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automata-7

# automata-7 - Automata Chapter 7 Pushdown Automata Chpater 7...

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Automata Chapter 7. Pushdown Automata

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Chpater 7 Pushdown Automata Automata for context-free languages? - can count without limit. i.e., L={a n b n | n 0} - Store and match a sequence of symbols in reverse order. i.e. L={ww R | w ∈∑ *} Stack as an unbounded storage. Pushdown automata(PDA). Control unit input Stack
7.1 Nondeterministic PDA Definition 7.1 A nondeterministic pushdown accepter (NPDA) is M=(Q, , Γ , δ , q 0 , z, F), where Q: a finite set of internal states of the control unit, : input alphabet, Γ : a finite set of symbols, stack alphabet, δ : Q x ( { λ }) x Γ finite subset of Q x Γ *, q 0 : initial state of the control unit z: stack start symbol, F Q : set of final states Control unit input Stack

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7.1 Nondeterministic PDA Ex 7.1 a transition rules of an NPDA δ (q 1 , a, b) = {(q 2 , cd), (q 3 , λ )}. Ex 7.2 L= {a n b n : n 0} {a} Q ={q 0 , q 1 , q 2 , q 3 }, = {a, b}, Γ ={0, 1}, z=0, F={q 3 }, δ (q 0 , a, 0)={(q 1 , 10), (q 3 , λ )}, δ (q 0 , λ , 0)={(q 3 , λ )}, δ (q 1 , a , 1)={(q 1 , 11 )}, δ (q 1 , b , 1)={(q 2 , λ )}, δ (q 2 , b , 1)={(q 2 , λ )}, δ (q 2 , λ ,0)={(q 3 , λ )}.
7.1 Nondeterministic PDA Triplet (q, w, u) : instantaneous description of a PDA where q: state, w: unread part of the input string, u: stack contents A move by (q 1 , aw, bx) (q 2 , w, yx) iff (q 2 , y) δ (q 1 , a, b). Control unit input Stack

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7.1 Nondeterministic PDA Definition 7.2 Let M=(Q, , Γ , δ , q 0 , z, F) be a NPDA.
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