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2. Use the construction in Theorem 3.1 to find an nfa that accepts the language L ((aab)* ab).

2. Use the construction in Theorem 3.1 to find an nfa that accepts the language L ((aab)* ab).

Database System Concepts
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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28 3.2 Regular Expressions and Regular Languages vertex at the left represents the initial state, the one on the right the fi- nal state. In Exercise 7, Section 2.3, we claim that for every nfa there is an equivalent one with a single final state, so we lose nothing in assuming that. there is only one final state. With M (r1) and M (r2) represented in this way, we then construct automata for the regular expressions r1 + 12, T1T2, and ri. The constructions are shown in Figures 3.3 to 3.5. As indicated in the drawings, the initial and final states of the constituent machines lose their status and are replaced by new initial and final states. By stringing together several such steps, we can build automata for arbitrary complex regular expressions. It should be clear from the interpretation of the graphs in Figures 3.3 to 3.5 that this construction works. To argue more rigorously, we can give a formal method for constructing the states and transitions of the combined machine from the states and transitions of the parts, then prove by induction tv M(r₂) 5 M(r₂) FIGURE 3.3 Automaton for L (r₁ + 12). -040 FIGURE 3.4 Automaton for L (rira). M(r₂) M(r₂) e M(r₂) 81 K MacBook Air AR
Transcribed Image Text:28 3.2 Regular Expressions and Regular Languages vertex at the left represents the initial state, the one on the right the fi- nal state. In Exercise 7, Section 2.3, we claim that for every nfa there is an equivalent one with a single final state, so we lose nothing in assuming that. there is only one final state. With M (r1) and M (r2) represented in this way, we then construct automata for the regular expressions r1 + 12, T1T2, and ri. The constructions are shown in Figures 3.3 to 3.5. As indicated in the drawings, the initial and final states of the constituent machines lose their status and are replaced by new initial and final states. By stringing together several such steps, we can build automata for arbitrary complex regular expressions. It should be clear from the interpretation of the graphs in Figures 3.3 to 3.5 that this construction works. To argue more rigorously, we can give a formal method for constructing the states and transitions of the combined machine from the states and transitions of the parts, then prove by induction tv M(r₂) 5 M(r₂) FIGURE 3.3 Automaton for L (r₁ + 12). -040 FIGURE 3.4 Automaton for L (rira). M(r₂) M(r₂) e M(r₂) 81 K MacBook Air AR
1. Use the construction in Theorem 3.1 to find an nfa that accepts the language L (a*a + ab). 2. Use the construction in Theorem 3.1 to find an nfa that accepts the language L ((aab)* ab).
Transcribed Image Text:1. Use the construction in Theorem 3.1 to find an nfa that accepts the language L (a*a + ab). 2. Use the construction in Theorem 3.1 to find an nfa that accepts the language L ((aab)* ab).
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