When I studied computer science 10 years ago, it was still an open question whether $\mathsf{L}$ and $\mathsf{NP}$ are truly different classes. Is that still the case or has the inequality been proven in the meantime?(I know this is a somewhat stupid question, but there's nothing about it in the complexity zoo, and googling L and NP is surprisingly ineffective ;-))
Is it possible that $\mathsf{L} = \mathsf{NP}$?
complexity theory
$L \subseteq NL \subseteq P \subseteq NP \subseteq PSPACE \subseteq EXP$From space hierarchy and time hierarchy theorems we can prove that$L \subsetneq PSPACE$$NL \subsetneq NPSPACE$Note that we know $PSPACE = NPSPACE$.$P \subsetneq EXP$$NP \subsetneq NEXP$Note that we don't know if $EXP \subsetneq NEXP$.Whether the other inclusions are strict, are still open problems. Even though there are no proofs, many, but not all, believe most of the inclusions to be strict.