You are missing the crucial role of propagation - looking at the current state and making inferences based on that. Admittedly, DPLL is pretty weak on that with “just” unit propagation, but it is still _very_ important.
If you told someone to "Guess-and-check" a Sudoku puzzle, they will innately "learn" about the puzzle from their guesses.
The question of "guess-and-check" is "how much time should I spend making a good guess" ?? If you spend a lot of time making inferences, you're doing "Strong guess and check".
If you spend almost no time making inferences, you're doing "weak guess and check".
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People who play Suduku puzzles know that "weak guess and check" solves easier puzzles faster, but "strong guess and check" solves harder puzzles faster. And worst of all, there's no way to really know if you have a hard or easy puzzle ahead of time.
So I argue that "guess and check" is a good layman's term for this whole affair. What you're calling "inference" and "unit propagation" are just the "strength of the guess"... the amount of time you spend thinking about your guess before dedicating yourself to it.
The question of "guess-and-check" is "how much time should I spend making a good guess" ?? If you spend a lot of time making inferences, you're doing "Strong guess and check".
If you spend almost no time making inferences, you're doing "weak guess and check".
--------
People who play Suduku puzzles know that "weak guess and check" solves easier puzzles faster, but "strong guess and check" solves harder puzzles faster. And worst of all, there's no way to really know if you have a hard or easy puzzle ahead of time.
So I argue that "guess and check" is a good layman's term for this whole affair. What you're calling "inference" and "unit propagation" are just the "strength of the guess"... the amount of time you spend thinking about your guess before dedicating yourself to it.