For N=4N = 4N=4: 4×1/8=1/24 \times 1/8 = 1/24×1/8=1/2. That matches our simulation. But we can only add probabilities when the events are mutually exclusive (no two can happen at the same time). Can two of these events overlap?
and like i said, the DFA can also be infinite, but it “blows up” at a rate of at most one state per character in the input, so it will terminate and likely not cause any real issues. the number of states is bounded by the maximum context distance that you need to keep track of for lookarounds, so using infinite context patterns like a(?=.*b) will never create more states than the length of the longest line in your input.
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