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Recognition, or recognize, is when humans or animals know something about the surrounding objects or beings. For example, an animal might recognize another animal as an enemy or friend, dangerous or harmless. These cognitive acts relate to the beings' perception, memory, learning, and experience.
Pattern recognition in software
In computer programs, pattern recognition tries to teach computers to perceive and recognize things as accurately as possible, how people do it or better. Pattern recognition by computers distinguishes objects, images, fingerprints, writing, audio, faces and other things automatically.
When a country recognizes another country, it means that the first country believes that the second country is legal and has a right to be a country. Countries that recognize each other have diplomatic relations. That means they send diplomats to each other, and make different kinds of agreements, about trade, international laws and other things.