Analysis of Stack Heights in a PDA

Here we make a simple analysis of stack heights after simplifying the PDA (single final state and every transition either pushes or pops, but not both). We note that the stack height after every transition, the height always changes by 1 (either up or down). We then look at the individual "mountains" of the computation (where the stack reaches a "peak" and then comes back down to "level 0"), and see how to solve a "smaller" version of the same problem. This gives insight into how to convert the PDA into a context-free grammar (CFG).

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