1
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1answer
51 views

Challenge on Property of Complement in Language

We have: and M be a finite automata. Suppose d(M) be a deterministic automata that equivalence to M. if $M_1$ and $M_2$ be two finite automata, $M_1 + M_2$ is the finite automata such that the ...
0
votes
0answers
25 views

Design an finite automata for 010 and 01? [duplicate]

I have tried below question for designing automata but didn't success . ...
0
votes
0answers
10 views

What are the classes in A.N. Maslov hierarchy of indexed languages corresponding to Chomsky Hierachy?

As we know,that classes in A.N. Maslov hierarchy of indexed languages of level 2 is in sensitive languages of Chomsky hierarchy. What are the classes in A.N. Maslov hierarchy of indexed languages ...
0
votes
0answers
17 views

Do automatons and formal grammars belong to formal systems

A formal system consists of a formal language, a formal grammar that generates the language, a set of axioms, and a set of inference rules. Are automatons also formal systems? Is an automaton ...
1
vote
1answer
35 views

Deterministic Push-Down Automata

Does there exist Deterministic Push-Down Automata for the language below. Any kind of answer will be highly appreciated! $$L =ba^nb^n U bba^nb^{2n}$$
1
vote
2answers
68 views

pumping lemma: ww^R not regular

I'm trying to prove that $L = \{ww^R : w \in \{a,b\}^*\}$ ($w^R$ is the reverse of $w$) is not regular using the pumping lemma. Let $p$ be the pumping length and $s = a^pbba^p$. $x = \epsilon$, $y = ...
1
vote
1answer
29 views

Checking my CFG to CNF answer

I attempted to transform the given CFG into CNF. $$S → ASA|A$$ $$A→aa|ε$$ Here are my steps: $$S→X$$ $$X→XA|AX|A$$ $$A→aa$$ $$S→X$$ $$X→XA|AX|YY$$ $$A→YY$$ $$Y→a$$ $$S→XA|AX|YY$$ ...
0
votes
0answers
22 views

CFG Convertion to GNF

I have a very simple CFG that I am trying to convert into GNF. The CFG is: S -> aSbS S -> epsilon I looked at the CFG and I think I can just do the ...
0
votes
1answer
26 views

Backus-Naur Form with automata

Parsers & compilers usually utilize deterministic finite automata to parse input. It's very easy to implement a generic DFA tool, that simulates any DFA table for example to validate input. ...
2
votes
2answers
41 views

Regular Expressions Help [duplicate]

I need a little help with Regular Expressions. The allowed operations are obviously + (union) , * (Kleene star) and concatenation. I have to write Regex for the following 2 examples. I have tried a ...
0
votes
2answers
32 views

DFA Construction with three strings in language

Draw DFA that recognizes the following language, with the alphabet {0, 1} {0011, 11, 0101} I'm having a lot of trouble with this, because I know DFA have to have a determined path from each state ...
-1
votes
1answer
50 views

Finding the CFG (Context Free Grammar) of a language

Can we write a CFG (Context Free Grammar) for the set of all non-empty string whose length are multiple of 3 on the alphabet $ \Sigma = \{A,R,G,C\} $
1
vote
1answer
37 views

Constructing PDA for a language

I want to prove or disprove that for a given two PDA's (Pushdown Automata) $M_1$ and $M_2$, we can build a PDA $M$ such that $$L(M) = \{w \in L(M_1) \mid w\text{ contains some string in ...
2
votes
0answers
64 views

Determine the language that corresponds to the following automata.

I want to determine that language that corresponds to the following automata Note: $q_{6}$ have arrow to $a$ to himself. I started with the minimal words: $aaabb$ $aaba$ $aaaba$ $bababa$ the ...
1
vote
1answer
104 views

Finite state machine

I am doing discrete math, and we are studying Finite State Machines. But i am a little confuse on how to do this. Here is a question, Write a regular expression for the language, and define a finite ...
1
vote
1answer
55 views

Prove or disprove whether the following is a regular language

I'm given the regular language L, and w being an element of L. If we remove the w from the language L, will the resulting language be still regular? Well I thought to be true. Since initially is a ...
0
votes
1answer
18 views

Eliminating Unit Productions

Eliminate all unit-productions from the grammar: $S \rightarrow abA\:|\:A\:|\:B$ $A \rightarrow B\:|\:ba\:|\:aBA$ $B \rightarrow A\:|\:aa\:|\:aA$ An article I was reading said that a unit ...
0
votes
1answer
28 views

Prove L is not a regular language (A Finite State Automaton cannot accept it)

$$\mathscr L = \{x \in \{0,1\}^* \mid \text{there is a } y \in \{0,1\}^* \text{ such that } x = yy\}$$ How can I prove that this is not a Regular language? I tried using proof by contradiction but ...
1
vote
1answer
44 views

Checking some Regular Expression problems

I'm given the alphabet $$ \Sigma = {\{a,b}\} $$ I tried to write a regular expressions for presenting the following sets: All strings in $$\Sigma ^ *$$ with: a-) number of 2s divisible by 4 b-) ...
1
vote
1answer
20 views

How to prove the following related with regular languages

How can we prove the following. If $$\sum$$ is any alphabet and L is any language $$L \subset \sum*$$ Then L*L* = L* ?
1
vote
0answers
57 views

Prove the following by using mathematical induction

If we define the alphabet such that $$ \Sigma = {\{a,b}\} $$ and let $w$ be a string over it. I'd like to prove $$ ( \operatorname{comp}(w))^R = \operatorname{comp}(w^R) $$ where $$ w^R$$ and ...
0
votes
1answer
54 views

find a regular expression and FA that each define L1 ∩ L2

from the following pairs I am trying to find a regular expression and FA that each define ...
0
votes
1answer
22 views

How can I show ithat a language is regular?

I have a very quick question about regular languages, I think $\{a^{2n}| n\geq 1\}$ is regular. I do know that pumping lemma can be used to show something that is not regular. I am wondering what ...
0
votes
1answer
27 views

Question About Pumping Lemma used on a FA

I am learning about pumping lemma and I am trying to solve a problem. I need to use pumping lemma to show that: the Language L(M) defined by the following machine is infinite. Here is the dfa: ...
2
votes
0answers
52 views

This proof in my textbook involving the pumping lemma appears incorrect - is it?

It states Let $B$ be the language $\{0^n1^n2^n | n \geq 0\}$. We use the pumping lemma to prove that $B$ is not regular. The proof is by contradiction. Assume to the contrary that $B$ is regular. ...
-1
votes
1answer
25 views

transition graph that accepts only Λ and language a*

I am trying to have a transition graph that accepts only Λ and also one that accepts language a* ...is this ok ??? transition graph that accepts only Λ transition graph that accepts language a*
0
votes
1answer
39 views

Creating a Push Down Automaton from a Grammar

I have the following grammar, but I'm not sure what exactly it is that it does: $\qquad\begin{align} S &\to S \vee T \mid T \\ T &\to T \wedge F \mid F \\ F &\to p \mid \thicksim p ...
0
votes
2answers
122 views

Prove the language $\{a^k b^l : k \neq l \}$ is not regular

Prove that the following language is not regular: $$L=\{a^k b^l : k,l \ge0, k\ne l\}$$ The problem is that I should use "distinguished states" not the pumping lemma, which is usually used for such ...
4
votes
1answer
59 views

Proving that a language is not context-free

Given the language $$L = \{ a^p \mid p\, \text{IS NOT prime} \}$$ is $L$ Context free? If not, prove that it's not. May I have some suggestions on how to use the pumping lemma to prove this, ...
2
votes
1answer
42 views

A correct proof for this pumping lemma example?

Given the language $L = \{0^{2^n} | n \geq 1\}$ So, the language contains all strings that have $2^n$ $0$s. First of all I take $z = a^{2^p}$ where $p$ is the constant guaranteed by the pumping ...
1
vote
2answers
65 views

The halting problem for tapes that are or are not completely blank

Is it possible to construct a Turing machine that halts only if the tape is not completely blank? Also, is it possible to construct one to halt if the tape is completely blank? Intuitively, I think ...
0
votes
2answers
321 views

Regular expression and DFA/NFA questions

If a language L is generated by a regular expression, then L is recognized by a DFA. I think this is true, because regular expressions describe regular languages, those of which are exactly ...
3
votes
1answer
44 views

Proof of a Known Claim About Languages

I would like to know how to prove that there is no non-trivial language $L$ that satisfies the following condition: $${\large \left(\overline{L}\right)^* = \overline{L^*}}$$ "Non-trivial" is ...
2
votes
1answer
57 views

Context free grammar for language

I'm learning how to generate context-free grammar for a language. $L=\{{a}^i {b}^j {c}^k\, |\,i=j\lor j=k$ Here is how I tried ...
0
votes
3answers
25 views

If $s \geq 3$, $3$ divides $s$, and $t = s/3$, then $t+1 < s$.

I am using the pumping lemma to prove a language is not regular, and would like to assert what I have stated in the title of the question to complete my proof. That is, if $s \geq 3$, $3$ divides $s$, ...
2
votes
1answer
59 views

Prove that RE is closed under reduction

Prove that the class RE is closed under reduction. Definitions: A language $ A \subseteq \Sigma^*$ is called reducible to $ B \subseteq \Gamma^*$ ( denoted by $A \leq B$) if there is a computable ...
1
vote
1answer
76 views

Push down automata for context free grammar

I'm having trouble finding the PDA for this language $L = \{x^{3i} y^j z^k\ |\ i \ge 0 \land k \gt 2j \gt 0\}$ The ...
1
vote
0answers
42 views

Language requiring a DFA with a certain number of states to implement

For any function $f\colon\{0,1\}^n\to\{0,1\}$, define a language $S_f = \{(b_1,b_2,\ldots ,b_n)\in\{0,1\}^n : f(b_1,b_2,\ldots ,b_n) = 1\}$. So all words in the langugage has same length $n$. I have ...
2
votes
1answer
55 views

(Transformation) Semigroups, the semigroup $\mathbf D_n$ and the wreath product

I have some trouble understanding the following proof, were I can't even figure out how some terms are defined. But first I state some definitions and preliminary lemmas. A transformation semigroup ...
0
votes
1answer
45 views

build finite automaton for language minimize states

I want to build a finite automaton that accepts $a^nb^n, n \gt 0, m \ge 0$. I can't do it unless the FA has two final states, i.e.: $delta(q0, a) = q1 delta(q1, a) = q1 delta(q1, b) = q2 delta(q2, ...
1
vote
2answers
101 views

Proving $L=\{0^n \mid \text{n is a perfect square}\}$ is not a Regular Language without the Pumping Lemma

Is this a valid way of going about proving the proposition? Let $L = \{0^n \mid \text{n is a perfect square}\}$. The regular languages are closed under concatenation. So if $x \in L, y \in L$, then ...
2
votes
1answer
83 views

DFA Rejection State

I'm being asked to construct a DFA for the language over $\{0,1\}$ such that each string of five consecutive symbols contain at least two zeroes. In my construction, it seems to me that it would make ...
1
vote
1answer
54 views

Grammar outside the Chomsky Hierarchy

This grammar describes a language that may fall outside the Chomsky Hierarchy (CH): \begin{array}{l} S \to abAbba \\ A \to abA \mid bbaB \\ B \to aab \\ \lambda \to Aab \mid aB \\ \end{array} Going ...
1
vote
1answer
39 views

Consider this grammar

Consider this grammar: \begin{array}{l} S \to aabBba \mid aAb \mid aab \\ bBb \to bCa \mid aaa\\ aA \to aC \mid bba\\ C \to aab \mid Cb \end{array} This is clearly context-sensitive (CS). It's not ...
0
votes
0answers
36 views

Context-sensitive grammar for this language

In order to write a context-sensitive grammar for: $L = \{ a^{n} b^{n} c^{n} d^{n} : n \ge 1 \}$ One possible set of productions is: $S \rightarrow aBCd | abcd $ $aB \rightarrow aaBb | ab | ...
0
votes
1answer
45 views

Assign Integer to Each Turing Machine

I have the following problem: suppose that we have an infinite set of symbols, $A = \{a_1, a_2, ...\}$ from which all Turing Machine input alphabets are chosen. Show how we could assign an integer to ...
2
votes
0answers
62 views

Blanks in the Tape of a Turing Machine

I used to have a lot of trouble with Turing Machines, primarily because I thought that in-between input symbols on the tape, one could have an arbitrary number of blanks, so every input would need to ...
0
votes
1answer
156 views

Grammar Construction from Given Language!

Just a fast question! I have this language L(G) = { z^n * x^2n with n>=1 } What is the grammar ? I think it should rather be: ...
1
vote
1answer
125 views

Languages and Grammar (Finding a language)

I have a trivial question (that I have actually solved, hopefully) although I am a bit curious if my result is alright. We have $N= \{S , C ,D\}$, $T=\{c, d\}$ and $P = \{S \to Dc, D \to Dd, D \to ...
0
votes
1answer
215 views

Using the Pumping Lemma to Prove $L = \{a^ib^jc^k \mid i < j < k\}$ is not Context-Free

I want to use the Pumping Lemma to prove that $$L = \{a^ib^jc^k \mid i < j < k\}$$ is not context-free. I think I have the intuition, but I don't know how to prove it. Help?