Automata Theory: DFA NFA for Language (na(w) − nb(w)) mod 3 divisible by | 128

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draw a dfa for given language L= {w : (na(w) -nb(w))mod3
dfa's for the following languages on = {a, b}. L = {w : |w| mod 3 = 0}
Find a DFA for the language L = {w : (na(w) −nb(w)) mod 3
na(w) mod 3 = 1 and nb(w) mod 3 = 2
Na(w) mod 3 = 0 and Nb(w) mod 2 = 0
w:(na(w) + nb(w)) mod 3
language L = {w : |na(w) − nb(w)| is odd}
language L = {w: na(w) = nb(w)} is not regular
L= na(w) = nb(w) + 1
na(w) = nb(w) + 1 and na(w) less than 100
na(w) = nb(w)+nc(w);
na(w) mod 3 = 1 and nb(w) mod 3 = 2
Give a regular expression for the following language.
na(w) mod 3 = 0 and there is exactly 1 b
w : |w| mod 3=0, |w| = 6
w: (na(w)- nb(w)) mod 3
For E = {a,b}, construct dfa's that accept the sets consisting of
(a) all strings with exactly one a,
(b) all strings with at least one a,
(c) all strings with no more than three a's, .
(d) all strings with at least one a and exactly two b's.
(e) all the strings with exactly two a's and more than two b's.
A run in a string is a substring of length at least two, as long as possible and consisting entirely of the same symbol. For instance, the string abbbaab
contains a run of b's of length three and a run of a's of length two. Find dfa's
for the following languageso n {a, b}.
(a) L = {w : w contains no runs of length less than four}
(b) L = {w: every run of a's has length either or three}
(c) L = {w: there are at most two runs of a.s of length three}
(d) L = {w: there are exactly two runs of a's of length 3}

Every 00 is followed immediately by a 1. For example. the strings
101. 0010. 0010011001 are in the language. but 0001 and 00100
are not. all strings containing 00 but not 000.
(c) The leftmost symbol differs from the rightmost one.
(d) Every substring of four symbols has at most two 0
(e) All strings of length five or more in the fourth symbol from
the right end is different from the leftmost symbol.
((fJ tAwllo sstryinmgbso linsa wreh iicdhe nthtiec alel.ftmost two symbols and the rightmost
1*10. Construct a dfa that accepts strings on {O. I} if and only. if the value of the
I j string, interpreted as a bin~. representation of an integer. is zero modulo five.
; For example, 0101 and 1111. representing the integers 5 and 15, respectively.
are to be accepted.
11. Show that the language L =