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GATE CSE
Push Down Automata and Context Free Language
Theory of Computation
Previous Years Questions
START HERE
Marks 1
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Consider the following languages: $$\eqalign{ & {L_1} = \{ ww|w \in \{ a,b\} *\} \cr & {L_2} = \{ {a^n}{b^n}{c^m}...
GATE CSE 2022
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Consider the following languages: L1 = {an wan | w $$\in$$ {a, b}*} L2 = {wxwR | w, x $$\in$$ {a, b}*, | w | , | x | > 0...
GATE CSE 2022
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Consider the language L = { $${a^n}|n \ge 0$$ } $$ \cup $$ { $${a^n}{b^n}|n \ge 0$$ } and the following statements. I. L...
GATE CSE 2020
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Which of the following languages is generated by the given grammar? $$$S \to aS|bS|\varepsilon $$$
GATE CSE 2016 Set 1
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The lexical analysis for a modern computer language such as java needs the power of which one of the following machine m...
GATE CSE 2011
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$$S \to aSa\,\left| {\,bSb\,\left| {\,a\,\left| {\,b} \right.} \right.} \right.$$ The language generated by the above g...
GATE CSE 2009
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Which one of the following is FALSE?
GATE CSE 2009
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Let $${L_1} = \left\{ {{0^{n + m}}{1^n}{0^m}\left| {n,m \ge 0} \right.} \right\},$$ $$\,\,\,{L_2} = \left\{ {{0^{n + m}...
GATE CSE 2006
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Which of the following grammar rules violate the requirements of an operator grammar ? $$P,$$ $$Q, R$$ are non-terminals...
GATE CSE 2004
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The language accepted by a pushdown Automation in which the stack is limited to $$10$$ items is best described as
GATE CSE 2002
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Which of the following statement is true?
GATE CSE 2001
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Let $${L_D}$$ be the set of all languages accepted by a $$PDA$$ by final state and $${L_E}$$ the set of all languages ac...
GATE CSE 1999
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Context free languages are closed under:
GATE CSE 1999
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Consider the grammar with the following productions. $$S \to a\,\alpha \,\,b\left| {\,\,b\,\alpha } \right.\,c\,\left| {...
GATE CSE 1995
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State whether the following statement is TRUE / FALSE. The problem is to whether a Turing Machine M accepts input $$w$$ ...
GATE CSE 1990
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State whether the following statement is TRUE / FALSE. A is recursive if both a and its complement are accepted by Turin...
GATE CSE 1990
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State whether the following statement is TRUE / FALSE. The intersection of two $$CFL's$$ is also $$CFL.$$
GATE CSE 1990
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State whether the following statement is TRUE / FALSE. All subjects of regular sets are regular.
GATE CSE 1990
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State whether the following statement is TRUE / FALSE. Regularity is preserved under the operation of string reversal....
GATE CSE 1990
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State whether the following statement is TRUE / FALSE. A minimal $$DFA$$ that is equivalent to an $$NFDA$$ with $$n$$ m...
GATE CSE 1990
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Marks 2
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Let $$\left\langle M \right\rangle $$ denote an encoding of an automation M. Suppose that ∑ = {0, 1}. Whi...
GATE CSE 2021 Set 1
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In a pushdown automaton P = (Q, ∑, Γ, δ, q0, F), a transition of the form, where p, q ∈ Q, a&nb...
GATE CSE 2021 Set 1
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Consider the following context-free grammar where the set of terminals is {a, b, c, d, f}. S → d a T | R f T ...
GATE CSE 2021 Set 1
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Suppose that L1 is a regular and L2 is a context-free language, Which one of the following languages is NOT necessarily ...
GATE CSE 2021 Set 1
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Consider the following languages. L1 = {wxyx | w, x, y ∈ (0 + 1)+} L2 = {xy | x, y ∈ (a + b)*, |x| = |y|, x ≠ y} Which o...
GATE CSE 2020
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Consider the following languages: $$\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ $$\left\{ {{a^m}{b^n}{c^p}{d^q}} \right.|...
GATE CSE 2018
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Consider the following context-free grammars: $$\eqalign{ & {G_1}:\,\,\,\,\,S \to aS|B,\,\,B \to b|bB \cr &am...
GATE CSE 2016 Set 1
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Which of the following languages are context-free? $$$\eqalign{ & {L_1} = \left\{ {{a^m}{b^n}{a^n}{b^m}|m,n \ge 1...
GATE CSE 2015 Set 3
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Consider the following languages over the alphabet $$\sum { = \left\{ {0,\,1,\,c} \right\}:} $$ $$\eqalign{ & {L_...
GATE CSE 2014 Set 3
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Consider the $$DFA$$ $$A$$ given below. Which of the following are FALSE? $$1.$$ Complement of $$L(A)$$ is context - f...
GATE CSE 2013
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A deterministic finite automation $$(DFA)$$ $$D$$ with alphabet $$\sum { = \left\{ {a,b} \right\}} $$ is given below W...
GATE CSE 2011
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Consider the languages $${L_1}$$, $${L_2}$$ and $${L_3}$$ are given below. $$$\eqalign{ & {L_1} = \left\{ {{0^p}{1...
GATE CSE 2011
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Consider the languages $$$\eqalign{ & {L_1} = \left\{ {{0^i}{1^j}\,\left| {i \ne j} \right.} \right\},\,{L_2} = \...
GATE CSE 2010
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Match the following List-$${\rm I}$$ with List - $${\rm II}$$ List-$${\rm I}$$ $$E)$$ Checking that identifiers are decl...
GATE CSE 2008
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Which of the following statements are true? $$1.$$ Every left-recursive grammar can be converted to a right-recursive g...
GATE CSE 2008
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Which of the following statement is false?
GATE CSE 2008
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Consider the $$CFG$$ with $$\left\{ {S,A,B} \right\}$$ as the non-terminal alphabet, $$\left\{ {a,b} \right\}$$ as the t...
GATE CSE 2007
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Consider the $$CFG$$ with $$\left\{ {S,A,B} \right\}$$ as the non-terminal alphabet, $$\left\{ {a,b} \right\}$$ as the t...
GATE CSE 2007
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The language $$L = \left\{ {{0^i}{{21}^i}\,|\,i \ge 0} \right\}$$ over the alphabet $$\left\{ {0,1,2} \right\}$$ is
GATE CSE 2007
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Consider the following statements about the context-free grammar $$G = \left\{ {S \to SS,\,S \to ab,\,S \to ba,\,S \to \...
GATE CSE 2006
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Consider the language : $${L_1}\, = \left\{ {w\,{w^R}\,\left| {w \in \left\{ {0,1} \right\}{}^ * } \right.} \right\}$$ ...
GATE CSE 2005
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Consider the language : $${L_1} = \left\{ {{a^n}{b^n}{c^m}\left| {n,m > 0} \right.} \right\}$$ and $${L_2} = \left\{...
GATE CSE 2005
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Let $${N_f}$$ and $${N_p}$$ denote the classes of languages accepted by non-deterministic finite automata and non-determ...
GATE CSE 2005
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Let $$M = \left( {K,\,\sum {,\,F,\,\Delta ,\,s,\,F} } \right)$$ be a pushdown automation. Where $$K = \left\{ {s,\,f} \r...
GATE CSE 2004
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The language $$\left\{ {{a^m}{b^n}{c^{m + n}}\left| {m,n \ge } \right.} \right\}$$ is
GATE CSE 2004
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Consider the following grammar $$G:$$ $$\eqalign{ & S \to bS\,\left| {\,aA\,\left| {\,b} \right.} \right. \cr ...
GATE CSE 2004
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Consider the following decision problems: $${P_1}$$ Does a given finite state machine accept a given string $${P_2}$$ Do...
GATE CSE 2000
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If $${L_1}$$ is a context free language and $${L_2}$$ is a regular which of the following is/are false?
GATE CSE 1999
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Which of the following statements is false?
GATE CSE 1998
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Let $$L$$ be the set of all binary strings whose last two symbols are the same. The number of states in the minimum sta...
GATE CSE 1998
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Which of the following languages over $$\left\{ {a,b,c} \right\}$$ is accepted by Deterministic push down automata?
GATE CSE 1997
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Let $$G$$ be a context free grammar where $$G = \left( {\left\{ {S,A,.B,C} \right\},\left\{ {a,b,d} \right\},P,S} \right...
GATE CSE 1996
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If $${L_1}$$ and $${L_2}$$ are context free languages and $$R$$ a regular set, one of the languages below is not necessa...
GATE CSE 1996
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Which of the following features cannot be captured by context-free grammars?
GATE CSE 1994
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Context-free languages are
GATE CSE 1992
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Context free languages and regular languages are both closed under the operation(s) of :
GATE CSE 1989
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FORTRAN is:
GATE CSE 1987
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A context-free grammar is ambiguous if:
GATE CSE 1987
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