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I was having a discussion earlier about a state machine, and there was a question as to whether it might not halt on some input. It seems like a property of state machines that is important and frequently mentioned, but I can't for the life of me figure out what the name of that property is. Is there such a term? Is it "haltable", "not-infinitely-loopy", or something else?

A: 

My guess would be "halting", derived from the famous "halting problem", which is similar to your question, namely whether it will halt on a given input. An important consideration is that a machine is not defined as "halting" in general, but rather for a specific input. The general case is proven to be unsolvable (by Turing himself).

nearlymonolith
it's my favorite
nearlymonolith
+8  A: 

A machine that always halts is called a decider.

A decider need only be a machine that halts on all inputs. For example, all DFAs are deciders, as are DPDAs.

Welbog
Ah, yes, that was it exactly! Thank you very much!
CaptainAwesomePants
Cool! Didn't know that. I'll leave my previous answer below just in case people are interested in the Halting Problem.
nearlymonolith