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build a PDA for the given language.

build a PDA for the given language.

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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for each question, build a PDA for the given language.

### Educational Content on Pushdown Automata #### Problem Statement (5) \{w ∈ \{a, b\}* : w = wᴿ\} #### Description of Diagrams The diagrams illustrate two Pushdown Automata (PDAs) that attempt to recognize the language L, where the language consists of strings w over the alphabet \{a, b\} such that w is equal to its reverse (wᴿ). **Graph Components:** - Each PDA has a set of states, represented by circles. - Directed arrows show transitions between states. - Transitions are labeled with instructions in the format `input, stack top; stack operation`. #### First Pushdown Automaton (PDA) 1. **States**: - `1` (Initial state, indicated by an arrow pointing toward it) - `s` - `f` (Final state) - `s2` - `t2` 2. **Transitions**: - From `1` to `s` on input ε, top of stack ε, push ε (ε, ε; ε). - State `s` loops to itself with transitions `b, ε; b` and `a, ε; a`. - From `s` to `f` on input ε, top of stack ε, push ε (ε, ε; ε). - State `s2` loops to itself with transitions `b, ε; b` and `a, ε; a`. - From `s2` to `t2` with transitions `b, b; ε` and `a, a; ε`. - From `t2` back to `t2` with transitions `b, b; ε` and `a, a; ε`. 3. **Notes**: - The automaton attempts to check for mirrored sequences from its initial state to the final state. #### Second Pushdown Automaton (PDA) 1. **States**: - `1` (Initial state, indicated by an arrow pointing toward it) - `s` - `f` (Final state) - `s2` - `t2` 2. **Transitions**: - From `1` to `s` on input ε, top of stack ε, push ε (ε, ε; ε). - State `s` loops
Transcribed Image Text:### Educational Content on Pushdown Automata #### Problem Statement (5) \{w ∈ \{a, b\}* : w = wᴿ\} #### Description of Diagrams The diagrams illustrate two Pushdown Automata (PDAs) that attempt to recognize the language L, where the language consists of strings w over the alphabet \{a, b\} such that w is equal to its reverse (wᴿ). **Graph Components:** - Each PDA has a set of states, represented by circles. - Directed arrows show transitions between states. - Transitions are labeled with instructions in the format `input, stack top; stack operation`. #### First Pushdown Automaton (PDA) 1. **States**: - `1` (Initial state, indicated by an arrow pointing toward it) - `s` - `f` (Final state) - `s2` - `t2` 2. **Transitions**: - From `1` to `s` on input ε, top of stack ε, push ε (ε, ε; ε). - State `s` loops to itself with transitions `b, ε; b` and `a, ε; a`. - From `s` to `f` on input ε, top of stack ε, push ε (ε, ε; ε). - State `s2` loops to itself with transitions `b, ε; b` and `a, ε; a`. - From `s2` to `t2` with transitions `b, b; ε` and `a, a; ε`. - From `t2` back to `t2` with transitions `b, b; ε` and `a, a; ε`. 3. **Notes**: - The automaton attempts to check for mirrored sequences from its initial state to the final state. #### Second Pushdown Automaton (PDA) 1. **States**: - `1` (Initial state, indicated by an arrow pointing toward it) - `s` - `f` (Final state) - `s2` - `t2` 2. **Transitions**: - From `1` to `s` on input ε, top of stack ε, push ε (ε, ε; ε). - State `s` loops
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