For example if I have "ABBC" and "BCCD", what is the rule? Is it any 4 letter string? Is it the same character repeated twice? Is it the same character repeated twice in a particular offset from the beginning of the string? There is some aspect of heuristics, and some aspect of "elegance" to a given solution - what a human would judge to be the "right" solution is surely some balance of specificity and simplicity.
It reminds me of Hofstadter's Jumbo experiment from the '80s: https://books.google.com/books?id=somvbmHCaOEC&pg=PA97&lpg=P... (Clojure implementation here: https://github.com/vemv/jumbo). If I remember right, his thesis was that this sort of pattern matching is at the core of what is intelligence, and maybe even what is consciousness.
For example if I have "ABBC" and "BCCD", what is the rule? Is it any 4 letter string? Is it the same character repeated twice? Is it the same character repeated twice in a particular offset from the beginning of the string? There is some aspect of heuristics, and some aspect of "elegance" to a given solution - what a human would judge to be the "right" solution is surely some balance of specificity and simplicity.
Also see relevant Stack Overflow posts: http://stackoverflow.com/questions/4880402/how-to-auto-gener... and http://cstheory.stackexchange.com/questions/1854/is-finding-...