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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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How to precisely know whether a language is regular ? , a regular expression can be generated for it ? , as well as dfa? [duplicate]

I feel difficulty in finding whether a language is regular and also is regular expression can be generated ?? Please anyone let me know about all the possible cases. This will help me very much..
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1answer
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Why does an extended transition function not work if the string does not result in a final state? [on hold]

If I am not wrong a string is only accepted by a finite automata if the string results in a final state. Why is that? With symbols we can transition into another non-final state, why is that not ...
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2answers
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Is the language L = {(a,b)* | #a * #b is an odd number} regular?

Is the following language regular? $$\{ w \in \{a, b\}^* |\ \text{the product of the number of $a$'s and the number of $b$'s is an odd number}\} $$ If i'm not mistaken the condition is the same as ...
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1answer
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Polynomial-time Compute the Number of States resulting from the NFA to DFA (greedy) conversion?

The canonical NFA to DFA conversion, starting with an NFA with $n$ states, can result in a DFA with $2^n$ states. However, in many cases, there are states that are "unnecessary," such as when ...
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1answer
42 views

Construct a DFA from the regular expression (a)*+(aab)*

I've broken down the expression into two simpler DFAs but right now I'm stuck. I don't know what to do with the expression a*, my solution currently (as presented above) is a NFA, not DFA.
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1answer
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Proving a language comprised of 2 languages is regular(with suffix and prefix)

I am having hard time proving that the following language,comprised from two regular languages $L_1,L_2$(over the same $\Sigma$)is indeed regular: $$L^\frown = \{ w\in \Sigma^* | w=u\sigma_1\mu_1...\...
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1answer
17 views

Proving a language comprised of 2 languages is regular

So glad to find this place. I have been struggling for quite a while with this given question and i am not sure how to fully address it. The question: $L_1$ and $L_2$ are regular languages over the ...
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25 views

Tree languages regular

Let $T_1,T_2 \subseteq T_\Sigma$ be regular tree languages, f a symbol with arity 2. To proof: $\{f(t_1,t_2) \mid t_1 \in T_1, t_2 \in T_2\} \subseteq T_{\Sigma \cup \{f\} }$ is regular. So it's ...
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1answer
50 views

Construction of a Deterministic Tree Automaton (DTA)

Let $L \subseteq \Sigma^*$ be a regular language. Let $\Sigma' = \Sigma_0 \cup \Sigma_2$ where $\Sigma_0 =\Sigma$ and $\Sigma_2=\{*\}$. We define $T_L=\{t \in t_{\Sigma'} \mid \text{The leafs from t ...
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1answer
61 views

Finding a regular expression of a language

Our alphabet is {a,b} and we need to find a regular expression for the language of all words of the form $a^*b^*$, which their length is a product of 3 (meaning their length is divisible by 3). ...
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What is the word “madness” doing in the first chapter's title of Automata Theory, Languages and Computation by Hopcroft, Motwani, Ullman?

The chapter's title is "Automata: The Methods and the Madness". This title came along in the second edition and remains in the third edition. In the first edition, the the second chapter's title is "...
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1answer
31 views

In which reference can I find a definition for the equivalence of DFAs?

How is the equivalence of DFA defined? I found the equivalence of states --- James Hein, section 5.3, page 301. But he doesn't define equivalence between entire automata. (Ullman and Hopcropft seem ...
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0answers
26 views

Using Nerode theorem to prove that the following languages are non-regular

I've been trying to understand the idea behind proving a language is not regular by using Nerode's theorem, but I just couldn't apply the idea on what I've been asked. The problem is to prove the ...
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1answer
32 views

Efficiently deciding whether TM accepts all inputs in at most $k$ steps

I want to decide if a deterministic TM $A=(Q, \varGamma, \delta, q_s, q_h)$ halts on every input in at most $k$ steps. If the TM $A$ stops after $k$ steps, then the positions $A$ can reach are ...
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3answers
55 views

DFA for a language that accepts the addition of multiple of 2 and multiple of 5

I am trying to draw a DFA that accepts the following language: $L=\{a^{2i+5j} : i , j \geq 0\}$ I started out by drawing an NFA, which I can then convert to a DFA but I am not sure if my NFA is ...
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1answer
71 views

NFA that accepts all numbers not divisible by 105

I have to create an NFA that accepts the following language L with no more than 15 states. $L = \{a^n \mid n \geq 1$ and $n \mod105 \neq 0 \}$. To me it seems that all multiples of 105 have the ...
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1answer
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Recognizing Regular Languages in Layman terms [duplicate]

I understand that regular languages are languages which can be computed by Finite Automata however i am having some trouble understanding how one can identify a regular from non-regular. I know that ...
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1answer
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Non-deterministic Finite Automata | Sipser Example 1.16

I am working through the Sipser Book (2nd edition) and came across this example, which I do not understand. In the book it states that this NFA accepts the empty string, $\epsilon$. Could someone run ...
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1answer
42 views

Dana Angluin's L* algorithm - Hypothesis inconsistent

is it possible for the Dana Angluin's L* algorithm that a hypothesis is inconsistent? So assume we have a closded observation table for a regular language L. Now after creating the hypothesis we will ...
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1answer
38 views

DFA multiple accepting states to Regular expression

I am trying to find the regular expression that defines this DFA, I am finding this particular case difficult since it has multiple accepting states. If I understand this DFA correctly, it recognises:...
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2answers
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Prove that the following language is regular [duplicate]

Let L1, L2 be regular languages. And let A1=〈Σ,Q,q0,𝛿1,F1), A2=〈Σ,P,p0,𝛿2,F2) be their DFA. Prove that the following language is regular, by making an appropriate NFA for it: 𝐿3={𝜎1𝜎1β€²πœŽ2𝜎2β€²β€¦πœŽ...
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1answer
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Ξ΅-NFA to DFA - initial state with only epsilon transitions

I am having trouble discovering how to convert a Ξ΅-NFA to DFA (image below) when all transitions in the initial state are epsilon transitions. I already know how to convert Ξ΅-NFA to DFA (common cases),...
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0answers
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Computational power of quantum finite automata

I am preparing some lecture notes on the computational power of quantum finite automata (QFA). I am a bit confused about which models of QFA are stronger and which models are weaker than standard ...
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2answers
56 views

Pumping lemma occurrence of c > d

I'm trying to prove a language is not regular through using pumping lemma, but can't seem to come up with any way of doing it. The alphabet is: $$ \Sigma = \{c, d\} $$ The language is: $$ A = \{z ...
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1answer
41 views

The order of Ξ΅-transitions in NFA

I'm reading 'Introduction to the Theory of Computation' by Michael Sipser. He gives an example of a NFA, stating that this particular automaton accepts $a$ (he lists other strings as well, I just want ...
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1answer
48 views

Help with question from Sipser chapter 1

Is this language regular? $0^k10^k \ with \ k\geq1$ It needs to count the starting and ending zeros which is impossible with finite states. Update: This is the whole problem from the book: Let $\...
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0answers
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Tree Automata Operators

I am trying to understand the Projection operation (linear tree homomorphism) and Cylindrification operation (inverse tree homomorphism) from the book. Linear Tree homomorphism is defined as follows: ...
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1answer
27 views

How to show a language is regular through creating DFA

I'm trying to prove that a given language is regular through proving that a DFA can be created from it, but have problems with how to the DFA should look. The alphabet is $\Sigma=\{0, 1\}$ and the ...
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1answer
72 views

Backtracking in DFA [closed]

Is it true that backtracking is allowed in deterministic finite automaton (as mentioned in many comparisons between DFA and NDFA)? If yes, how is it possible when transition in DFA is to a single ...
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1answer
63 views

Limitations of DFA [duplicate]

In this link it is mentioned: A DFA is not powerful enough to recognize many context-free languages because a DFA can't count. But counting is not enough -- consider a language of ...
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1answer
39 views

Simple property of DFAs

Do you know if this simple property of a DFA is stated as a property (or theorem) in some Automata theory book (possibly with a particular name)? Property: Given a DFA $A = \{ Q, \Sigma, \delta, q_0, ...
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1answer
33 views

How to check if DFA is actually a correct model of the intended system?

Suppose I have modeled a deterministic finite automaton of my system. How can I check if the traces generated by this system, actually represent the model I had in mind? For example, say I have DFA ...
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1answer
49 views

Why are those very similar languages in a different complexity class?

i am having a real time understand why the following two languages are in two different complexity classes(the first is NP-Hard and the second is in P). tried to look online at various resources and ...
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3answers
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Define a finite automaton accepting the language below [duplicate]

$\{ w∈(a,b)^\ast | w $ does not contain '$ab$' as a subword $\}$. About questions like this, I always want to construct the regular expression for it, then convert the regular expression to a finite ...
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1answer
30 views

State Transition Diagrams for XOR

I have found two different versions for State Transition Diagrams for XOR. I'm confused as to why one has 2 states and the other has 3. What are the implied states in each please? Are they both ...
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0answers
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Characterization of NFA whose equivalent (minimal) DFA has exponential number of states

(I don't know if there are standard names for this, so) Let's say that a Nondeterministic Finite Automaton (NFA) is $n$-expansive if it has $n$ states and any Deterministic Finite Automaton (DFA) ...
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1answer
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Modelling regex replacement via a DFA

I wish to model the following common construction in code via a finite state automaton for the purposes of static analysis: ...
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2answers
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Is intersection used in regular expression?

As union is part of regular expression in form of positive closure, similarly intersection is also a part of regular expression? in which form it can be used?
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0answers
63 views

How to find the minimum number of states of a deterministic finite automaton accepting a given language [duplicate]

Let $L$ be a language over $\Sigma$. And $\Sigma = \{0,1\}$ is a set of input alphabets. $L = \{ w \mid w \in \Sigma^*, \text{ where $w$ is a string with numbers of 0s divisible by 3 and number of ...
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0answers
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Arden theorem with 3 input [duplicate]

I have just started learning Arden's theorem to convert finite automata but I am stuck on its execution when we have 3 inputs. Because I am not able to simplify any equation to have only 2 inputs ...
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1answer
50 views

Brzozowki's algorithm doesn't work for this corner case

I'm a newbee learning DFA minimization. And I found that(strangely) Brzozowki's algorithm cannot give me a minimized DFA on this example: In this DFA, $S_0$ and $S_1$ are nondistinguishable and ...
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1answer
88 views

Is the language of words with equal number of 010s and 101s as substrings regular?

Is the language of words containing same number of 101s and 010s regular? If yes, how can I design a DFA for it? In general, is the language of words containing equal number of strings which one is "...
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3answers
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Is it possible to define a DFA for the language of words having exactly one double letter? [closed]

Consider the language $\{ w \in \Sigma^*~|~ w~\text{contains exactly one double letter}~\}$. For example, $baaba$ has exactly one double letter, but $baaaba$ has two double letters. Suggested answer ...
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proving DFA stuck

This DFA fulfills: Define a function $diff: \{0,1\}^*\to\Bbb Z$, for $w \in\{0,1\}^*$, $diff(w)=($# of 1's in $w)- ($# of 0's in $w$). Thus, $diff(\epsilon)=0$; $diff(0)=βˆ’1$; $diff(1)=1$. Let $L = ...
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Is there a reasonable and studied concept of reduction between regular languages?

Have been any interesting formulations for the concept of reduction between regular langauges, and if so -- are there regular-complete languages under those reductions?
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dfa subtract multiple of 3 [duplicate]

Define a function 𝑑𝑖𝑓𝑓 ∈{0,1}β†’β„€ so: for everything w ∈{0,1}, diff w = # of 1's in w- # of 0's in w. Thus: 𝑑𝑖𝑓𝑓 πœ€=0; 𝑑𝑖𝑓𝑓 0=βˆ’1; 𝑑𝑖𝑓𝑓 0=βˆ’1; Let 𝐿 = {π‘€βˆˆ {0,1} * | 𝑑𝑖𝑓𝑓 𝑀 = 3π‘š ...
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2answers
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One counter automaton as a function

We can associate a one counter finite automaton with a function $f:\Sigma^* \to \mathbb{N} \times \{0,1\}$, where $f(x)=(n,b)$ describes the state where the automaton terminates when fed an input word ...
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How to understand DFA's and how to understand how to construct them based on a given regular language? [duplicate]

I have practiced DFA's for an upcoming test and I haven't been able to grasp how to construct more difficult DFA's. An example would be this question : Construct a deterministic finite state automata ...
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1answer
264 views

Irregularity of language of prefixes of decimal expansion of pi

Let $L_{\pi}$ be the language consisting of prefixes of the decimal expansion of $\pi$: $$L_\pi = \{3, 31, 314, 3141, 31415, 314159, \ldots\}.$$ Prove that LΟ€ is not DFA-recognizable. You may use the ...
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1answer
29 views

Do all DFA's containing an “accepting path containing a cycle” accept infinite languages?

So I've seen this claim being made on different questions: Do self-loops in DFA cause infinite languages? I'd like to find formal proof for this. I think I should also note that an "accepting path ...