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Computer Science
Posted 3 months ago

Construct a pushdown automaton for the following language:
L= (ai bj ck li,j,k > = 0, i + k = j}
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Answer from Sia
Posted 3 months ago
To construct a pushdown automaton (PDA) for the language L={aibjcki,j,k0,i+k=j} L = \{a^i b^j c^k \mid i, j, k \geq 0, i + k = j\} , we need to design a PDA that can keep track of the number of 'a's and 'c's to ensure their sum equals the number of 'b's. Here's a high-level description of how the PDA can work:

1. Push a special symbol (e.g., )ontothestacktoindicatethebottom.2.Foreveryaread,pushasymbol(e.g.,A)ontothestack.3.Whenbsstart,foreachbread,donothingifthereareAsonthestack;otherwise,pushasymbol(e.g.,B).4.Whencsstart,foreachcread,popasymbolfromthestack.5.Acceptifthestackisempty(exceptforthebottomsymbol) onto the stack to indicate the bottom.
2. For every 'a' read, push a symbol (e.g., 'A') onto the stack.
3. When 'b's start, for each 'b' read, do nothing if there are 'A's on the stack; otherwise, push a symbol (e.g., 'B').
4. When 'c's start, for each 'c' read, pop a symbol from the stack.
5. Accept if the stack is empty (except for the bottom symbol ) after reading the entire input.

This PDA will be non-deterministic because it has to guess when to switch from pushing for 'a's to doing nothing for 'b's and when to start popping for 'c's.

Key Concept
Pushdown Automaton Construction
Explanation⚹ ⚹A pushdown automaton for the given language uses the stack to balance the number of 'a's and 'c's against the number of 'b's, ensuring that the sum of the number of 'a's and 'c's is equal to the number of 'b's.⚹

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