GATE CSE

Recursively Enumerable Language and Turing Machine

Theory of Computation

(Past Years Questions)

Marks 1

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Consider the following types of languages: $${L_1}:$$ Regular, $${L_2}:$$ Context-free, $${L_3}:$$ Recursive, $${L_4}:$$...
GATE CSE 2016 Set 2
Consider the following statements. $$\,\,\,$$ $${\rm I}.\,\,\,\,\,\,\,\,\,$$ The complement of every Turing decidable la...
GATE CSE 2015 Set 2
For any two languages L1 and L2 such that L1 is context-free and L2 is recursively enumerable but not recursive, which o...
GATE CSE 2015 Set 1
Let $$A\,\,{ \le _m}\,\,B$$ denotes that language $$A$$ is mapping reducible (also known as many-to-one reducible) to la...
GATE CSE 2014 Set 2
Which of the following statements is/are FALSE? $$1.$$ For every non-deterministic Turing machine, there exists an equiv...
GATE CSE 2013
Which of the following is true for the language $$\left\{ {{a^p}} \right.\left| P \right.$$ prime $$\left. \, \right\}$...
GATE CSE 2008
Nobody knows yet if $$P=NP$$. Consider the language $$L$$ defined as follows $$L = \left\{ {\matrix{ {{{\left( {0 + 1...
GATE CSE 2003
If the strings of a language $$L$$ can be effectively enumerated in lexicographic (i.e., alphabetic$$(c)$$ order, which ...
GATE CSE 2003
Regarding the power of recognition of languages, which of the following statement is false?
GATE CSE 1998
Which of the following statements is / are true / false? Union of two recursive languages is recursive
GATE CSE 1992
Which of the following statements is / are true / false? The language $$\left\{ {{0^n}\,\left| {\,n} \right.} \right.$$ ...
GATE CSE 1992
Which of the following statements is / are true / false? Regular languages are closed under infinite union.
GATE CSE 1992

Marks 2

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The set of all recursively enumerable languages is
GATE CSE 2018
Consider the following problems. $$L(G)$$ denotes the language generated by a grammar $$G.$$ $$L(M)$$ denotes the langua...
GATE CSE 2018
Consider the following languages. $$\,\,\,\,\,\,\,\,\,\,\,\,$$ $${L_1} = \left\{ {\left\langle M \right\rangle |M} \righ...
GATE CSE 2016 Set 2
Let $$X$$ be a recursive language and $$Y$$ be a recursively enumerable but not recursive language. Let $$W$$ and $$Z$$ ...
GATE CSE 2016 Set 1
Let $$ $$ be the encoding of a Turing machine as a string over $$\sum { = \left\{ {0,1} \right\}.} $$ Let $$L = \left\...
GATE CSE 2014 Set 2
Let $$L$$ be a language and $$\overline L $$ be its complement. Which one of the following is NOT a viable possibility?
GATE CSE 2014 Set 1
If $$L$$ and $$\overline L $$ are recursively enumerable then $$L$$ is
GATE CSE 2008
For $$s \in {\left( {0 + 1} \right)^ * },$$ let $$d(s)$$ denote the decimal value of $$s(e. g.d(101)=5)$$ Let $$L = \lef...
GATE CSE 2006
Let $${L_1}$$ be a regular language, $${L_2}$$ be a deterministic context-free language and $${L_3}$$ a recursively enum...
GATE CSE 2006
Let $${L_1}$$ be a recursive language, and Let $${L_2}$$ be a recursively enumerable but not a recursive language. Which...
GATE CSE 2005
A single tape Turing Machine $$M$$ has two states $${q_0}$$ and $${q_1}$$, of which $${q_0}$$ is the starting state. The...
GATE CSE 2003
Define Languages $${L_0}$$ and $${L_1}$$ as follows $${L_0} = \left\{ { \left| {M\,\,} \right.} \right.$$ halts on $$\l...
GATE CSE 2003
Which of the following is true?
GATE CSE 2002
The $$C$$ language is:
GATE CSE 2002
Which one of the following is not decidable?
GATE CSE 1997
Which of the following conversions is not possible (algorithmically)?
GATE CSE 1994
In which of the cases stated below is the following statement true? “For every non-deterministic machine $${M_1}$$ there...
GATE CSE 1992
Recursive languages are:
GATE CSE 1990

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