Automata Theory, including abstract machines, grammars, parsing, grammatical inference, transducers, and finite-state techniques

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Matrix representation of Automata

Is anyone know if there is any tutorial for the matrix representation of automata?? I am taking a theoritical computer science in this semester and the professor uses the matrix in his lecture. I ...
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3answers
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Why is this the $L(M)$ of this DFA?

Why is this the $L(M)$ of this DFA? Can someone please explain it? I am new to this course. When I tried alone answering the question of "What is special about the words that get accepted by this ...
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1answer
1k views

Give a push down Automata for this language: the length of is odd and it's middle symbol is 0

Give a push down automaton for this language: {w| the length of w is odd and it's middle symbol is 0} Here is the CFG I wrote for this language: ...
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1answer
67 views

Automata and power series

I am taking a class on Automata and Formal Languages and I need to solve an exercise, but I have no idea where to start from. It sounds like this: Decide the coefficients of the words in ...
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1answer
419 views

Show that a language is not regular using Myhill-Nerode Theorem

I'd like to show that the language below is not regular using Myhill-Nerode Theorem. How can I do that? Let Σ = {0, 1}. Let L = {ww|w ∈ Σ*} I am not sure where ...
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1answer
41 views

Is this language regular ? [automata]

Is this a regular language : $$L = \{w : w \in \{a,b\}^*\text{ and }abw = wba\}$$ Does my automata only need to start with $a$ and $b$, then loop on $a,b$ and finish with $b\to a$, or do I don't ...
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349 views

Is it true that any infinite subset of a non-regular unary language is non-regular?

My question is very similar to this: Is there a subset of a non regular language that is regular My claim is that because the subset is infinite, Myhill Nerode says that the language is not regular. ...
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131 views

Pumping Lemma to show a language is not regular

Let $\Sigma = \{a, b\}$. Use the Pumping Lemma to show that $\mathcal L = \{ a^pab^q: p < q \}$ is not regular. Not sure how to apply PL here, if someone can give some direction.
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118 views

Finite state automata for two regular languages

I have to draw FSAs that accept the following languages over {0,1} and {a, b} (0 | 1)* a* | b* Now for 1, the language is just any word that consists of 1s and 0s but it also contains the empty ...
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0answers
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Is there a 2D 3-colorstate mobile automaton that grows like $ln^{0,5}(t)$?

Define an integer function $f(t)$ for an integer $t>25$ such that $|f(f(t)) - ln(t)| < \sqrt {ln(t)}+2$. Define $L(X(t))$ as the number of nonwhite states at iteration $t$ of mobile automaton ...
2
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1answer
407 views

Verification: DFA/NFA that accepts all strings over $\{0,1\}$ with exactly one block of $00$

I am trying to design a DFA or NFA that accepts all strings over $\Sigma = \{0,1\}$ in which the block $00$ appears only once. Here is what I've tried. Can you verify that this accepts all string ...
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1answer
40 views

Post-concatenation of the languages represented by the null set

I have a small question regarding concatenation of regular languages: Is it true that the concatenation $L\varnothing$, where $L$ is any regular language, result in $\varnothing$? Namely, does ...
2
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1answer
72 views

NFA from grammar productions

Based on this grammar: \begin{align} G = (\{S,A,B\}, \{a,b, c\}, S, P) \end{align} \begin{matrix} \\P: \\S → abaS | cA \\A → bA | cB | aa \\B → bB | cA | bb \end{matrix} I created this NFA: ...
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0answers
115 views

Constructing an NFA accepted by a grammar

Contruct an NFA of the language accepted by the grammar below. $$G=(\{S,A,B\}, \{a,b,c\},S,P)$$ $P: S\rightarrow abaS\ \ | \ cA\\ \ \ \ \ \ \ A\rightarrow bA\ \ | \ cB \ \ | \ aa\\ \ \ \ \ \ ...
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1answer
214 views

Right-linear grammar from regular expression

I made a right-linear grammar that from this regular expression: The alphabet is: $Σ = \{a, b, c\} $ Regular expression: $r = cc^*(ba)^*bb$ My solution, it seems a little too short like I'm ...
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1answer
53 views

NFA from regular expression

I'm trying to make an NFA from the following regular expression. I'm not sure about the edges between nodes $q2$ and $q4$, maybe someone can point out where everything went wrong.
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1answer
30 views

Language made by a regular expression

I created a language from this regular expression but I'm not sure about it, especially where I wanted to use the $w$ to express a sequence of terminals. The expression: $r = a a ^{*} (b + bb + bbb) ...
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1answer
27 views

Regular expression for a language

I made a regular expression to match this language but I'm not sure it's right. Perhaps someone can show me where it deviates. The language: $L = {a^{n} c b^{m} (cc)^{p} : n \geq 1, m \leq 1, p\geq ...
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77 views

Constructing regular grammar

I'm trying to make a regular grammar for this language: $$ L = \{ a^ncb^m(cc)^p : n\ge 1, m\le 1, p\ge 0\} $$ Where the alphabet is $ \Sigma = \{a,b,c\}$ It seemed like right-linear. This may be ...
4
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2answers
179 views

context free grammar problem

$L$ is the context free grammar over $\{a, b\}$ $S \rightarrow aSb \; | \;bR \; |\;Ra$ $R \rightarrow bR \;|\;aR\;|\;\epsilon$ Briefly describe this CFG with English sentences and prove your ...
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63 views

context free grammar design

Design a context free grammar and PDA for the following language. $$\Sigma = \{0,1\},\qquad L = \left\{uv \mid u \in \sum^{*} \;v\in \sum^{*}1\sum^{*} \text{ with }|u| \geq |v| \right\}$$ I'm not ...
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156 views

interpreting language for finite state machine

Can someone explain to me what this means in clear english and maybe give me a hint for how to make a NDFSM (non-deterministic finite state machine) that accepts this language? I understand that the 3 ...
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60 views

$2^E$ where $E$ is a set

I'm studing the definition of automaton $G=(X, E, f, \Gamma, x_o, X_m)$ where $X$ is the set of states and $E$ is the set of events. My sources report that $\Gamma:X \rightarrow 2^E$ is the indicator ...
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1answer
125 views

Constructing a parallel composition from a given transition system and automaton

I am looking at an exercise, where it asks me to construct a parallel composition from a given transition system and an automaton. The transition system looks like this: and the automaton (with ...
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496 views

Finite automata for any even number of a's followed by any even number of b's

I'm new to formal languages. I'm stuck with the following question. Any help is appreciated. Find finite automata for $$L = \{a^i b^j \mid i, j\text{ are even, }j\ge0\}$$ Thank you
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2answers
121 views

Number of states required to recognize $\{ ss : s \in \{ 0 , 1 \}^*, |s| = i \}$ and its complement

$$\Sigma = \{0,1\}\;\\ S_{i} = \left\{ss: s\in {\Sigma}^{*} \text{and $s$ has length $i$}\right\}$$ Prove that for any $i$, any DFA recognizing $S_{i}$ must have $2^{i}$ or more states. Design a ...
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1answer
541 views

Does closure under the union and concatenation operations imply closure under the star operation?

Given any two languages $A$ and $B$, recall the following regular operations: Union: $A \cup B = \{x \mid x \in A \text{ or } x \in B\}$ Concatenation: $A \circ B = \{xy \mid x \in A \text{ ...
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2answers
367 views

Constructing a finite automata from a subset of its language

I am attempting to solve the following problem: Let $M=(Q,\Sigma,\delta,q_0,F)$ be a deterministic finite automata which accepts $L(M)$, and let $E$ be the subset of $L(M)$ consisting of all words of ...
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94 views

The Relation of Cellular Automata to Languages

In Conway's Game of Life, would a cell be considered a deterministic finite automata? Is there a language for the automata, and would it be a regular language? In probabilistic cellular automata, are ...
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Connection of closed subsets of $A^{\omega}$ and deterministic Büchi-Automata, Question from Book: Infinite Word by D. Perrin & J.-E. Pin

In the Book Infinite Words (homepage) it is proofed that: If $X \subseteq A^{\omega}$, then regarding the Cantor-Topology, the following is equivalent: (1) $X$ is closed (2) $X$ is recognized by a ...
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1answer
205 views

Understanding how to convert a PDA to a CFG

Given a PDA, initialized with $\#$ on the stack, and with accepting states $q_a, q_b, q_c$ and the following transitions: (current state, stack head, input character, replacement for old stack head, ...
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2answers
315 views

Converting from NFA to a regular expression.

This is a NFA, I have been working to covert it to a regular expression. After I'am done, I arrive at an expression as follows $$ \left(((a\cup b)a^*b) (ba^*b)^*a\right)^* \left(((a\cup b)a^*b) ...
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1answer
72 views

Is there an (explicit?) bijection from the set of all automatons to the set of all regular expressions that conserves the recongnised language

Let $\Sigma$ be an alphabet, $R$ be the set of regular expressions on $\Sigma$ (that is, trees with leave's values in $\left\{\varepsilon\right\}\cup \Sigma$ and three types of interior nodes, one ...
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752 views

To design a Finite State machine

Design a FSM for a binary number in which the input is valid if no. of 0's divisible by 5 and no. of 1's divisible by 3
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103 views

Finite automata and languages question

I have attempted these few simple questions, can someone let me know if this is correct please? If not please provide the answer as I learn better that way and if possible explain. i) FA1 Start = ...
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Expressiveness of finite memory programs

Assume we have a simple programming language with while, if, := (assignment), ...
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0answers
53 views

Quality of Reduction of finite automata

I am looking for an example, which corresponds to what I've learned in my Applied Automata Theory Class: Given a NFA $\mathcal{A}$, a $\approx _\mathcal{A}$ quotient automaton can be bigger then a ...
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1answer
298 views

Best book for automata theory and compiler design?

I am currently pursuing my M.Tech in Digital Image Processing, I want to take admission in PhD program using subjects either Formal Language and Automata Theory or Compiler Design, Can anyone please ...
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24 views

Given two minimal FSMs with one accepting a subset of the other, must a simulation exist?

As part of an example, Abstract and Concrete Categories, section 3.35, claims: For every two minimal [by number of states] $\Sigma$-acceptors $A$ and $A'$, there exists at most one simulation $A ...
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1answer
45 views

Stochastic Automaton accepting every word with same probability

I am looking for a stochastic automaton, which induces the same probability $c \in [0,1]$ for all words in $\Sigma^*$, where $\Sigma$ is some finite alphabet. A stochastic automaton over an alphabet ...
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1answer
161 views

Is this language regular?

Given $m,n∈Z$, A is a finite alphabet set ,and $L=\{(a^m,a^n)\}^*$ is subset of $A^*\times A^*$ . Is this language regular ? For example, is $L=\{(a^3,a^7)\}^*$ regular ? Here L is not the set ...
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Whether $L=\{(a^m,a^n)\}^*$ is regular or not?

I am condidering the automatic structure for Baumslag-Solitar semigroups. And I have a question. For any $m,n \in Z$, whether the set $L=\{(a^m,a^n)\}^*$ is regular or not. Here a set is regular means ...
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2answers
54 views

Regular composition of non-regular language

I've got the following problem: Let's take language $L$. Is it posible that $L$ is not regular itself, but it's composition $L\cdot L$ becomes regular? I suspect that's correct, yet I ...
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1answer
936 views

Proof that equal-length-concatenation is a context-free language?

If A and B are languages, define A⋄B={xy | x ∈ A and y ∈ B and |x|=|y|}. For example, if A = {00, 101, 111} and B= {1, 11, 00110}, we would have A⋄B={0011}. Show that if A and B are regular, ...
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Algorithm for a regular expression

This was a question for an exam that I received 0 points on, I'd like to get some input on what the correct answer should have been. Imagine that you are asked to write an algorithm P that takes a ...
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3answers
973 views

Find push down automata and context free grammar

I have the following language: $$ L = \{a^nb^{2n+1} \mid n \ge 0\} $$ I must find the push down automaton and a context free grammar for the language. For the push down I have no idea how to ...
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1answer
114 views

Give a regular grammar for L

Give a regular grammar for L= {a^n b^n : n<=100} I would do something like this : S---> A | empty string A---> aB| empty String B---> Ab but How do we keep count of the number in the grammar? ...
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208 views

regular expression

I would like to write the regular expression for the set of all binary strings where there are no three consecutive 0's. The following strings are part of the language: ...
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222 views

Prove $L=\{ 1^n| n\hspace{2mm}\text{is a prime number} \}$ is not regular.

Prove $L=\{ 1^n| n\hspace{2mm}\text{is a prime number} \}$ is not regular. It seems to use one Lemma: Pumping Lemma.
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2answers
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Automata: 1=2, 2= 26, 3=1054, 4=5768, 5 =139314069504, 6 = ???

I am in my own Automaton (finite-state deterministic automata) research, so i have four sets of automata. 2 states automata, 3 states, 4 states and 5 states. Input alphabet $\{0,1\}$ so... the ...