> My point is that your initial argument was missing several key pieces My initial example was a response to "If you think it is possible then I'd like to see

> My point is that your initial argument was missing several key pieces My initial example was a response to "If you think it is possible then I'd like to see an implementation of a sudoku puzzle solver as Markov chain", describing how a Sudoku solver could be implemented as a Markov chain. I don't think there's anything missing from it - it solves all proper Sudokus, and I only left open the choice of how to handle improper Sudokus because that was unspecified (but trivial regardless of what's wanted). > I'm not saying it can't be done but that it's actually much more complicated If that's the case, then I did misinterpret your comments as saying it can't be done. But, I don't think it's really complicated regardless of whatever "ok but now it must encode choice points in its state" are thrown at it - it's just a state-to-state transition look-up table. > so compiling a sudoku solver to a Markov chain requires more than just tracking the board state in the context. As noted, you can keep all the same variables as a regular Sudoku solver as part of the Markov chain's state and transition instruction-by-instruction, if that's what you want. If you mean inputs from a user, the same is true of LLMs which are typically ran interactively. Either model the whole universe including the user as part of state transition table (maybe impossible, depending on your beliefs about the universe), or have user interaction take the current state, modify it, and use it as initial state for a new run of the Markov chain.