Q. Give a state transition diagram of a DFA that recognizes thefollowing language over the alphabet {0,1}):(A) The set of all strings such that every occurrence of 1 is followed byat least two Os, e.g., 01000100100, 10010000001000000, 00001000are in this language, but 001 is not.(B) The set of all strings that does not contain pattern 0101.(C) The set of all strings except 101 and 11.(D) The set of all string such that every even position contains 0. Forexample, 00000,101,100010 are in this language, but 010 and 1101are not.

Deterministic finite automata of the given languages

Answered: Q. Give a state transition diagram of a…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Consider the following languages over the alphabet Σ = {a, b}: 1. L1 = {xwx : x, w ∈ Σ∗}2. L2 = {xwx : x, w ∈ Σ∗, |w| = 1}3. L3 = {xwx : x, w ∈ Σ∗, |x| = 1} For each language, decide whether it is regular or not regular. Prove each of your claims. If you construct a FA or a regular expression, you do not need to prove the correctness of your construction.
Consider the languages L and L: L = {ww | w ∈ {a,b}∗}, all even-length strings of as and bs whose first and second halves are equal, and its complement L = {w | w ∈ {a,b}∗ ∧ w 6∈ L}, all strings of as and bs that are not in L. One of these languages is a CFL and the other is not. Either show that L or L̅ is context free by giving (design and formalize) either a PDA that recognizes it, or a CFG that generates it. Explain precisely why your PDA or CFG generates exactly L or L̅ .
Please give me the proper answer with step by steo solution Qns: Consider the CFL: L = {w | w is a string of a's and b's such that for every pair of adjacent b's, there is at least one a between them}. Design the PDA that recognizes the language L (Show Step-By-Step)
Let L be a language: L = {: M be TM which runs in polyno time}, and prove L is undecidable for the following scenario: A TM runs in polyno time if there exists a constant n > 0 such that, for all inputs y ∈ {0, 1} *, M(y) will halt at most |y| steps.
The question is to create the conversion function from an NFA to the PDA. Given that some NFA N = (Qn, Σ, δn, qn, Fn), produces an equivalent P = (Qp, Σ, Γ, δp, qp, Fp). This also proves that every regular language is also a CFL.
Give a state transition diagram of a DFA that recognizes the following language over the alphabet{0,1}): The set of all string such that every even position contains 0. For example, 00000,101,100010 are in this language, but 010 and 1101 are not.
Provide DFA diagrams to recognizes the same languages as each of the regular expressions in a. The set of chess moves, in the formal notation, such as p-k4 or kbp x qn. b. All stings of a’s and b’s that do not contain the substring abb. c. All strings of a’s and b’s that do not contain the subsequence abb.
Show, by giving an example, that if M is an NFA the recognizes language B, swapping the accept andnonaccept states in M doesn't necessarily yield a new NFA that recognizes the complement of B. Isthe class of languages recognized by NFAs closed under complement? Say why or why not.
Suppose L is any Regular language defined over the alphabet Σ = {0, 1} where every string contains atmost one 0's and atleast two 1's. If M is the DFA that Accepts L, then least number of states required to be in minimal DFA will be?
Let Z = { 0 0 ! , 0 1 ! , 1 0 ! , 1 1 ! }. Decide whether each of the following languages over Σ is regular: • The set of all strings such that the “top row” is the reverse of the bottom “row.” For instance, 0 0 ! 1 0 ! 0 1 ! 0 0 ! ∈ L, and 0 0 ! 1 1 ! 0 1 ! 0 0 ! ∈/ L, • The set of all strings such that the “top row” is the complement of the bottom “row.”
For any string w over ∑, writing its individual symbols so that w = w1w2…wn, we define the reverse wR of w as simply w written backwards: Given w = w1w2…wn with wi ∈ ∑ for 1 ≤ i ≤ n, wR = wn…w2w1. Similarly, for any language A over ∑, we define its reverse language as the language containing the reverse of all its strings: Given a language A, AR = { wR | w ∈ A}. Show that the class of context-free languages is closed under reversal
For any string w=w1w2…wn, the reverse of w, written wR, is the string w in reverse order, wn…w2w1. For any language L ={w0k | w ∈ L, k ≥ 0}, let LR={wR0k | w ∈ L, k ≥ 0}. Show that if L is regular, so is LR by buiding formal construction of an NFA M with L(M) = L.

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