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The theory of groups is called group theory, not groups theory; the theory of functions is function theory, not functions theory; the theory of lattices is lattice theory, and so on.

How come the theory of automata is called "automata theory" and not (or hardly ever) "automaton theory"?

A StartPage search for "automaton theory" got two (2) hits. Is "automaton theory" wrong or just unusual? Is there a rule for this, something like "regular English plurals ending in -s aren't used attributively but this doesn't apply to foreign plurals like automata and data"?

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  • Interesting question. Ngram and dictionary agree that the automata theory as a defined area came to be in the 50s. Beforehand any theory regarding automata was described in the general way automaton theory. I guess the automata theory focusing on the math automata wanted to 1/2
    – Helmar
    Aug 16, 2016 at 13:45
  • differentiate itself from the one regarding physical automata. 2/2
    – Helmar
    Aug 16, 2016 at 13:45
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    Group is a regular English noun with a regular English plural groups. It is subject to the regular English rule that says noun compounds should not use plurals except for the last noun. Hence *groups theory is not a grammatical English noun compound. But automaton is not a regular English word with a regular English plural; it is a borrowed Greek neuter noun with a Greek neuter singular ending -on, and a Greek neuter plural ending -a. Since that plural is not recognized as a regular plural by English speakers, it is not subject to the regular English rule. That is all. Sep 3, 2016 at 18:21
  • @JohnLawler Thanks. That sounds like an answer. Does it mean that for words like automaton there is no rule, the compound could just as well be automaton theory or automata theory, and it's just a matter of random chance that automata prevailed?
    – bof
    Sep 3, 2016 at 22:05
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    Yes, it's like data and datum or alumnus and alumni. In America, at least, it's always the Alumni Association, for instance, never the *Alumnus Association. If a word is not recognized as a plural, it doesn't meet the conditions for applying the rule. Sep 3, 2016 at 23:03

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They are two different terms altogether.

Automata theory refers to a subject in the theory of computation

Automaton theory refers to a concept in psychology

There are occurrences of 'automaton theory' in biology and quantum mechanics too. Besides, 'automaton theory' was proposed in late 19th century (around 1890) far before the 'automata theory' which was introduced in the 1950s.

It could be that whoever coined the term, 'automata theory', could be weary of the term, 'automaton theory', in history and wanted to avoid the term conflict. But that is only a possibility.

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