what lives in m1 x1 do the same thing we'll find what how likely is each x2 assuming I get to match it with the best possible choice for x0 and x1 and so it's exactly the same thing instead of saying was a probability for some x2 value summed over x0 and x1 we're just saying if we got to pick the best x0 and x1 so there's a replacing that sum with a max otherwise the same thing is happening same for them x3 and so forth now generally this would be the update equation just as simple as the ones we saw for filtering but now the summation