List the first 5 shortlex order of strings that are accepted and first 5 shortlex order os strings that are rejected by this PDA. The diagram is a state machine or automaton, specifically a pushdown automaton, which is typically used to recognize context-free languages. It consists of seven states labeled $ q1 $ through $ q7 $.### Description of States and Transitions:- **State $ q1 $**: - Initial state marked by an incoming arrow. - Transition to $ q2 $ with input $ \lambda $, stack operation $ \lambda \rightarrow $ push $\$$.- **State $ q2 $**: - Transition to itself with input $ a $, stack operation $ \lambda \rightarrow $ push $ a $. - Transition to $ q3 $ with input $ b $, stack operation $ a \rightarrow \lambda $.- **State $ q3 $**: - Transition to itself with input $ b $, stack operation $ a \rightarrow \lambda $. - Transition to $ c5 $ with input $ \lambda $, stack operation $ a \rightarrow \lambda $. - Transition to $ q4 $ with input $ b $, stack operation $ \lambda \rightarrow \lambda $.- **State $ c5 $**: - Transition to itself with input $ \lambda $, stack operation $ a \rightarrow \lambda $. - Transition to $ q7 $ with input $ \lambda $, stack operation $ \$ \rightarrow \lambda $.- **State $ q4 $**: - Transition to itself with input $ b $, stack operation $ \lambda \rightarrow \lambda $. - Transition to $ q6 $ with input $ \lambda $, stack operation $ \$ \rightarrow \lambda $.- **State $ q6 $**: - Accepting state indicated by a double circle.- **State $ q7 $**: - Accepting state indicated by a single circle.### Explanation of Automaton Functionality:- **Input String Processing**: The automaton processes input strings composed of symbols $ a $ and $ b $, using a stack for auxiliary memory operations.- **Stack Operations**: The stack operations are denoted as; push or pop actions based on the input symbol and the top of stack.- **Acceptance States**: The string is accepted if the automaton can transition to the accepting states $ q6 $ or $ q7 $ after

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Description: List the first 5 shortlex order of strings that are accepted and first 5 shortlex order os strings that are rejected by this PDA. The diagram is a state machine or automaton, specifically a pushdown automaton, which is typically used to recognize con

Pushdown Automata (PDA) is a fundamental concept in theoretical computer science and automata…

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List the first 5 shortlex order of strings that are accepted and first 5 shortlex order os strings that are rejected by this PDA.

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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List the first 5 shortlex order of strings that are accepted and first 5 shortlex order os strings that are rejected by this PDA.

The diagram is a state machine or automaton, specifically a pushdown automaton, which is typically used to recognize context-free languages. It consists of seven states labeled $ q1 $ through $ q7 $.

### Description of States and Transitions:

- **State $ q1 $**:
- Initial state marked by an incoming arrow.
- Transition to $ q2 $ with input $ \lambda $, stack operation $ \lambda \rightarrow $ push $\$$.

- **State $ q2 $**:
- Transition to itself with input $ a $, stack operation $ \lambda \rightarrow $ push $ a $.
- Transition to $ q3 $ with input $ b $, stack operation $ a \rightarrow \lambda $.

- **State $ q3 $**:
- Transition to itself with input $ b $, stack operation $ a \rightarrow \lambda $.
- Transition to $ c5 $ with input $ \lambda $, stack operation $ a \rightarrow \lambda $.
- Transition to $ q4 $ with input $ b $, stack operation $ \lambda \rightarrow \lambda $.

- **State $ c5 $**:
- Transition to itself with input $ \lambda $, stack operation $ a \rightarrow \lambda $.
- Transition to $ q7 $ with input $ \lambda $, stack operation $ \$ \rightarrow \lambda $.

- **State $ q4 $**:
- Transition to itself with input $ b $, stack operation $ \lambda \rightarrow \lambda $.
- Transition to $ q6 $ with input $ \lambda $, stack operation $ \$ \rightarrow \lambda $.

- **State $ q6 $**:
- Accepting state indicated by a double circle.

- **State $ q7 $**:
- Accepting state indicated by a single circle.

### Explanation of Automaton Functionality:

- **Input String Processing**: The automaton processes input strings composed of symbols $ a $ and $ b $, using a stack for auxiliary memory operations.
- **Stack Operations**: The stack operations are denoted as; push or pop actions based on the input symbol and the top of stack.
- **Acceptance States**: The string is accepted if the automaton can transition to the accepting states $ q6 $ or $ q7 $ after

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