Algorithms of informatics, vol. 1 by Ivanyi A. (ed.)

By Ivanyi A. (ed.)

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Extra resources for Algorithms of informatics, vol. 1

Sample text

N}. k We can prove by induction that sets Rij can be described by regular expresk sions. Indeed, if k = −1, then for all i and j languages Rij are finite, so they can be expressed by regular expressions representing exactly these languages. Moreover, k−1 if for all i and j language Rij can be expressed by regular expression, then lank guage Rij can be expressed also by regular expression, which can be corresponding k−1 k−1 k−1 and , Rkk , Rik constructed from regular expressions representing languages Rij k−1 k Rkj respectively, using the above formula for Rij .

13 Let A = ({q0 , q1 , q2 }, {a, b}, E, {q0 }, {q2 }) be a DFA, where E = (q0 , a, q0 ), (q0 , b, q1 ), (q1 , b, q2 ), (q2 , a, q2 ) . The corresponding transition table is δ a b q0 q1 q2 {q0 } ∅ {q2 } {q1 } {q2 } ∅ 38 1. Automata and Formal Languages The transition graph of A is in Fig. 8. 11 we define regular grammar G = ({q0 , q1 , q2 }, {a, b}, P, q0 ) with the productions in P q0 → aq0 | bq1 , q1 → bq2 | b, q2 → aq2 | a . One may prove that L(A) = {am bban | m ≥ 0, n ≥ 0}. 11 easily can be given as an algorithm.

27 does not accept word 101. 24 A language L is accepted by a nondeterministic pushdown automaton V1 by empty stack if and only if it can be accepted by a nondeterministic pushdown automaton V2 by final state.

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