Related to (part of) Theory of computation.
Automata theory is the study of abstract machines or automata, as well as the computational problems that can be solved using them
An automaton (plural: automata or automatons) is a self-operating machine, or a machine or control mechanism designed to follow automatically a predetermined sequence of operations, or respond to predetermined instructions. Automata include finite-state machines , etc.
Discrete dynamical system (e.g., networks of automata)
Finite-state transducer, a FSM with output from transitions.
Symbolic dynamics, Discrete dynamical system with output from states visited.
Finite-state machine + infinite data structure
For instance a Boolean network
See Formal language
Computer - Theory of Automata, Formal Languages and Computation
a new approach to formal language theory by kolmogorov complexity
http://www.eecs.wsu.edu/~ananth/CptS317/Lectures/IntroToAutomataTheory.pdf
Automata, Computability, and ComplexityOr, Great Ideas in Theoretical Computer Science Spring, 2010
Grail: finite automata and regular expressions
FAdo Symbolic Manipulation of Code Properties FAdo Documentation
http://fado.dcc.fc.up.pt/software/
Build your own finite transducer: http://examples.mikemccandless.com/fst.py?terms=pepe%2F33%0D%0Amoth%2F1%0D%0Apop%2F2%0D%0Astar%2F3%0D%0Astop%2F4%0D%0Atop%2F5%0D%0A&cmd=Build+it%21