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0
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1answer
124 views

Which of the following sets are regular and which are not? Give justification.

Which of the following sets are regular and which are not? Give justification. a) $\{a^nb^{2m}\mid n\ge 0\text{ and }m\ge 0\}$ b) $\{a^nb^m\mid n\ne m\}$ c) $L((a^*b)^*a^*)$ d) $\{a^nb^nc^n\mid n\ge ...
0
votes
2answers
72 views

Regular expresson a's and b's

Need to construct a regular expression that recognizes the following language of strings over the alphabet {a,b}: - The set of all strings over alphabet {a,b} in which every occurrence of b is ...
0
votes
1answer
62 views

Regular Expression of alternative 0's and 1's?

Let $L$ be the language of $0$'s and $1$'s in alternate positions, where $$ L = \{ \epsilon, 0, 1, 01, 10, 01010,\ldots\}. $$ Is $(0)*$ + $(1)*$ a valid regular expression that represents this ...
2
votes
1answer
119 views

regex for binary string which doesnt contain 11110

Here's my attempt, although I'm not sure if i missed any edge cases: $(0,10,110,1110)^*(1)^*$ it seems to work for any random string i test in a regex program, but is this correct?
-2
votes
1answer
51 views

What is the Regular Expression for this DFA? [closed]

What is the Regular Expression for this DFA? Progress: q0 has 0* loop and q1 has 1* loop... Perhaps the answer is 0*(10∪01)1*.
1
vote
1answer
14 views

Regular expression building: Comment delimited strings

I'm attempting to build a regular expression that will accept only strings of the form: ...
1
vote
1answer
35 views

Isn't $L=\{ww|w \in \{0,1\}^*\}$ a Non Deterministic Context Free Language?

My book says that it is not a Non Deterministic CFL. If $ww^R$ can be a N-CFL, then why not the one in the question? I think it might be a printing mistake, not sure.
1
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0answers
40 views

Why is $a^nb^n|n\geq1$ not regular and $a^nb^n|n\leq {10^{10}}$ regular?

I've heard somewhere that since the latter is bounded, it is regular. Can anyone explain me what a bound actually means? And if the latter is regular, then how would you write the regular expression ...
1
vote
1answer
470 views

Blocks of Pyramid Pattern Expression [duplicate]

There is a pattern following, and trying to find the algebraic expression Each layer (from the top). Diagram. So the first layer has 1, second has 4, third has 9, and the fourth has 16. That's ...
1
vote
2answers
41 views

Did I find the right expression for the regular language for this FSA?

I have the following FSA, and the regular language that I found for it: Is this language correct? It doesn't match the solution in the book, but my teacher says there can be multiple equally ...
2
votes
3answers
92 views

regular language proof, a language partial to a regular one

So, I've been trying to solve a question I got and I think I'm correct but I'm not positive. Is the language {w| www belongs to L' and L' is regular} regular? I couldnt find any way to prove it isnt ...
1
vote
1answer
113 views

$L_1 =(a^nb^n)$ and $L_2 =(a^nb^{2n})$. Is $L_1 \cup L_2$ DCFL?

I think that since $a^nb^n$ is not regular (applied pumping lemma), so is $L_2$. Therefore, $L_1 \cup L_2$ is not cfL. Is that correct?
0
votes
1answer
42 views

Binomial theorem - number of terms in expansion

Question: Find the number of terms, after simplifying, in $$(x + y + \frac{1}{x} + \frac{1}{y})^{16}$$ I was unable to find any approach to this question. Fully expanding the expression isn't a ...
1
vote
3answers
24 views

Expression of Equation

Find the next three terms for the pattern following : (-1276),(+425),(-142),(+47) Simple pattern here.... Only pattern I can find is that, the odd number term goes up by 1134, and the even number ...
1
vote
5answers
38 views

Finding expression for pattern

This seems easy.... Pattern: 3, 6, 10, 15, 21.... How do I find expression for this? It looked easy, but I couldn't find it. I tried graphing it, but it turned out that it is not quadratic... ...
0
votes
1answer
25 views

Are regular expressions in mathematics related to PCRE or POSIX regexps?

I've recently come across a number of questions tagged with (regular-expressions), and talking about some type of regular expressions, here's an example of such ...
0
votes
2answers
68 views

Regular expression 00 or 11 not both

Can anyone help me with this question: I know it before, but I have tried to solve it myself and didnt succeed. what is the regular expression for this language: L=all words that have 00 or 11 but not ...
-1
votes
1answer
63 views

Regular expression with xor [duplicate]

Can anyone help me with this question: I know i asked a similar question not a while ago but i'm not able to understand how its possible. If anyone could give me a lot of examples instead of an ...
0
votes
1answer
24 views

Regular expression problem

I have this question and no clue how to solve. Thanks for your help I need to build the regular expression matching this language $$L=\{ 0^m~1^n | (m+n) \pmod 3 = 1 \}$$
0
votes
1answer
119 views

Converting NFA to DFA and then to regular expression.

Convert the NFA into a DFA and then into a regular expression defining the language accepted by this NFA. NFA So far I have converted to a DFA (I hope) but do not know how I can convert to a ...
0
votes
2answers
77 views

Arithmetic Progressions Formula

I'm studying progressions in math class in Portugal, and I don't know the words/translation in english for certain things so I'll try to explain. I have this arithmetic progression: 2, 8, 18, 32 ... ...
1
vote
1answer
93 views

For any regular expression for a finite automata, how do you find the shortest word accepted?

So in the question "For the following regular expression α over the alphabet {a, b}, find one of the shortest words in the language L(α) defined by this expression" a*abab* As far as I understand, ...
2
votes
2answers
187 views

Combinatorics problem involving a regular expression

If formal definition of a regular expression is required, please comment and I'll add it. I was given the assignment of determining how many words of length $n$ can be produced from a regular ...
1
vote
0answers
30 views

Equality of regular language

I am showing that two regular expressions are equal. In one of intermediate steps, I thought of the equaility: $$(RS+R)^* = (RS)^*R(RS)^*R(RS)^*....R(RS)^* = R^*(RS)R^*(RS)...R^*$$ Is it true? I ...
1
vote
1answer
57 views

How do I generate regular expression from this deterministic finite state automaton?

I want to create a regular expression from the following deterministic finite automaton: "abb" substring search How do I generate regexp from above dfa and what are the steps for doing so? ...
1
vote
1answer
66 views

Instead of mid-point, how do i find a third of the way up the line instead.

I'm working with the program Maya, and i need to script a way to find various fractions up a line for each 3D vector. For example, lets say I have the vector (0, 0, 0), and the vector (12, 12, 12). ...
0
votes
1answer
38 views

I don't understand the value of the following regular expressions.

$$\begin{align} 0^{*}10^{*} &= \{w ~\mid ~ w \text{ contains a single } 1\} \\ \Sigma^{*}1\Sigma^{*} &= \{w ~\mid ~w \text{ has at least one } 1\} \\ 0 \Sigma^{*}0~\cup ~1\Sigma^{*}1~\cup ...
0
votes
1answer
33 views

Proving non-regularity of a language

How can I prove $L = (01^n2^n | n\geq 0)$ is not regular? Would it be sufficient to say that $01^p2^p$ is in $L$ and by pumping lemma, $01^p2^p$ can be written as $xyz$ such that $|y|>0, ...
0
votes
1answer
23 views

converting to regular expression

{w | w can be written as $0^k l 0^k$ for some $k \geq 1$ and for any $l$ in ${0,1}*}$ i.e. 00010111000 can be written as 0^3 10111 0^3 How can I convert this description into a regular expression? ...
2
votes
1answer
34 views

Why is $\left\{a\right\}^*\cap L(A)=\emptyset$? where $\delta(q,a)=q$

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 states ...
0
votes
2answers
60 views

Rewriting an expression

I got the following problem and can't solve it. Factorize the following statement: C(n+2, n) + C(n+3, n+2). So basically they are asking to rewrite the expression as a X*P expression instead of A+B ...
2
votes
1answer
70 views

$L=${$a^nb^nc^n : n \geq 0 $} CFG Recognizing

Suppose $L=${$a^nb^nc^n : n \geq 0 $} and I. $h(L), h(a)=a, h(b)=bb, h(c)=b$ II. $L^R$ III. $L^*$ IV. $h(L), h(a)=a, h(b)=bb, h(c)=a$ Why just I is a CFG and other is not? anyone can help me to ...
0
votes
2answers
118 views

Language of a grammar vs regular expression vs 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 ...
0
votes
1answer
86 views

Intersection / Union of two regular expressions

Is there a way to directly form a new regular expression when given two regular expressions and the desired operation (Union or Intersection). $$ (a+b)^*aa(a+b)^*\cup (a+b)^*aa(a+b)^* $$ $$ ...
0
votes
2answers
117 views

Simplifying modulus expressions and an unknown expression? discrete math

I have a few questions below that I need help with a) I don't really understand what that symbol means and how to solve it b) How do u simplify this without a calculator c) I got 2^-r = 0, iss this ...
0
votes
1answer
37 views

Solving an Equation for a Variable with $\max()$ and $\min()$ Functions

I came across an expression in 3 variables involving the max and min functions: $$x = y - \max(x,z) + \min(x,y,z).$$ I need to solve this expression for $y$. Is there any way we can do this? ...
1
vote
2answers
117 views

Substitutions in Maple

Can any one tell me what am I doing wrong in the following expression in Maple? subs(a*b*c=A, e*f/d=B, a*b*c*e*f/d) I am getting the output $\frac{abcef}{d}$ ...
0
votes
1answer
33 views

Proof the 1 language is contained in another

Does anyone know what the best method is to prove that the intersection of Language1 and Language 2 = Language1? Where both languages are over alphabet {a,b,c}.
2
votes
0answers
52 views

how to covert regular expression in simplest form?

I have made this expression from nfa (NFA to regular expression) : (a+ab+aa*b)*(a+a*a) but at book answers it is written like this : (a+aa*b)*(a*a) I am thinking that the my answer is same as ...
1
vote
1answer
689 views

induction proof for kleene star

i am going through some past exam paper questions on regular languages for some revision, and i am having a bit of trouble with converting general ideas into formal mathematical proofs. the question ...
0
votes
1answer
37 views

Which is true about this NFA?

Let $M$ be an NFA with alphabet {0,1} that accepts every binary string. Which of the following is true? a) Every state of $M$ must be an accept state b) $M$ does not have any accept state c) The ...
0
votes
2answers
54 views

Gives regular expressions which defines regular language and what does {1,2} mean

The question is give a regular expression which defines a regular language. Question: The language over {0,1} consisting of all strings which either have length less than 3 or have 0 as their third ...
0
votes
1answer
18 views

Finding a Regular Expression with a Specific Length from a language

Given this language, I was supposed to find the Regular Expression that represented it. Having given up and getting the answer later (below) I couldn't understand the regular expression. Given ...
1
vote
2answers
29 views

Regular expression translation.

Given a set {1,2,...9} how can I construct a regular expression starts with a 3 has no 8's and has even number of 6's? Here's what I tried: $$$$ Define a new set no8 = {1,2,3,4,5,6,7,9} ...
0
votes
1answer
39 views

Regular expression construction.

I would like to construct a regular expression of length at least 5 that starts with 'f' and ends with 'y' and who's second symbol is 'u' from the alphabet {a,b,...,z}. My solution to this problem ...
2
votes
2answers
49 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 ...
1
vote
2answers
126 views

Formal Languages - Regular Expression

I've been battling the following two questions for more than a day today. Write a regular expression (comprised of {a, b}) that contain at least two b and do not contain abb. Write a regular ...
1
vote
3answers
289 views

Draw a finite state machine which will accept the regular expression $(a^2)^* + (b^3)^*$

Draw a finite state machine which will accept the regular expression: $(a^2)^* + (b^3)^*$ In particular, I am confused by the $+$ sign, what does it exactly mean? Most literature I could find about ...
1
vote
0answers
73 views

Minimal DFA for a given regular expression

How can I construct a minimal DFA from the following definition? $L=\{w \in \{a,b,c\}^* $: if the second-to-last letter from w is an $a$, then the number of $c$'s $\le 1\}$ I've already made a ...
2
votes
2answers
876 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 ...