**Construct a PDA that accepts the language defined by the grammar \( S \rightarrow abSb \mid \lambda \).**In this task, we are asked to construct a Pushdown Automaton (PDA) for a given context-free grammar (CFG). The grammar consists of the following rules:- \( S \rightarrow abSb \)- \( S \rightarrow \lambda \)**Explanation:**- This grammar defines a language where strings have matching 'a's and 'b's such that each 'a' is eventually matched with a 'b' in reverse order, and the string can also be empty (denoted by \(\lambda\)).To construct a PDA for this language, consider the following general approach:1. **Initial State**: Start in an initial state \(q_0\), with an empty stack.2. **Push 'a'**: When 'a' is read, push it onto the stack.3. **Match 'b' with 'a'**: When 'b' is read, pop 'a' from the stack. If the stack is empty before reading 'b', the input should be rejected.4. **Accept Empty**: The state transitions allow for acceptance when the stack is empty and the input is fully read.This PDA processes the string by checking balance and order of 'a's and 'b's. The acceptance condition can be either by empty stack or final state, as applicable for the specific configuration you design.

A pushdown automata for the given grammar

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Construct a PDA that accepts the language defined by the grammar S abSb | 2.

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Question

**Construct a PDA that accepts the language defined by the grammar \( S \rightarrow abSb \mid \lambda \).**

In this task, we are asked to construct a Pushdown Automaton (PDA) for a given context-free grammar (CFG). The grammar consists of the following rules:

- \( S \rightarrow abSb \)
- \( S \rightarrow \lambda \)

**Explanation:**
- This grammar defines a language where strings have matching 'a's and 'b's such that each 'a' is eventually matched with a 'b' in reverse order, and the string can also be empty (denoted by \(\lambda\)).

To construct a PDA for this language, consider the following general approach:

1. **Initial State**: Start in an initial state \(q_0\), with an empty stack.
2. **Push 'a'**: When 'a' is read, push it onto the stack.
3. **Match 'b' with 'a'**: When 'b' is read, pop 'a' from the stack. If the stack is empty before reading 'b', the input should be rejected.
4. **Accept Empty**: The state transitions allow for acceptance when the stack is empty and the input is fully read.

This PDA processes the string by checking balance and order of 'a's and 'b's. The acceptance condition can be either by empty stack or final state, as applicable for the specific configuration you design.

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