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I understand the terms automata or automaton to mean "self operating machine".

I can't think of any such "machine" besides maybe (if it is even a machine and even exits) cyclic universe of a big-bang--big-crunch phenomena;
either in sequence ("finite automata"), or in eternal occurrence ("infinite automata").

Is automata concept theorized in computer science and what would be a simple example?

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    $\begingroup$ What is or isn't "self operating" might be a matter of interpretation, and what is "integral" sounds like a matter of opinion to me. Computer science focuses on technical matters; interpretation is up to you, and sounds to me more like philosophy than science. $\endgroup$ – D.W. Nov 18 at 3:07
  • $\begingroup$ I know LMGTFY is an anti-pattern, but surely you've come across automata theory? $\endgroup$ – Raphael Nov 20 at 18:14
  • $\begingroup$ @Raphael I recall I did try to read the opener, but didn't understand what was written there. $\endgroup$ – JohnDoea Nov 21 at 5:21
  • $\begingroup$ Please don't edit your question in a way that invalidates existing answers. Post a new question instead. $\endgroup$ – David Richerby Nov 30 at 10:01
  • $\begingroup$ @DavidRicherby please quote such change in any of my edits. $\endgroup$ – JohnDoea Nov 30 at 10:11
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In computer science, "automaton" refers to some kind of finite state machine. This is a basic and fundamental model of computation, and automata are widely used in implementing simple electronic devices and in writing parsers, e.g., for programming languages.

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  • $\begingroup$ Hello David; I complement on the shortness of your answer and appreciate the care you showed for the question (also in comments); I have only one comments: I do computing about 27 years and never heard of automatons before; so either computation and computing have sharp different meaning in the CS literature or the phrasing of basic and fundamental model of computation should be changed a bit; I believe that in either case it should be changed a bit because in my personal philosophy one goes from the fundamentals to a base. Thanks, $\endgroup$ – JohnDoea Dec 1 at 19:52
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The automaton is mainly used as a simple model of computation to check input strings on some defined conditions by reading the string and giving out whether the string is accepted in a defined language or not.

There are a lot of examples. A really crucial for example in terms of computing are the RegEx-expressions, if you heard of that. There are some languages which can be checked, and for some of the languages you just can't find any automaton to check, whether an string is in this language or not (for example the language of unlimited correct balanced parentheses). Those that can be checked are the so called regular expressions.

A simple example would be a drinks machine, which is accepting inputs depending on the current state (coins, pressing buttons, ...).

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  • $\begingroup$ That's what I wrote. Maybe the sentence is a little bit confusing, I'm sorry. Those languages that can be checked by an automaton are the regular languages, which can be matched by a regular expression. But there are languages that "can't" be checked by an automaton, such as the language of balanced parentheses. For those, no regular expression is existing. $\endgroup$ – MarcoChristian Nov 20 at 12:58
  • $\begingroup$ Oops. I think I just misread your answer. What you wrote seems clear enough to me, now. I made a trivial edit to your answer so I could undo my downvote. Sorry for messing up. $\endgroup$ – David Richerby Nov 20 at 13:06
  • $\begingroup$ Building on @MarcoChristian's answer, the preface to my thesis elaborates - in layman's terms - a bit further on the drink vending machine example: hermann-gruber.com/data/teaser.pdf $\endgroup$ – Hermann Gruber Nov 28 at 8:25

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