• A deterministic finite automaton is represented formally by a 5-tuple (Q,Σ,δ,q0,F), where: Q is a finite set of states. Σ is a finite set of symbols, called the alphabet of the automaton. ...


A deterministic finite automaton is represented formally by a
5-tuple (Q,Σ,δ,q0,F), where:

Q is a finite set of states.Σ is a finite set of symbols, called the alphabet of the automaton.δ is the transition function, that is, δ: Q × Σ → Q.q0 is the start state, that is, the state of the automaton before any input has been processed, where q0∈ Q.F is a set of states of Q (i.e. F⊆Q) called accept states.

转载于:https://www.cnblogs.com/huangzejun/p/8143128.html
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• Pushdown Automata
Pushdown Automata
Pushdown automata is an extension of the NFA with

ϵ
$\epsilon$-transitions, it’s essentially an

ϵ
$\epsilon$-NFA with the addtion of a stack.
It recognize all and only the context-free languages.
It cannot recognize non-context-free languages like

{0n1n2n|n≥1}
$\{0^n1^n2^n|n\geq 1\}$(A TM can, however).
Two different versions:
Accepts by entering an accepting state.Accepts by emptying its stack.
(Of CFL)

1. Definition

P=(Q,Σ,Γ,δ,q0,Z0,F)

P=(Q, \Sigma, \Gamma, \delta, q_0, Z_0, F)

δ(q,a,X)=(p,γ),

\delta(q, a, X) = (p, \gamma),
where

X
$X$ is the top of the stack and would be replaced by γ$\gamma$.

2. Instantaneous Description

(q,aw,Xβ)⊢(p,w,αβ)

(q, aw, X\beta) \vdash (p, w, \alpha\beta)

aw
$aw$ and

w
<script type="math/tex" id="MathJax-Element-12">w</script> here are the remaining input.

3. The Languages of a PDA
4. Equivalence of PDA’s and CFG’s
From Grammars to Pushdown AutomataFrom PDA’s to Grammars
5. Deterministic Pushdown Automata
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