Abstract
Automata theory is the branch of computer science that is concerned with the study of abstract machines and automata. These include finite-state machines, pushdown automata and Turing machines. Finite-state machines are abstract machines that may be in one state at a time (current state), and the input symbol causes a transition from the current state to the next state. Pushdown automata have greater computational power, and they contain extra memory in the form of a stack from which symbols may be pushed or popped. The Turing machine is the most powerful model for computation, and this theoretical machine is equivalent to an actual computer in the sense that it can compute exactly the same set of functions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The transition function may be undefined for a particular input symbol and state.
- 2.
It may be a total or a partial function (as discussed in Chap. 4).
- 3.
The use of {Σ ∪{ε}} is to formalize that the PDA can either read a letter from the input, or proceed leaving the input untouched.
- 4.
This could also be written as δ :Q × {Σ ∪{ε}} × Γ →ℙ(Q × Γ*). It may also be described as a transition relation.
- 5.
We may also allow no movement of the tape head to be represented by adding the symbol “N” to the set.
References
G. O’Regan, Guide to Discrete Mathematics (Springer, Switzerland, 2016)
J.E. Hopcroft, J.D. Ullman, Introduction to Automata Theory, Languages and Computation (Addison-Wesley, Boston (1979)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
O’Regan, G. (2017). Automata Theory. In: Concise Guide to Formal Methods. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-64021-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-64021-1_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64020-4
Online ISBN: 978-3-319-64021-1
eBook Packages: Computer ScienceComputer Science (R0)