Let M be a Turing machine, let w be an arbitrary input string, and let s and t be positive integers. We say that M accepts w in space s if M accepts w after accessing at most the first s cells on its tape, and M accepts w in time t if M accepts w after at most t transitions. Prove that the following languages are decidable or undecidable: $3.($a$)$M$,$ w$$ M accepts w in time $|$w$|2($b$)$M$$ M accepts at least one string w in time $|$w$|2($c$)$M$,$ w$$ M accepts w in space $|$w$|2($d$)$M$$ M accepts at least one string w in space $|$w$|2$