## Marks 1

Which of the following decision problems are undecidable?
$$\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ Given $$NFAs$$ $${N_1}$$ and $${N_2},$...

Let $$\sum \, $$ be a finite non - empty alphabet and let $${2^{\sum {{}^ * } }}$$ be the power set of $$\sum {{}^ * .\,} $$ Which one of the followin...

Which of the following problems are decidable?
$$1.$$ Does a given program ever produce an output?
$$2.$$ If L is a context-free language, then, is $$...

Which of the following are decidable?
$$1.$$ Whether the intersection of two regular languages is infinite
$$2.$$ Whether a given context-free languag...

Which of the following statements is false?

## Marks 2

Which of the following languages are undecidable? Note that $$\langle M\rangle $$ indicates encoding of the Turing machine M.
L1 = $$\left\{ {\langle ...

Language $${L_1}$$ is polynomial time reducible to language $${L_2}$$ . Language $${L_3}$$ is polynomial time reducible to $${L_2}$$ , which in turn i...

Which one of the following problems is un-decidable?

Which of the following is/are undecidable?
$$1.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \Phi ?$$
$$2.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \ri...

Consider three decision problems $${P_1},$$ $${P_2}$$ and $${P_3}.$$ It is known that $${P_1}$$ is decidable and $${P_2}$$ is un-decidable. Which of t...

Consider the following problem $$X.$$ Given a Turing machine $$M$$ over the input alphabet $$\sum , $$ any state $$q$$ of $$M$$ And a word $$w\,\,\var...

Which one of the following is the strongest correct statement about a finite language over some finite alphabet $$\sum ? $$

It is decidable whether:

Which of the following problems are un-decidable?