7th Estonian Winter School in Computer Science (EWSCS)
VII Eesti Arvutiteaduse Talvekool (EATTK)
Palmse, Estonia
March 3 - 8, 2002
Prof. Dr. H. Peter Gumm
FB Mathematik, FG Informatik
Philipps Universitaet Marburg
Universal Coalgebra: A theory of state based systems
Abstract
Universal coalgebra is a mathematical theory of state based systems, which in many respects is dual to universal algebra. Equality must be replaced by indistinguishability, coinduction replaces induction as a proof principle and maps are defined by co-recursion. Bisimulations turn out to be the basic structure preserving relations.
In our course we explain applications of coalgebras in various branches of Computer Science and of Mathematics. Then we develop the general structure theory and introduce co-equations as "forbidden patterns", which can be used to specify any property invariant under certain basic algebraic constructions. Finally, we develop a syntactical description of co-equations as equivalence classes of infinite labelled trees.
Course materials
Course material, including exercises, will be made available at the school. In part they will be based on a (substantially updated) version of ( http://www.mathematik.uni-marburg.de/~gumm/Papers/Luatcs.ps).
H.-P. Gumm. Elements of the general theory of coalgebras. Course notes. (Based on the notes for a course delivered at LUATCS'99.)
H.-P. Gumm, T. Schröder. Coalgebras of bounded type. To appear in Math. Struct. Comp. Science, special issue CMCS'01.
About the Speaker
E-mail: gumm@mathematik.uni-marburg.de
URL: http://www.mathematik.uni-marburg.de/~gumm/