Q. 2 Design a NFA for the following language{ L = {w e {0-9}* : w represents the decimal encoding of a natural number whose encoding contains, as a substring, the encoding of a natural number that is divisible by 3}. {Note that 0 is a natural number that is divisible by 3. So any string that contains even one 0, 3, 6, or 9 is in L, no matter what else it contains. Otherwise, to be in L, there must be a sequence of digits whose sum equals 0 mod 3

Q. 2 Design a NFA for the following language{ L = {w e {0-9}* : w represents the decimal encoding of a natural number whose encoding contains, as a substring, the encoding of a natural number that is divisible by 3}. {Note that 0 is a natural number that is divisible by 3. So any string that contains even one 0, 3, 6, or 9 is in L, no matter what else it contains. Otherwise, to be in L, there must be a sequence of digits whose sum equals 0 mod 3

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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-Give a DFA for the language {w ∈ {a,b}*| w does not end in ba} -Give a DFA for the language {w ∈ {a,b}*| #a(w) + 2#b(w) ≡5 0 } -Give a possibly nondeterministic FA (an NFA) that recognizes the following language: {w ∈ {0,1}*| w corresponds to the binary encoding of a positive integer that is divisble by 16 or is odd} -If w is a string, we let #a(w) denote the number of occurences of 'a' in w. Give a formal recursive definition of the function #a.
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:
Consider the following languages over {0, 1}: L3 = {w : w begins and ends with different symbols, |w| £ 3} L4 = {w : w = wR, |w| £ 3} Enumerate the first 6 strings in the L-ordering of the following. If there are fewer than 6 string, enumerate the entire language: L3 L4 L33 L4*
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Draw a DFA over the alphabet {a,b,c}that only accepts strings with no c's and an even number of a's, or an odd number of c's and an odd number of b's. For example, it should accept aa, aba, abbabaa, cbacabcb, cbcca, and abc but not aca, bacc, or aaa.