of this line starting at index and ...
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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 ...
Suppose the strings are of the form x#y#z , where x,y,z are strings formed from the alphabet $\Sigma=(0,1,2,3,4,5,6,7,8,9)$ . The language is accepted if x+y=z is satisfied, for example : 56#65#121 is ...