$[$

$1$

$]$

$($

$1$

$6$

$$pts

$)$

$$Decide whether each statement is true or false and answer

$\text{'}$

$$

$\text{'}$

$$or

$\text{'}$

$$

$\text{'}$

$.$

a

$)$

$$If

$$

$$is a CFL

$,$

$$then

$$

$$is generated by some non

$-$

linear, ambiguous CFG

$.$

b

$)$

$$If

$$

$$is a linear CFL

$,$

$$then

$$

$$is generated by a left

$-$

linear CFG and a right

$-$

linear CFG

$.$

c

$)$

$$Given a CFG

$$

$,$

$$if

$$

$($

$$

$)$

$$is inherently ambiguous, then there is an infinity of strings in

$$

$$that all have at least two

parse trees according to

$$

$.$

d

$)$

$$If

$$

$=$

$$

$($

$$

$)$

$$for some DFA

$$

$$with

$$

$$states$,$ then

$$

$=$

$$

$($

$$

$)$

$$for some CFG