New PDF release: Algorithms of informatics

By Ivanyi A. (ed.)

ISBN-10: 9638759615

ISBN-13: 9789638759610

Ivanyi A. (ed.) Algorithms of informatics, vol.1.. foundations (2007)(ISBN 9638759615)

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30 a regular expression. 2-10 Associate to regular expression ab∗ ba∗ + b + ba∗ a a DFA. 2-11 Prove, using the pumping lemma, that none of the following languages are regular: L1 = an cbn | n ≥ 0 , L2 = an bn an | n ≥ 0 , L3 = ap | p prím . 2-12 Prove that if L is a regular language, then {u | u ∈ L} is also regular. 2-13 Prove that if L ⊆ Σ∗ is a regular language, then the following languages are also regular. pre(L) = {w ∈ Σ∗ | ∃u ∈ Σ∗ , wu ∈ L}, suf(L) = {w ∈ Σ∗ | ∃u ∈ Σ∗ , uw ∈ L}. 1. 26. Associating nite automaton to regular expression ε + (0 + 1)∗ 1.

30. 2-9 ❄ 0,1 ✲ ❄ r ✯ 1. Automata and Formal Languages 60 a1 a2 ... an input tape ✻ stack ✲ zk ... 31. Pushdown automaton. 3. Pushdown automata and context-free languages In this section we deal with the pushdown automata and the class of languages  the context-free languages  accepted by them. 1, a context-free grammar G = (N, T, P, S) is one with the productions of the form A → β , A ∈ N , β ∈ (N ∪ T )+ . The production S → ε is also permitted if S does not appear in right hand side of any productions.

For the newly obtained states we determine the states accessible from them. This can be continued until no new states arise. In our previous example q 0 := {q0 , q1 } is the initial state. 2. Finite automata and regular languages δ(q 0 , 0) = {q1 }, where q 1 := {q1 }, δ(q 1 , 0) = ∅, δ(q 2 , 0) = {q 2 }, 33 δ(q 0 , 1) = {q 2 }, where q 2 := {q2 }, δ(q 1 , 1) = {q 2 }, δ(q 2 , 1) = {q 2 }. The transition table is δ 0 1 q0 q1 q2 {q 1 } ∅ {q 2 } {q 2 } {q 2 } {q 2 } which is the same (excepted the notation) as before.

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Algorithms of informatics by Ivanyi A. (ed.)


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