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- Introduction of Finite Automata
- Arden's Theorem in Theory of Computation
- Solving Automata Using Arden's Theorem
- L-graphs in TOC
- Hypothesis (language regularity) and algorithm (L-graph to NFA) in TOC
- Regular Expressions, Regular Grammar and Regular Languages
- Identify a Regular Language.
- Designing Finite Automata from Regular Expression (Set 1)
- Star Height of Regular Expression and Regular Language
- Generating Regular Expression from Finite Automata
- Code Implementation of Deterministic Finite Automata (Set 1)
- Program for Deterministic Finite Automata
- DFA for Strings not ending with "THE"
- DFA of a string with at least two 0’s and at least two 1’s
- DFA for accepting the language L = { a<sup>n</sup>b<sup>m</sup> | n+m =even }
- DFA machines accepting odd number of 0’s or/and even number of 1’s
- DFA of a string in which 2nd symbol from RHS is 'a'
- Union Process in DFA
- Concatenation Process in DFA
- DFA in LEX code which accepts even number of zeros and even number of ones
- Conversion from NFA to DFA
- Minimization of DFA
- Reversing Deterministic Finite Automata
- Complementation process in DFA
- Kleene's Theorem in TOC
- Mealy and Moore Machines in TOC
- Mealy Machine vs Moore Machine
- Relationship between grammar and language in Theory of Computation
- Simplifying Context Free Grammars
- Closure Properties of Context Free Languages
- Union and Intersection of Regular languages with CFL
- Converting Context Free Grammar to Chomsky Normal Form
- Converting Context Free Grammar to Greibach Normal Form
- Pumping Lemma in Theory of Computation
- Check if the language is Context Free or Not
- Ambiguity in Context free Grammar and Languages
- Operator Grammar and Precedence Parser
- Context-sensitive Grammar (CSG) and Language (CSL)
- Introduction of Pushdown Automata
- Pushdown Automata Acceptance by Final State
- Construct Pushdown Automata for given languages
- Construct Pushdown Automata for all length palindrome
- Detailed Study of PushDown Automata
- NPDA for accepting the language L = {a<sup>n</sup>b<sup>m</sup> c<sup>n</sup> | m,n>=1}
- NPDA for accepting the language L = {a<sup>n</sup> b<sup>n</sup> c<sup>m</sup> | m,n>=1}
- NPDA for accepting the language L = {a<sup>n</sup>b<sup>n</sup> | n>=1}
- NPDA for accepting the language L = {a<sup>m</sup>b<sup>2m</sup>| m>=1}
- NPDA for accepting the language L = {a<sup>m</sup> b<sup>n</sup> c<sup>p</sup> d<sup>q</sup> | m+n=p+q ; m,n,p,q>=1}
- Construct Pushdown automata for L = {0<sup>n</sup>1<sup>m</sup>2<sup>m</sup>3<sup>n</sup> | m,n ≥ 0}
- Construct Pushdown automata for L = {0<sup>n</sup>1<sup>m</sup>2<sup>n+m</sup> | m, n ≥ 0}
- NPDA for accepting the language L = {a<sup>m</sup>b<sup>n</sup>c<sup>m+n</sup> | m,n ≥ 1}
- NPDA for accepting the language L = {a<sup>m</sup>b<sup>(m+n)</sup>c<sup>n</sup>| m,n ≥ 1}
- NPDA for accepting the language L = {a<sup>2m</sup>b<sup>3m</sup>|m>=1}
- NPDA for accepting the language L = {a<sup>m</sup>b<sup>2m+1</sup> | m ≥ 1}
- NPDA for accepting the language L = {a<sup>i</sup>b<sup>j</sup>c<sup>k</sup>d<sup>l</sup> | i==k or j==l,i>=1,j>=1}
- Construct Pushdown automata for L = {a<sup>2m</sup>c<sup>4n</sup>d<sup>n</sup>b<sup>m</sup> | m,n ≥ 0}
- NPDA for L = {0<sup>i</sup>1<sup>j</sup>2<sup>k</sup> | i==j or j==k ; i , j , k >= 1}
- NPDA for accepting the language L = {a<sup>n</sup>b<sup>2n</sup>| n>=1} U {a<sup>n</sup>b<sup>n</sup>| n>=1}
- NPDA for the language L ={wЄ{a,b}* | w contains equal no. of a's and b's}
- Turing Machine in TOC
- Turing Machine for addition
- Turing machine for subtraction | Set 1
- Turing machine for multiplication
- Turing machine for copying data
- Construct a Turing Machine for language L = {0<sup>n</sup>1<sup>n</sup>2<sup>n</sup> | n≥1}
- Construct a Turing Machine for language L = {wwr | w ∈ {0, 1}}
- Construct a Turing Machine for language L = {ww | w ∈ {0,1}}
- Construct Turing machine for L = {a<sup>n</sup> b<sup>m</sup> a<sup>(n+m)</sup> | n,m≥1}
- Construct a Turing machine for L = {a<sup>i</sup>b<sup>j</sup>c<sup>k</sup> | i*j = k; i, j, k ≥ 1}
- Turing machine for 1's and 2’s complement
- Recursive and Recursive Enumerable Languages in TOC
- Turing Machine for subtraction | Set 2
- Halting Problem in Theory of Computation
- Turing Machine as Comparator
Context free languages and Push-down automata
Question 1
Consider the following languages.
Which one of the following statements is FALSE?
- A
L2 is context-free.
- B
L1 intersection L2 is context-free.
- C
Complement of L2 is recursive.
- D
Complement of L1 is context-free but not regular.
Question 2
Which of the following pairs have DIFFERENT expressive power?
- A
Deterministic finite automata(DFA) and Non-deterministic finite automata(NFA)
- B
Deterministic push down automata(DPDA)and Non-deterministic push down automata(NPDA)
- C
Deterministic single-tape Turing machine and Non-deterministic single-tape Turing machine
- D
Single-tape Turing machine and multi-tape Turing machine
Question 3
Let P be a regular language and Q be context-free language such that Q ⊆ P. (For example, let P be the language represented by the regular expression p*q* and Q be {pn qn | n ∈ N}). Then which of the following is ALWAYS regular?
(A) P ∩ Q
(B) P - Q
(C) ∑* - P
(D) ∑* - Q
- A
A
- B
B
- C
C
- D
D
Question 4
Consider the languages L1, L2 and L3 as given below.
LI= {0P1q |p, q∈N}
L2={0p1q |p, q∈ N and p=q} and
L3= {0P1q0r |p, q, r∈ N and p =q = r}
Which of the following statements is NOT TRUE?
[GATE | CS | 2011 |]
- A
Push Down Automata (PDA) can be used to recognize L1 and L2
- B
L1 is a regular language
- C
All the three languages are context free
- D
Turing machine can be used to recognize all the three languages
Question 5
Consider the languages -
L1 = {0i1j | i != j}.
L2 = {0i1j | i = j}.
L3 = {0i1j | i = 2j+1}.
L4 = {0i1j | i != 2j}.
- A
Only L2 is context free
- B
Only L2 and L3 are context free
- C
Only L1 and L2 are context free
- D
All are context free
Question 6
S -> aSa|bSb|a|b; The language generated by the above grammar over the alphabet {a,b} is the set of
- A
All palindromes
- B
All odd length palindromes.
- C
Strings that begin and end with the same symbol
- D
All even length palindromes
Question 7
Let L = L1∩L2, where L1 and L2 are languages as defined below:
L1 = {am bm can bn | m, n >= 0}
L2 = {ai bj ck | i, j, k >= 0}
Then L is
- A
Not recursive
- B
Regular
- C
Context free but not regular
- D
Recursively enumerable but not context free.
Question 8
Which of following statement(s) is/are not correct? (I) Languages generated by the grammar S→aSa ∣ aa is not regular. (II) Languages generated by the grammar S→aSb ∣ aa is not regular. (III) Languages generated by the grammar S→S1|S3, S1→aS1c |S2|λ, S2→aS2b|λ, S3→aS3b|S4| λ, S4→bS4c|λ is {a^nb^mc^k | k = |n - m|, n≥0, m≥0, k≥0}. (IV) Languages generated by the grammar S→S1S3, S1→aS1c |S2|λ, S2→aS2b|λ, S3→aS3b|S4| λ, S4→bS4c|λ is {a^nb^mc^k | k = |n - m|, n≥0, m≥0, k≥0}.
- A
Only (II), (IV)
- B
Only (I), (III), (IV)
- C
Only (I), (II), (III)
- D
All of the above
Question 9
Consider the following languages.
L1 = {ai bj ck | i = j, k ≥ 1}
L1 = {ai bj | j = 2i, i ≥ 0}
Which of the following is true?
- A
L1 is not a CFL but L2 is
- B
L1 ∩ L2 = ∅ and L1 is non-regular
- C
L1 ∪ L2 is not a CFL but L2 is
- D
There is a 4-state PDA that accepts L1, but there is no DPDA that accepts L2
Question 10
Match the following:
- A(1)
- B(2)
- C(3)
- D(4)
There are 94 questions to complete.
