CS2303 – Theory Of Computations Important Questions For V SEMESTER CSE

UNIT I

1. Consider the following ε–NFA. Compute the ε–closure of each state and find it’s equivalent DFA.

ε A b C

p Ф {p}

{q}

Ф

q {p}

{q}

{r}

Ф

*r {q}

{r}

ф {p}

2. Construct a NFA over the alphabet {0,1} that accepts all strings end in 01

3. For the finite state machine M given in the following table, test whether the strings 101101,11111 are accepted by M.

4. Consider the following ε–NFA. Compute the ε–closure of each state and find it’s equivalent DFA.

ε a b c p

{q,r}

Ф {q}

{r}

q Ф {p}

{r}

{p,q}

*r Ф ф ф ф 5. Convert a NFA which accepts the string ends with 01 to a DFA.

6. Consider the following ε–NFA. Compute the ε–closure of each state and find it’s equivalent DFA.

ε a b c p

{q}

{p}

Ф Ф

q {r}

ф {q

Ф

} *r Ф ф ф {r

} 7. Convert the NFA string that ends with 01 to equivalent DFA

UNIT II

1. Find The regular expression for the set of all strings denoted byR132

from the DFA given below.

2. Draw the table of distinguishabilities for this automaton & Construct the minimum – state equivalent DFA.

3. Find the regular expression for the set of all strings denoted by R13

3

from the deterministic finite automata given below

4. Construct the NFA –Σ For the given regular expression Using Thompson’s and Construct DFA For the above NFA –Σ and find the Minimized DFA? (b/a)*bba

5. Find whether the languages (ww, w is in (1+0)*} and {1k | k=n2, n ≥1} are regular or not.

UNIT III1. Obtain the regular expression that denotes the language accepted by the

following DFA

2. Find the regular expression for the set of all strings denotes by R13

3 from the deterministic finite automata given below

3. Find a derivation tree of a*b +a*b given that a*b+a*b is in L(G) where G is given by S → S + S | S * S , S → a | b.

4. Suppose the PDA P= ({q,p},{0,1},{Z0,X}, δ,q, Z0,{p}) has the following transition function :

1. δ(q,0, Z0) ={(q, XZ0)} 2. δ(q,0, X) = {(q,XX)} 3. δ(q,1, X) = {(q,X)} 4. δ(q,ε, X) = {(p,ε)} 5. δ(p,ε, X) = {(p,ε)} 6. δ(p,1, X) = {(p,XX)} 7. δ(p,1, Z0) = {(p,ε)} starting from the intial ID (q,w, Z0), show all

the reachable ID’s when the input w is a) 01 b) 0011 c) 010.

UNIT IV

1. Show that set of all strings over {a,b} consisting of equal number of a’s & b’s is accepted by a deterministic PDA.

2. Convert the grammar S → 0S1 | A, A→1A0 | S | ε to a PDA that a accepts the same language by empty stack.

3. The following grammar generates the language of regular expression 0*1(0+1)* S → A1B , A → 0A | ε, B → 0B | 1B | ε. Give leftmost & rightmost derivation of the following strings: a) 00101 b) 1001 c) 00011

4. Design context free grammar for the following languagesa) The set {0n1n | n≥1}, that is the set of all strings of one or more 0’s followed by an equal number of 1’s.

UNIT V

1. Consider the Language Lwwr={wwR | w is in (0+1)*}. Design the PDA P to accept the Lwwr. Starting from the initial ID (q,w, Z0), show all the reachable ID’s when the input w is a) 11111 b) 0011 c) 011.

2. Convert the PDA P= ({p,q},{0,1},{X,Z0},δ,q, Z0) to a CFG , if is given by

1. δ(q,1, Z0) ={(q, XZ0)} 2. δ(q,1, X) = {(q,XX)}

3. δ(q,0, X) = {(p,X)} 4. δ(q,ε, X) = {(q,ε)} 5. δ(p,1, X) = {(p,ε)} 6. δ(p,0, Z0) = {(q, Z0)}

3. Prove the theorem, Let L be L(PF) for some PDA PF=(Q, ∑, Γ, δN, q,

Z0,F), then there Is a PDA PN such that L=L(PN)

4 Convert the PDA P= ({q,p},{0,1},{Z0,X}, δ,q, Z0,{p}) to a Context free grammar.

1. δ(q,0, Z0) ={(q, XZ0)} 2. δ(q,0, X) = {(q,XX)} 3. δ(q,1, X) = {(q,X)} 4. δ(q,ε, X) = {(p,ε)} 5. δ(p,ε, X) = {(p,ε)} 6. δ(p,1, X) = {(p,XX)} 7. δ(p,1, Z0) = {(p,ε)}