Plenary talk presented at the 2011 IEEE International Symposium of Information Theory, St. Petersburg, Russia.

Ants have always been helping people to solve vari- ous problems. Everybody remembers how they sorted seeds for Cinderella. For the IT community, ants have helped to show that Information Theory is not only an excellent mathematical theory but that many of its results can be considered laws of Nature. Re- ciprocally, we helped ants to be distinguished among other "intel- lectuals" such as counting primates, crows and parrots as one of the smartest species (1, 2). Our long-term experimental study on ant "language" and intelligence were fully based on fundamen- tal ideas of Information Theory, such as the Shannon entropy, the Kolmogorov complexity, and the Shannon's equation connecting the length of a message l and its frequency of occurrence p, i.e., l = − log p. This approach enabled us to discover a developed sym- bolic "language" in highly social ant species based on their ability to transfer the abstract information about remote events and to estimate the rate of information transmission. We also succeeded to reveal important properties of ants' intelligence. These insects appeared to be able to grasp regularities and to use them for "com- pression" of data they communicate to each other. They can also transfer to each other the information about the number of objects and can even add and subtract small numbers in order to optimize their messages. Introductiontime immemorial, people have been dreaming about under- standing animal "languages"- a dream with which many legends are associated. The title of the book of the famous ethologist Kon- rad Lorenz, King Solomon's Ring (1952), refers to the legend about King Solomon who possessed a magical ring that gave him the power of speaking with animals. However, decoding the function and meaning of animal communications is a notoriously difficult problem. A bottleneck here is the low repeatability of standard liv- ing situations, which could give keys for cracking animals' spe- cies-specific codes. Up to now, there are only two types of natural communication systems that have been partly deciphered: the fragments of honeybees' "dance language", and acoustic signal- ization in vervet monkeys and several other species (see (3) for a review). In both types of communications, expressive and dis- tinctive signals correspond to repeatable and frequently occurring situations in the context of animals' life. The problem of cracking animals' codes have become especially attractive since the great "linguistic" potential was discovered in several highly social and intelligent species by means of intermediary artificial languages. Being applied to apes, dolphins and gray parrots, this method has revealed astonishing mental skills in the subjects (4, 5, 6). How- ever, surprisingly little is known yet about natural communication systems of those species that were involved in language-training experiments based on adopted human languages. Explorers of an- imal "languages" thus have met a complex problem of resolving the contradiction between their knowledge about significant "lin- guistic" and cognitive potential in some species and limitations in understanding their natural communications.