**DFA Transition Graph and Regular Expressions**The diagram represents a Deterministic Finite Automaton (DFA) with four states, labeled $ q_1, q_2, q_3, $ and $ q_4 $. Each state is depicted as a circle. The transitions between the states are represented by arrows labeled with the input symbols:- **State Transitions:** - $ q_1 $ transitions to: - $ q_2 $ on input $ a $ - $ q_3 $ on input $ c $ - $ q_4 $ on input $ b $ - $ q_2 $ transitions to itself on input $ a $. - $ q_3 $ transitions to: - $ q_1 $ on input $ a $ - $ q_3 $ on input $ c $ - $ q_4 $ on input $ b $ - $ q_4 $ transitions to: - $ q_3 $ on input $ c $ - $ q_4 $ on input $ b $ - $ q_1 $ on input $ a $Given a DFA, we define the notion of a regular expression $ R_{ij}^{(k)} $ for the language $ L_{ij}^{(k)} $ consisting of all strings that go from state $ q_i $ to state $ q_j $ without visiting a state numbered larger than $ k $ along the way (visiting the first and last state is not considered).For the DFA given above, specify the following regular expressions. You do not need to justify your answer.(a) $ R_{44}^{(0)} $(b) $ R_{12}^{(0)} $(c) $ R_{12}^{(4)} $(d) $ R_{11}^{(0)} $(e) $ R_{11}^{(4)} $

2. Consider the DFA defined by its transition graph as below. Given a DFA, we define the notion of a regular expression R) for the language L consisting of all strings that go from state q, to state q; without visiting a state numbered larger than k along the way (visiting the first and last state is not considered). (b) For the DFA given above, specify the following regular expressions. You do not need to justify your answer. (a) 440) (c) (d) (e) R12 F RO q2 R

2. Consider the DFA defined by its transition graph as below. Given a DFA, we define the notion of a regular expression R) for the language L consisting of all strings that go from state q, to state q; without visiting a state numbered larger than k along the way (visiting the first and last state is not considered). (b) For the DFA given above, specify the following regular expressions. You do not need to justify your answer. (a) 440) (c) (d) (e) R12 F RO q2 R

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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