Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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- Given N = (Q, {a, b}, δ, q0, F) is an NFA that recognizes language L. Define a new language concatenate(L) that is formed by concatenating symbol a to the end of every string in L. That is, concatenatea(L) = {wa | w ∈ L(N)}. Please construct an NFA N′ with exactly one accepting state that recognizes language concatenate(L). All you need to do is fill in the missing parts in the definition below. N′ = (Q′ , {a, b}, δ′ , q′ 0 , F′ ) where (a) Q′ = (b) q ′ 0 = (c) F ′ = (d) δ ′ is defined as follows:arrow_forwardConsider the language L = { |‡x such that ï ¤ L(M₁)~ L(M₂)}. Show that L is not decidable.arrow_forwardConsider the language L = { x ∈ [a,b]* | x starts with b, does not contain the substring aa and ends with an a} Draw the finite automata.arrow_forward
- For any string w 6=/ E, the principal suffix of w is the string resulting by removing the first symbol from w. We will denote this string by ps(w). For any language L, define ps(L) := {ps(w) : w ∈ L ∧ w 6=/ E}. Show that if L is regular, then ps(L) is regular. (The underlying alphabet is arbitrary.) Show by giving rules to transform a regex for L into a regex for ps(L).arrow_forwardFor a Turing machine M, (M) refers to the binary representation of M. For a Turing machine M, L(M) contains the set of all strings accepted by M. For a Turing machine M and an input x € {0,1}*, Steps(M, x) refers to the number of steps taken by M to execute on x before it halts. Here, one step of execution of M on x = one movement (left or right) of the tape head. For a Turing machine M and an input x = {0,1}*, we define the following: ReachCells(M,x) = {i : M reaches ith tape cell when M is executed on x} Informally, it contains all locations on the tape that are visited when M is ecuted on x. The leftmost location on the tape is the first tape cell, the location next to it is the second tape cell, and so on. A string w₁ is an anagram of w2 if w₁ can be obtained by rearranging the alphabets of w2. Formally, if w₁ is an n length string, wê is called an anagram of w₁ if there exists a permutation à on n elements such that π(w₁) = W2.arrow_forwardConsider the language L = {w010w | w ∈ Ld} Is this language recursively enumerable? Justify your answerarrow_forward
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