Give algorithms (i.e., a well-defined, deterministic, always-terminating decision procedures, and state their time complexities) to determine whether for a given finite automaton M, L(M) is:

a) countable

b) empty c) Sigma* d) finite

e) infinite f) co-finite (i.e., with a finite complement) g) regular h) also accepted by a smaller FA (i.e., with fewer states)