largest language class for which inclusion is decidable am wondering what is the largest language class that is known for which set inclusion is decidable, ie a class such that if $A, B$ are in that class then $A \subset B$ is decidable.

am also interested in the same question for what were once called "GSMs", generalized sequential machines, or maybe more modernly, FSM "transducers", where if $f(x)$ is the transducer, $C \subset f(C)$, $C$ in the class.

(of course, the problem is also equivalent to determining whether the intersection of a complement is empty.)

[simply asking for the "largest known" language is a literature related question. however some kind of proof that there exists a "largest class" I believe is an open question. although, there might be a straightfwd argument of nonexistence via diagonalization...?]

unfortunately wikipedia does not have some of this basic info for major language classes. wonder if there is any table, paper, or reference esp online.

there is a nice table of decidability &amp; undecidability of basic language questions in [1] but its quite dated at this point.

[1] Hopcroft/Ullman, Intro to Automata Theory, Languages &amp; Computation, 1979
Converted from comment: language inclusion is decidable for very simple deterministic pushdown automata ("On the Inclusion Problem for Very Simple Deterministic Pushdown Automata (1999)" by E. Makinen, 1999) 
and a restricted version of timed finite state machine ("On the Language Inclusion Problem for Timed Automata: Closing a Decidability Gap" by J. Ouaknine and J. Worrell, 2004).