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Peter Linz Edition 4 Exercise 3.2 Question 4 (Page No. 87)
Find dfa's that accept the following languages. (a) $L (aa^* + aba^*b^*)$. (b) $L (ab (a + ab)^* (a + aa))$. (c) $L ((abab)^* + (aaa^* + b)^*)$. (d) $L (((aa^*)^* b)^*)$.
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Peter Linz Edition 4 Exercise 3.2 Question 3 (Page No. 87)
Give an nfa that accepts the language $L((a + b)^* b(a + bb)^*)$.
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Peter Linz Edition 4 Exercise 3.2 Question 2 (Page No. 87)
Find an nfa that accepts the complement of the language in $L (ab^*aa + bba^*ab)$.
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Peter Linz Edition 4 Exercise 3.2 Question 1 (Page No. 87)
Find an nfa that accepts the language $L (ab^*aa + bba^*ab)$.
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Peter Linz Edition 4 Exercise 3.1 Question 26 (Page No. 77)
Find an nfa that accepts the language $L (aa^* (a + b))$.
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Peter Linz Edition 4 Exercise 3.1 Question 24,25 (Page No. 77)
Formal languages can be used to describe a variety of twodimensional figures. Chaincode languages are defined on the alphabet $Σ =$ {$u, d, r, l$ }, where these symbols stand for unitlength straight lines in ... is a closed contour in the sense that the beginning and ending points are the same? Are these conditions also necessary?
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Peter Linz Edition 4 Exercise 3.1 Question 23 (Page No. 77)
For the case of a regular expression $r$ that does not involve $λ$ or $Ø$, give a set of necessary and sufficient conditions that $r$ must satisfy if $L(r)$ is to be infinite.
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Peter Linz Edition 4 Exercise 3.1 Question 22 (Page No. 77)
Prove rigorously that the expressions in $r= (1^*011^*)^* (0 + λ) + 1^* (0 + λ)$ do indeed denote the specified language.
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Peter Linz Edition 4 Exercise 3.1 Question 21 (Page No. 77)
Give a general method by which any regular expression $r$ can be changed into $\widehat{r}$ such that $(L(r))^R = L(\widehat{r})$.
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Peter Linz Edition 4 Exercise 3.1 Question 20 (Page No. 77)
Determine whether or not the following claims are true for all regular expressions $r_1$ and $r_2$. The symbol $≡$ stands for equivalence of regular expressions in the sense that both expressions denote the same language. (a) $(r_1^*)^*≡r_1^*$. (b) $r_1^*(r_1+r_2)^*≡(r_1+r_2)^*$. (c)$(r_1+r_2)^*≡(r_1^*r_2^*)^*$. (d)$(r_1r_2)^*≡r_1^*r_2^*$.
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Peter Linz Edition 4 Exercise 3.1 Question 19 (Page No. 77)
Repeat parts (a), (b), and (c) of Peter Linz Edition 4 Exercise 3.1 Question 18 (Page No. 76) with $Σ =$ {$a, b, c$}.
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Peter Linz Edition 4 Exercise 3.1 Question 18 (Page No. 76)
Find regular expressions for the following languages on {$a, b$}. (a) $L =$ {$w : w$ mod $3 = 0$}. (b) $L =$ {$w : n_a (w)$ mod $3 = 0$}. (c) $L =$ {$w : n_a (w)$ mod $5 > 0$}.
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Peter Linz Edition 4 Exercise 3.1 Question 17 (Page No. 76)
Write regular expressions for the following languages on {$0, 1$}. (a) all strings ending in $01$, (b) all strings not ending in $01$, (c) all strings containing an even number of $0$'s, (d) Peter Linz Edition 4 ... (e) all strings with at most two occurrences of the substring $00$, (f) all strings not containing the substring $101$.
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Peter Linz Edition 4 Exercise 3.1 Question 16 (Page No. 76)
Give regular expressions for the following languages on $Σ =$ {$a, b, c$}. (a) all strings containing exactly one $a$, (b) all strings containing no more than three $a$'s, (c) Peter Linz Edition 4 Exercise 3.1 Question 16.c ... Question 16.d (Page No. 76) (e) all strings in which all runs of $a$'shave lengths that are multiples of three.
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Peter Linz Edition 4 Exercise 3.1 Question 15 (Page No. 76)
Find a regular expression for $L =$ {$w∈ $ {$0,1$}$^* : w$ has exactly one pair of consecutive zeros} .
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Peter Linz Edition 4 Exercise 3.1 Question 14 (Page No. 76)
Find a regular expression for $L =$ {$vwv: v, w ∈${$a, b$}$^*, v≤3$}.
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Peter Linz Edition 4 Exercise 3.1 Question 13 (Page No. 76)
Find a regular expression for $L =$ {$vwv: v, w ∈${$a, b$}$^*, v =2$}.
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Peter Linz Edition 4 Exercise 3.1 Question 12 (Page No. 76)
Find a regular expression for the complement of the language in $L (r) =$ {$a^{2n}b^{2m+1}: n ≥ 0, m ≥ 0$}.
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Peter Linz Edition 4 Exercise 3.1 Question 11 (Page No. 76)
Find a regular expression for $L =$ {$ab^nw: n ≥ 3, w ∈$ {$a, b$}$^+$}.
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Peter Linz Edition 4 Exercise 3.1 Question 8 (Page No. 76)
Give a simple verbal description of the language $L ((aa)^* b (aa)^* + a (aa)^* ba (aa)^*)$.
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Peter Linz Edition 4 Exercise 3.1 Question 6 (Page No. 75)
Give regular expressions for the following languages. (a) $L_1=$ {$a^nb^m: n ≥ 4,m ≤ 3$}. (b) $L_2=$ {$a^nb^m: n < 4,m ≤ 3$}. (c) The complement of $L_1$. (d) The complement of $L_2$.
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Peter Linz Edition 4 Exercise 3.1 Question 4 (Page No. 75)
Find a regular expression for the set {$a^nb^m: n ≥ 3,m$ is even}.
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Peter Linz Edition 4 Exercise 3.1 Question 3 (Page No. 75)
Show that $r = (1 + 01)^* (0 + 1^*)$ also denotes the language in $L =$ {$w∈${$0,1$}$^* : w$ has no pair of consecutive zeros}. Find two other equivalent expressions.
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Peter Linz Edition 4 Exercise 3.1 Question 2 (Page No. 75)
Does the expression $((0 + 1) (0 + 1)^*)^* 00 (0 + 1)^*$ denote the language in $L(r) =$ {$w ∈ Σ^*: w$ has at least one pair of consecutive zeros}.?
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Peter Linz Edition 4 Exercise 3.1 Question 1 (Page No. 75)
Find all strings in $L((a + b) b (a + ab)^*)$ of length less than four.
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Virtual GATE
Let A be a regular set. Consider the two sets below L1={x  $\exists n\geq 0, \exists y\epsilon A :$ y=$x^n$} L2={x  $\exists n\geq 0, \exists y\epsilon A :$ x=$y^n$} which of the following statements is true? L1 and L2 both are regular L1 is regular but L2 is not L1 is not regular but L2 is L1 and L2 both are nonregular
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#TOC What will be the minimal DFA of this regular language?
Given L = { 0*1 + 0 + 1* + 10*1} where + symbol is UNION and NOT positive closure. Please draw the Minimal DFA for this.
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Peter Linz Edition 4 Exercise 3.1 Question 5 (Page No. 75)
what is the regular grammar for L={$a^nb^m$  n+m is even}
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Peter Linz Edition 4 Exercise 3.2 Question 10.b (Page No. 88)
What is the regular expression for this
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MadeEasy WorkBook: Theory of Computation  Regular Expression
Given answer is option c. Can anyone tell me how?
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