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This is part one of Jan Rutten's lectures on Coalgebra in Tehran, Iran.
Abstract: Since the early nineties, coalgebra has become an active area of research in which one tries to understand all kinds of infinite data types, automata, transition systems and dynamical systems from a unifying perspective. The focus of coalgebra is on observable behaviour and one uses coinduction as a central methodology, both for behavioural specifications and to prove behavioural equivalences. These days, one uses coalgebraic techniques in a wide variety of areas, ranging from automata theory to software engineering to economy.
In a series of three lectures, we will discuss the following subjects:
(i) The coalgebraic method
(ii) A coinductive calculus of streams
(iii) Algebra meets coalgebra: automata and formal languages