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(Solved): Solve these Formal Languages and Automata questions by hand. Q1: Design a PDA that accepts the langu ...
Solve these Formal Languages and Automata questions by hand.
Q1: Design a PDA that accepts the language , Give context-free grammar that generate the same language. Apply three different examples using ID transitions Q2: Design a PDA for accepting a language give the ID form as we explain in the lecture. Apply the string "00011000" on this PDA using ID transitions. Q3: Convert the following CFG to Chomsky Normal Form, write and explain all the steps you do. 1. 2.
Expert Answer
Q1. PDA Design: The PDA will use a single stack to keep track of the symbols. Initially, the stack will contain a special symbol '$' to indicate the bottom of the stack. The PDA will have two states: 'q0' and 'q1', where 'q0' is the initial state and 'q1' is the final accepting state.PDA Description: The PDA starts in state 'q0' with the stack containing only the symbol '$'. When it reads a '0' from the input, it pushes '0' onto the stack. When it reads a '1' from the input, it pushes '1' onto the stack. When it reads a '2' from the input, it pushes '2' onto the stack. When it reads a '3' from the input, it pops a symbol from the stack. If the PDA reaches the end of the input while in state 'q0' and the stack contains only '$', it moves to the final state 'q1', indicating the input is accepted.Context-Free Grammar: We can also provide a context-free grammar that generates the same language. The grammar rules are as follows: S -> 0S3 | A A -> 1A2 | 12 This grammar generates strings of the form 0^n1^m2^m3^n, where n and m are both greater than or equal to 1. Three Examples using ID Transitions:Input: 01122330 PDA Transition Sequence: (q0, 01122330, $) -> (q0, 1122330, 0) -> (q0, 122330, 01) -> (q0, 22330, 012) -> (q0, 2330, 0122) -> (q0, 330, 01223) -> (q1, 33, 0122) -> (q1, 3, 012) -> (q1, ?, 01) Accepted!Input: 00112233 PDA Transition Sequence: (q0, 00112233, $) -> (q0, 0112233, 0) -> (q0, 112233, 01) -> (q0, 12233, 012) -> (q0, 2233, 0122) -> (q0, 233, 01223) -> (q1, 33, 0122) -> (q1, 3, 012) -> (q1, ?, 01) Accepted!Input: 01233210 PDA Transition Sequence: (q0, 01233210, $) -> (q0, 1233210, 0) -> (q0, 233210, 01) -> (q0, 33210, 012) -> (q0, 3210, 0122) -> (q0, 210, 01223) -> (q1, 10, 0122) -> (q1, 0, 012) -> (q1, ?, 01) Rejected!