Decidable Language
Definition. A Turing machine is a decider if it halts on every input. A language is decidable if some decider recognizes it.
A decider always answers, so a decidable language is one with an algorithm that is guaranteed to terminate, which is the formal version of "this problem is solvable". Decidable is strictly stronger than Turing-recognizable: the halting problem of Lecture 7 is recognizable but not decidable. Every context-free language is decidable, so the containments of the Chomsky hierarchy run regular inside context-free inside decidable inside recognizable, each properly. Introduced in Lecture 6. Older sources say recursive.