A1. Design a DFA for each of the following languages under the alphabet 2 = (0, 1). a1dfa1.jff = {w | 00 is not a substring of w} a1dfa2.jff = {w|neither 00 nor 000 is a substring of w} • a1dfa3.jff = {w|neither 00 nor 010 is a substring of w} a1dfa4.jf={w | neither 00 nor 0100 is a substring of w}
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- Write a regular expression to describe each of the following languages. Example: {w = {a, b}* : w has both aa and bb as substrings} Regular expression: (a U b)* aa (a U b)* bb (a U b)* U (a U b)* bb (a U b)* aa (a U b)*Write a regular expression to describe each of the following languages. Example: {w € {a, b}* : w has both aa and bb as substrings} Regular expression: (a U b)* aa (a U b) bb (a U b) U (a U b)* bb (a U b)* aa (a U b)*Find the regular expressions describing the following languages defined over the alphabet E = {0,1}: i. L, = {0*1" : n2 2, m z 1, n+m 2 4} ii. L, = {x : x| mod 3 = 0} i11. L; = {pqp : p,g E {0,1}* and | p |= 3}
- Design a PDA for the language L = {we {a,b} *:na(w)=nb (w)}, where n a (w) = the number of a's that appear in the string w. ApoDesign a TM that accepts the following language L={w ∈ {a, b}* | na(w)=nb (w)} , where na(w) indicates the number of symbol a’s in the string w.Design DFA for the following languages. Design a DFA for the language L where L={ 0i 1j both i and j are odd }. For example, 01, 000111, 011111 are valid strings belonging to L. Ʃ={0, 1}
- Construct a DFA/NFA that accepts the language L defined over the alphabet (5, 1, 2) as follows: L=(ww contains the substring 512)1. Design DFA's accepting the following languages over the alphabet {0, 1} 1.1. The set of strings that either begin or end with 01. 1.2. The set of strings such that the number of 0's is divisible by 5 and the number of 1's is divisible by 3. 1.3. The set of strings with even number of O's and odd number of 1's.Q3: Give CFG for the following Language L= {1²m0" such that m, n>= 0}.
- Construct a DFA that accepts the language Lover the alphabet E ={0,1}defined as follows. L= {w: w contains both 101 and 11 as substrings}Create an NPDA for the following language:On summation = {0.1}Language 1 (L1) every string in the language begin and end with 1Language 2 (L2) all strings in the language begin with 001The union of L1 and L22- Write a regular expression for each of the following languages over {a,b}: • String of a's and b's that begin with a and end with b. • Strings that have at least two a's. • Strings that have an even number of a's. • Strings that do not have two a's in a row. • Strings that do not end with the substring ab.