How does the Instantaneous Description ( ID ) automata work?

Instantaneous Description (ID) is an informal notation of how a PDA “computes” a input string and make a decision that string is accepted or rejected. 1. q is the current state. 2. w is the remaining input. 3.α is the stack contents, top at the left. one move. ⊢* sign represents a sequence of moves. Let us see how this automata works for aaabbb.
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