# What is the smallest time/space complexity class that is known to contain complxity class $\mathsf{SPARSE}$

Is it known if complexity class of all sparse languages is contained within e.g. $$\mathsf{EXP}$$ or $$\mathsf{EXPSPACE}$$? Or what is the smallest time or space complexity class that contains complexity class $$\mathsf{SPARSE}$$?

• What is the complexity class called SPARSE? – nir shahar Aug 8 '20 at 20:04
• The complexity class containing all sparse languages. – rus9384 Aug 8 '20 at 20:15
• All unary languages are sparse, so there are undecidable sparse languages. – Ariel Aug 8 '20 at 20:41

I'm not sure if it's the smallest class, but the natural candidate is $$P/poly$$ - for each $$n$$, the "advice" can just encode all acceptable strings of length $$n$$ (by definition of $$SPARSE$$, their number is polynomial).
$$P/poly$$ is also a strict superset of $$SPARSE$$: for example, it contains $$\Sigma^*$$.