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. They have limited computational power due to memory and state constraints. 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. The memory of the Turing machine is a tape that consists of a potentially infinite number of one-dimensional cells.
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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. 2).
- 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.
Reference
Introduction to Automata Theory, Languages and Computation. Hopcroft, J.E., Ullman, J.D.: Addison-Wesley, Boston (1979).
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© 2016 Springer International Publishing Switzerland
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O’Regan, G. (2016). Automata Theory. In: Guide to Discrete Mathematics. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-44561-8_7
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DOI: https://doi.org/10.1007/978-3-319-44561-8_7
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