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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1answer
26 views

Converting DFA to regular expression

I have the following DFA. (Yellow stated are accepting states.) I want to eliminate states step by step to find the regular expression of it. In my steps, I think there is a bug because I do not know ...
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0answers
19 views

Construction of a nondeterministic pushdown automation

I have a solution for the pushdown automaton that accepts the language $$\{x\#y \mid x,y\in \{0,1\}^* \text{ and } x\neq y\}\,,$$ which looks like this: I am trying to work from this in order to ...
0
votes
1answer
29 views

How to prove that $\{0^n 1^{5n} \mid n \ge 10000 \}$ is not a regular language?

I proved that $$ \{ 0^n 1^{5n} \mid n \geq 0 \}$$ is not a regular language using Pumping Lemma by following way. Solve by contradiction that $ L = \{0^n 1^{5n} \mid n \geq 0 \}$ is regular ...
0
votes
1answer
19 views

What is the purpose of $\epsilon$ transition?

$A = \{a^i b^j c^k\mid i = j\text{ or } j = k; i, j, k \ge 0\}$. In its push down automaton should not there be the red colored transition instead of the black colored one?
0
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1answer
37 views

LR(0) expressive power

So I have grouped the following formalisms into a power hierarchy (and made classes for them): Class 1 DFA NFA NFAϵ reg.exp Class 2 (DCFL expressivity?) LR(1) DPDA Class 3 CFG PDA Class 4 ...
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0answers
10 views

Regular expression in Automta [closed]

Give an example of a set S such the language S closure has more six letters words than seven letters words
0
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1answer
56 views

Intersections of some context-free languages

Suppose We have Some language as follows: $L_1=\{w^* | w=x \text{ and } x \in \Sigma^*\}$ $L_2=\{ww^R ww^R | w \in ( \Sigma + \Sigma)^*\}$ $L_3=\{w | w=xy, x,y \in \Sigma^*, y \text{ is a ...
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0answers
13 views

To check L = a^m b^n | m<n is Non Regular by Pumping Lemma [duplicate]

I want to check whether language L = a^m b^n | m < n. By Intuitively it is not Regular as there is comparison between m and n.So require memory which is not possible in FA. But I want to prove it ...
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votes
1answer
34 views

Equivalence of some Automata & Language & NFA

I read some note about Automaton Course. i see this note, that following all is the same. but i think the L(g) is not equal to NFA and regular expression. anyone could help me with defining the ...
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votes
0answers
48 views

How does Myhill-Nerode show number of states

In this question: NFA with exponential number of states when deteminized Yuval Filmus answer states Myhill-Nerode theorem shows that the number of states is $2^n$. I understand that MH is used to ...
0
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1answer
55 views

Set containment of MinimumBadPrefix and BadPrefix of a Safety Property

This question is related to formal model checking theory, but I cannot find a tag for it. Let $P_{safe}$ be a safety property. $BadPref(P_{safe})$ is the set of bad prefixes for $P_{safe}$ A Safety ...
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0answers
16 views

Deterministic finite automaton question [duplicate]

I don't have any idea what this question wants. Any tips ? I am concerned with part(a) now.
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1answer
83 views

How to determine the set of numbers read by a DFA from one state to another?

Using the Deterministic Finite Automaton (Q, Σ, Δ, q_0, F): Alphabet: Σ is {(0 0), (0 1), (1 0), (1 1)} Definition of Δ to strings recursively: Δ*(q, ε) = q for all q ∈ Q Δ*(q, xa) = Δ(Δ*(q, x), ...
0
votes
1answer
38 views

DFA for every run of a's=2 or 3

I am trying to create a dfa for L={w: every run of a's has length either two or three} this is my attempt at the solution..i feel like I am missing something..?
1
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0answers
28 views

Using induction to prove transition states are the same

Suppose that you have a DFA $M=\left(S,\Sigma,s_0,\delta,{s_f}\right)$ with $s_f\neq s_0$. Suppose further that $for\,all\,a\in\Sigma\,\delta\left(s_0,a\right)=\delta\left(s_f,a\right)$. Show that ...
0
votes
0answers
14 views

Classification of one-dimensional CA based on the number of inputs each cell receives during an update?

Consider Wolfram's rule 30 and Wolfram's rule 62. In the case of rule 30, only two bits of information must be passed to each new cell in the CA during an update, while for Wolfram's rule 62, three ...
0
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1answer
43 views

Is a door lock a finite state machine?

Must the states of a finite state machine be worked off sequentially or could you understand the different shaped parts of the key as input and the position of the pins as states? If not all the input ...
1
vote
1answer
25 views

Why does a DFA either contain all or no words $a^k$ if it loops for $a$ in all states?

I am trying to solve this particular problem from Automata Theory by Ullman, Hopcroft, it is as shown below: Let $A$ be a $DFA$ and $a$ be a particular input symbol of $A$, such that for all ...
2
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1answer
65 views

Computational equivalences between a calculus and an automaton model

This Wikipedia table (template for "Formal languages and grammars") maps grammar to language to abstract machine for more than a dozen languages. ...
0
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1answer
37 views

NFA state complexity for the complement of EPAL restricted to a fixed length

I've been having trouble proving the next statement: Let $L_n=\{ww, |w|=n\}$ (the set of equal-length palindromes (EPAL) restricted to length $2n$). Prove that $L^c_n$ can be accepted by an NFA ...
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votes
1answer
83 views

Converting NFA to regular expression

Here is the regular expression I made for it This is my first answer, used the naive method aka don't know what am doin' method. $$ \epsilon \cup a^* \cup (a^*b) \left((a| b^*a) | \left( ...
1
vote
1answer
61 views

Don't understand closure under string reversal

I am trying to learn from http://www.cs.uiuc.edu/class/su08/cs273/lectures/lect_06.pdf #2 and I understand everything except for the 2nd line of delta prime prime function, I having breaking down ...
1
vote
0answers
60 views

Given a non-deterministic Mealy machine $M$, if $L$ is regular, is $M(L)$ regular?

Consider a nondeterministic Mealy machine, $M$, defined as follows: $M = (Q, \Sigma, \Delta, \delta, \tau, q_0)$ where $Q$ is a finite set of states $\Sigma$ is an input alphabet $\Delta$ is an ...
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0answers
26 views

Describe in English the pattern in the following regular expressions [duplicate]

Describe (in English phrases) the languages associated with the following regular expression. it says to be as simple as possible ...
1
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1answer
26 views

Sampling from a Acyclic Deterministic Finite Automaton

Assume you have a finite language $L$ succinctly represented as a acyclic DFA $M$ (models can't be much simpler than that :) ). How can we efficiently sample a word from $L$ with uniform ...
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votes
1answer
106 views

Pushdown Automata Challenge

I read one old-midterm exam on Automata. consider: the language that accepted by above pushdown automata is not generated by which of the following grammar? 1) S->aBaa|a$\epsilon$ ...
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votes
1answer
27 views

Do NFAs with ϵ-transitions accept languages that no PDA can?

Is it correct to say that there are languages that a NFA with epsilon recognizes but a PDA is not? I think that it is wrong but I cannot find a suitable explanation.
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votes
2answers
56 views

Strange TM Language on Definition [closed]

i prepare for Autotmata Course Final Exam. in one of lecture, our professor draw this Turing Machine, and wrote DELTA is Neutral element of TM. it'w wrote: Language of this TM is: {$W \in ...
1
vote
1answer
187 views

Deciding if a finite automata accepts strings of any length

Question is you're given a DFA. Give an algorithm which tells you whether strings of all lengths $n\in \mathbb{N}$ are acceptable or not. What I doing was, I have algorithm to count the number of all ...
3
votes
1answer
41 views

Converting generalized NFAs to NFAs

I came across generalized nondeterministic finite automata (GNFAs) in Sipser's Introduction to the Theory of Computation. These are automata where transitions are labelled with regular expressions, ...
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1answer
102 views

How to construct a DFA for this?

Let $C = shuffle(A, B)$ denote the shuffle $C$ of two languages $A$ and $B$, it consists of all strings $w$ of the form $w = a_1b_1a_2b_2....a_kb_k$, for $k > 0$, with $a_1a_2 ··· a_k \in A$ and ...
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votes
1answer
49 views

Why is there still nondeterminism in my automaton?

I've been solving some exercises recently and it appears my answer was wrong for this particular example. The task is to convert this NFA into a DFA: My attempt is this: Now the tool I'm using ...
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votes
1answer
107 views

Why is the language of even-length non-palindromes context-free?

We know $L_1=\{w_1 w_2 \in (a+b)^*\mid |w_1|=|w_2|, w_2 \neq w_1^{\;\mathrm{R}}\}$ is a context-free language. Can anyone help me produce a PDA or give me any hint how I can quickly understand why ...
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1answer
62 views

Language of a grammar

What's the language of following grammar? $G: S \to S_1B$ $S_1 \to aS_1b$ $bB \to bbbB$ $aS_1b \to aa$ $B \to \lambda$ any hint or solution?
0
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0answers
20 views

Converting DFA to Regular Expression “equation-method(?)” [duplicate]

I have trouble understanding my text-book on how to convert a DFA to a Regular Expression using "equation-method"(don't no what it's called). If someone could explain step by step in detail what's ...
1
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1answer
68 views

Non Deterministic PDA accepted language not clear

This is a PDA from the lecture slides I'm using: They say it accepts all words that contain double a's. While it makes some sense it's not full proof. What prevents the second a to be read in the ...
4
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1answer
142 views

Counting the number of words accepted by an acyclic NFA

Let $M$ be an acyclic NFA. Since $M$ is acyclic, $L(M)$ is finite. Can we compute $|L(M)|$ in polynomial time? If not, can we approximate it? Note that the number of words is not the same as the ...
2
votes
2answers
73 views

Language to Construct Finite State Transducer

I am attempting to write a Finite State Transducer module in OCaml, because I think it's a good exercise, which is because I have been teaching myself Natural Language Processing. You typically ...
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2answers
41 views

How deciding if 2 deterministic finite automatas decide the same language? [duplicate]

Is there any polynomial procedure to decide if 2 deterministic finite automatas decide the same language?
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1answer
268 views

Suffix automaton algorithm to find occurrences of substrings

Here is an attached link to a problem, the Substring query problem that I am trying to solve. It requires the use of suffix automaton,but I could not understand what is a suffix automaton. Can ...
0
votes
1answer
73 views

A DFA recognizing my name

How can I know if my DFA is implemented correctly? For example, I need to build a DFA, and then minimize it which will recognize my name. Language which describe my name is: L = {pustai, marius} I ...
0
votes
3answers
332 views

Problem understanding DFA & NFA equivalence in Theory of Computation

Before asking this question,I had gone through Equivalence of NFA and DFA - proof by construction but my question is a bit different from that. I was reading Michael Sipser's ...
0
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1answer
41 views

Proof that finite automata is closed under intersection

I'm looking at a proof that says that: If $M_1=(Q_1, \Sigma , q_1, A_1, \delta)$ and $M_2=(Q_2, \Sigma , q_2, A_2, \delta)$ are two finite automata(FA) then $M=M_1 \cup M_2$ is also an FA. We define ...
3
votes
3answers
63 views

generate possible inputs valid for automata

I find lots of solution where you have an Automata and a input string , you can validate whether input string is accepted by automata or not. Can we do the reverse ? I am looking for solution which ...
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0answers
54 views

(Symbolic) Equivalence of deterministic infinite word transducers with restriction

Given a deterministic infinite word transducer (also called deterministic generalized sequential machine) with the following restriction: There is exactly one initial state All states are final The ...
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2answers
134 views

Theory of computation introductory curriculum

I want to study theory of computation on my own, so I am looking for books. What set of books would you recommend for the equivalent of a one-semester course that introduces theory of computation? ...
3
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2answers
100 views

Correspondence between automata and formal grammars?

From Wikipedia Since there is a one-to-one correspondence between linear-bounded automata and such grammars, no more tape than that occupied by the original string is necessary for the string ...
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1answer
189 views

Model marbel toy with finite automata

I'm resolving this question of Hopcroft and et al Book. Figure 1 below is a marble rolling-toy. A marble is dropped at A or B. Levers $x_1,x_2$ and $x_3$ cause the marble to fall either to the left or ...
0
votes
4answers
135 views

How is a nondeterminisitic automaton running on an input?

A nondeterministic automaton, after reading an input symbol at some state, may jump into any of a (finite?) number of states. Does the automaton uniformly randomly choose one out of the several ...
0
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2answers
50 views

Can a language be the one recognized by more than one automatons?

The language recognized by an automaton is defined as the set of strings that are accepted by the automaton. I wonder if it is possible that the languages recognized by two automatons are the same? ...