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What is Instantaneous Description and Turnstile Notation?
The instantaneous description (ID) of a push down automata (PDA) is represented by a triple (q,w,s)
Where,
- q is the state.
- w is unconsumed input.
- s is the stack contents.
ID is an informal notation of how a PDA compares an input string and makes a decision that string is accepted or rejected.
Turnstile Notation
It is used for connecting pairs of ID's that represent one or more moves of a PDA.
The process of transition is denoted by the turnstile symbol "⊢"
⊢ it represents one move.
⊢ sign describes a sequence of moves.
Example
(P,b,T) ⊢ (q,w,a)
While taking a transition from P to q the input symbol 'b' is consumed and top of the stack 'T' is represented.
Consider another example to understand more about ID and Turnstile Notation
Problem: Find out IDs for input string w = "aaabb" of PDA. and check whether string is accepted by PDA or not?
Solution: Let us see the Instantaneous Description for string w = "aaabb"
(q0,aaabb,Z0) |- (q0, aabb, aZ0) {based on Transition rule 1}
|-(q0,abb,aaZ0) {Based on transition rule 2}
|-(q0,bb,aaaZ0) {Based on transition rule 2}
|-(q1,b,aaZ0){ Based on transition rule 3}
|-(q1,λ,aZ0){ based on transition rule 3}
|- There is no defined move.
So finally the pushdown automaton stops at this move and the string is not accepted because the input string w is completed or input tape is empty, but the PDA stack is not empty.
So the string 'w' is not accepted.
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