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.