Question

Define a deterministic PDA (give table of moves) that accepts the language of balanced strings of parentheses. For convenience, a special end-marker is added to the end of each string. Use the grammar S rightarrow T$ T rightarrow T[T] elmentof (b) Show the moves that parses the string []$, alongside with the corresponding steps in the left derivation of the string.

Answer 1

PDA for given language is given here.

Here at state A :- push '[' on to stack for each input string '[' . and pop one '[' for each input string ']'.

CI) PDA , C, CC ヲ

when end of string is reached, i.e $ found, and stack is empty accept the string at state B.

--> here symbol Z₀ indicates empty stack.

----> Here is the parse tree and derivation for the given string []$ :

Denvaten os string c1$ &T ㄈㄏㄧ ㄒ ㄒ

note : Here given language is left recursive, so there can be ambiguity in derivation.

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