LFASTER $=\{($M$1,$M$2,$ x$)$ : M$1($x$)$ runs for strictly fewer steps than M$2($x$)$ does$\}.$

A computation that halts takes strictly fewer steps than one that loops. If both computations

loop, then neither takes strictly fewer steps than the other.

$(8$ pts$)($b$)$ LSUBSET $=\{($M$1,$M$2)$ : M$1,$ M$2$ are TMs and L$($M$1)$ L$($M$2)\}.$

$(10$ pts$)($c$)$ LDFA $=\{$M$$ : M is a TM and L$($M$)$ is decided by some DFA$\}.$