Creating something Turing-incomplete is not the same thing as using something not Turing-incomplete. For instance, the people who created Houdini are programmers. The people who use Houdini are not. I can program a dishwasher using a FSA, but that doesn’t make people who use dishwashers programmers.
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Are finite state automata turing complete? No. But any normal person would say that programming them is indeed programming.
Creating something Turing-incomplete is not the same thing as using something not Turing-incomplete. For instance, the people who created Houdini are programmers. The people who use Houdini are not. I can program a dishwasher using a FSA, but that doesn’t make people who use dishwashers programmers.