They are heavily used in natural language processing, e.g. for modeling dictionaries (using finite state transducers, where the input side has the inflected for

They are heavily used in natural language processing, e.g. for modeling dictionaries (using finite state transducers, where the input side has the inflected form, output side has the dictionary form+part of speech), part of speech taggers (markov chains can be implemented by finite state machines). Note also that regular expressions (the kind you find in sed/awk, not the perl extended stuff) are equivalent in power to finite state machines – a regex can be modelled by an FSM, and an FSM can be turned into a regex. Outside of NLP, they can be used anywhere you can implement your logic as a transition table with rows like "fromstate,input,tostate,action". I believe it's common for many servers and network stuff to do this. https://en.wikipedia.org/wiki/State_pattern https://en.wikipedia.org/wiki/State_pattern and https://en.wikipedia.org/wiki/Automata-based_programming#Example https://en.wikipedia.org/wiki/Automata-based_programming#Exa... have some fairly traditional examples. One of the plus-sides of finite state machines is that they are formally less powerful than full turing machines. This might make it easier to check that a program does what it should, but they also compose in ways that full turing machines (or intermediate-level machines like context-free or context-sensitive) can't. E.g. you can take two FSM's, and do a set intersection/union/difference/kleene star/concatenation/reverse and still stay within finite state (unlike e.g. context free, where you can't do intersection/difference). But it also means there are certain types of logic you can't express within finite state.