Bongard Problem

A Bongard problem is a kind of puzzle invented by the Russian computer scientist Mikhail Moiseevich Bongard (Михаил Моисеевич Бонгард, 1924–1971), probably in the mid-1960s. They were published in his eponymous 1967 book on pattern recognition. Bongard, in the introduction of the book (which deals with a number of topics including perceptrons) credits the ideas in it to a group including M. N. Vaintsvaig, V. V. Maksimov, and M. S. Smirnov.

The idea of a Bongard problem is to present two sets of relatively simple diagrams, say A and B. All the diagrams from set A have a common factor or attribute, which is lacking in all the diagrams of set B. The problem is to find, or to formulate, convincingly, the common factor.

Many computational architectures have been devised to solve Bongard problems, the most extensive of which being Phaeaco, by Dr. Harry Foundalis. Such tasks were relevant to the early days of machine learning and are still unsolved to this date. The problems were popularised by their occurrence in the 1979 book Gödel, Escher, Bach by Douglas Hofstadter, himself a composer of Bongard problems. Bongard problems are also at the heart of the game Zendo.