A lexical analyzer uses the following patterns to recognize three tokens $${T_1},{T_2},$$ and $${T_3}$$ over the alphabet $$\left\{ {a,b,c} \right\}.$$

$$\eqalign{ & {T_1}:\,\,\,a?{\left( {b|c} \right)^ * }a \cr & {T_2}:\,\,\,b?{\left( {a|c} \right)^ * }b \cr & {T_3}:\,\,\,c?{\left( {b|a} \right)^ * }c \cr} $$

Note that $$'x?'$$ means $$0$$ or $$1$$ occurrence of the symbol $$x.$$ Note also that the analyzer outputs the token that matches the longest possible prefix.

If the string $$bbaacabc$$ is processed by the analyzer, which one of the following is the sequence of tokens it outputs?

Which one of the following statements is FALSE?

Consider the following parse tree for the expression $$a \ne b\$ c\$ d \ne e \ne f,$$ involving two binary operators $$\$ $$ and $$ \ne $$.

Which one of the following is correct for the given parse tree?

Consider the following statements regarding the slow start phase of the $$TCP$$ congestion control algorithm. Note that $$cwnd$$ stands for the $$TCP$$ congestion window and $$MSS$$ denotes the Maximum Segment Size.

$$(i)$$ $$\,\,\,\,\,\,\,\,\,\,\,$$ The $$cwnd$$ increases by $$2$$ $$MSS$$ on every successful acknowledgment.
$$(ii)$$ $$\,\,\,\,\,\,\,\,\,$$ The $$cwnd$$ approximately doubles on every successful acknowledgement.
$$(iii)$$ $$\,\,\,\,\,\,\,$$ The $$cwnd$$ increases by $$1$$ $$MSS$$ every round trip time.
$$(iv)$$ $$\,\,\,\,\,\,\,\,\,$$ The $$cwnd$$ approximately doubles every round trip time.

Which one of the following is correct?