The procedure given below is required to find and replace certain characters inside an input character string supplied in array $$A.$$ The characters to be replaced are supplied in array $$oldc,$$ while their respective replacement characters are supplied in array $$newc.$$ Array $$A$$ has a fixed length of five characters, while arrays $$oldc$$ and $$newc$$ contain three characters each. However, the procedure is flawed. void find_and_replace (char $$^ * A,$$ char $$^ * oldc,$$, char $$^ * newc$$)
$$\left\{ \, \right.$$ for (int $$i=0; i<5; i++$$)
for (int $$j=0; j<3; j++$$)
if ( $$A$$ [ $$i$$ ] $$==oldc$$ [ $$j$$ ] $$A$$ [ $$i$$ ]
$$=newc$$ [ $$j$$ ]; $$\left. \, \right\}$$

The procedure is tested with the following four test cases;
$$\eqalign{ & \left( 1 \right)\,\,\,oldc = ''abc'',\,\,newc\, = \,''dab'' \cr & \left( 2 \right)\,\,\,oldc\, = \,''cdc'',\,\,newc\, = \,''bed'' \cr & \left( 3 \right)\,\,\,oldc\, = \,''bca'',\,newc\, = \,''cda'' \cr & \left( 4 \right)\,\,\,oldc\, = \,''abc'',\,newc\, = \,''bac'' \cr} $$

The tester now tests the program on all input strings of length five consisting of characters $$'a', 'b', 'c', 'd'$$ and $$'c'$$ with duplicates allowed. If the tester carries out this testing with four test cases given above, how many test cases will be able to capture the flaw?

Which of the following is/are undecidable?
$$1.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \Phi ?$$
$$2.$$ $$G$$ is a $$CFG.$$ Is $$L\left( G \right) = \sum {{}^ * } ?$$
$$3.$$ $$M$$ is a Turing Machine. Is $$L(M)$$ regular?
$$4.$$ $$A$$ is a $$DFA$$ and $$N$$ is an $$NFA.$$
Is $$L(A)=L(N)?$$

Consider the languages $${L_1} = \phi $$ and $${L_2} = \left\{ a \right\}.$$ Which one of the following represents $${L_1}\,L_2^ * UL_1^ * ?$$

Consider the following languages
$${L_1} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0} \right.} \right\}$$
$${L_2} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0,p \ne r} \right.} \right\}$$

Which one of the following statements is FALSE?