17. Consider the following finite-state automaton. S1 Start So S2 What is the regular set that is recognized by this finite-state automaton? 18. We know there is a regular grammar that generates a language that is recognized by the automaton above. Let that regular grammar be G = (V, T, S, P), where V = {0, 1, A, S} T= {0, 1} %3D Give the productions in P.

17. Consider the following finite-state automaton. S1 Start So S2 What is the regular set that is recognized by this finite-state automaton? 18. We know there is a regular grammar that generates a language that is recognized by the automaton above. Let that regular grammar be G = (V, T, S, P), where V = {0, 1, A, S} T= {0, 1} %3D Give the productions in P.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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1. Prove that the grammar S -> TV | XY ; T -> aTb | λ; V -> cV | λ; X -> aX | λ; Y -> bYc | λ is ambiguous. 2. Construct a PDA for the following language. Is that a deterministic PDA? Justify your claim.L11={anbn | n ≥ 1} U {a2nbn | n ≥1}
24. Show that the grammars and are not equivalent. S → aSb|bSa|SS|a S aSb|bSala
1 1.12 3 4. 5. . ... Theorem: Let G= (V,T,P.S) be a rghtlimear grammar. Then there exists a language L(G) which is accepted by a FA. i. , the language generated from the regular grammar is regular language. 1/1 lilil
2. Are the following languages context-free or non-context-free? • If a language is context-free, give a context-free grammar that generates it. • If a language is not context-free, prove this using the pumping lemma. A = { a*b'c*d² |k > i > 0, l>0 } B = {a²i+1fk+1c3l (2k+1q* | i > 1, k > 1, l > 1 } (a) (b)
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Given a regular grammar G and a list of strings, identify the strings that are in L(G).
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Consider the Finite Automata D in Figure 2. a. List 3 strings of different lengths that D accepts and also 3 that it rejects. b. What is the shortest string that D accepts? What is the shortest string that D rejects? c. Describe, in your own words, what is the language of D, i.e., L(D). 93 42 Figure 2. Finite automata D
Complete the proof of Theorem 6.4. Theorem 6.4: Let G = (V, T, S, P) be any context-free grammar without λ-productions. Then there exists a context-free grammar bG = (bV , b T, S, b P) that does not have any unit-productions and that is equivalent to G. 1