determine whether the given grammar is context$-$sensitive$,$ context$-$free, regular, or none of these. Give all characterizations that apply.

T$=\{$a$,$b$\},$ N$=\{\backslash$sigma $,$A$\},$ with productions

$\backslash$sigma $->$ b$\backslash$sigma $,\backslash$sigma $->$ aA$,$A $->$ a$\backslash$sigma $,$A $->$ bA$,$A $->$ a$,\backslash$sigma $->$ b$,$

and starting symbol $\backslash$sigma $.$

In Exercises $1-6,$ determine whether the given grammar is context$-$sensitive$,$ context$-$free, regular, or none of these. Give all characterizations that apply.

T$=\{$a$,$b$\},$N$=\{\backslash$sigma $,$A$\},$ with productions

$\backslash$sigma $->$b$\backslash$sigma $,\backslash$sigma $->$aA$,$A$->$a$\backslash$sigma

A$->$bA$,$A$->$a$,\backslash$sigma $->$b

and starting symbol $\backslash$sigma $.$

T$=\{$a$,$b$\},$N$=\{\backslash$sigma $,$A$,$B$\},$ with productions

$\backslash$sigma $->$A$,\backslash$sigma $->$AAB,Aa$->$ABa

A$->$aa$,$Bb$->$ABb,AB$->$ABB

B$->$b$,$

and starting symbol $\backslash$sigma $.$

T$=\{$a$,$b$,$c$\},$N$=\{\backslash$sigma $,$A$,$B$\},$ with productions

$\backslash$sigma $->$AB$,$AB$->$BA$,$

B$->$Bb$,$A$->$a$,$

B$,$B$->$b

and starting symbol $\backslash$sigma $.$

T$=\{$a$,$b$,$c$\}$N$=\{\backslash$sigma $,$A$,$B$\},$ with productions

$\backslash$sigma $->$BAB,$\backslash$sigma $->$ABA,A$->$AB$,$

B$->$BA$,$A$->$aA$,$A$->$ab$,$

B$->$b$,$

and starting symbol $\backslash$sigma $.$

::$=$b$|$a$|$a

::$=$a$|$b

::$=$b$|$a$|$bT$=\{$a$,$b$\},$N$=\{\backslash$sigma $,$A$,$B$\}.$

T$=\{$a$,$b$\},$N$=\{\backslash$sigma $,$A$,$B$\},$ with productions