Which of the following statements are CORRECT?

1) Static allocation of all data areas by a compiler makes it impossible to implement recursion.

2) Automatic garbage collection is essential to implement recursion.

3) Dynamic allocation of activation records is essential to implement recursion.

4) Both heap and stack are essential to implement recursion.

In the context of modular software design, which one of the following combinations is desirable?

The length of the shortest string NOT in the language (over $$\sum { = \left\{ {a,\,\,b} \right\}} $$) of the following regular expression is ____________. $$$a{}^ * b{}^ * \left( {ba} \right){}^ * a{}^ * $$$

Consider the following languages over the alphabet $$\sum { = \left\{ {0,\,1,\,c} \right\}:} $$
$$\eqalign{ & {L_1} = \left\{ {{0^n}\,{1^n}\,\left| {n \ge } \right.0} \right\} \cr & {L_2} = \left\{ {wc{w^r}\,\left| {w \in \left\{ {0,\,1} \right\}{}^ * } \right.} \right\} \cr & {L_3} = \left\{ {w{w^r}\,\left| {w \in \left\{ {0,\,1} \right\}{}^ * } \right.} \right\} \cr} $$

Here, $${w^r}$$ is the reverse of the string $$w.$$ Which of these languages are deterministic Context- free languages?