$5.(20\%)$ Given the language L $=\{$wxw: w$\{$a$,$ b$\}*,$ x is a fixed terminal symbol$\},$ answer the following questions: $($a$)$ Write the context$-$free grammar that generates L $($b$)$ Construct the pda that accepts L from the grammar of $($a$)($c$)$ Construct the pda that accepts L directly based on the similar skill used in ww$.($d$)$ Is this language a deterministic context$-$free language?