RESEARCH STATEMENT My current research interests lie in ...

6 STEFAN MILIUS[7] Jiří Adámek, Stefan Milius and Jiří Velebil, Elgot Algebras, preprint (2005), available viahttp://www.iti.cs.tu-bs.de/~milius, extended abstract to appear in Electron. Notes Theor. Comput. Sci.[8] Jiří Adámek, Stefan Milius and Jiří Velebil, Algebras with Parameterized Iterativity, submitted, available viahttp://www.iti.cs.tu-bs.de/~milius.[9] Jiří Adámek, Stefan Milius and Jiří Velebil, Bases for Parameterized Iterativity, preprint (2005), available viahttp://www.iti.cs.tu-bs.de/~milius.[10] Jiří Adámek, Stefan Milius and Jiří Velebil, Iterative Algebras for a Base, Electron. Notes Theor. Comput. Sci. 122 (2005),147–170.[11] Jiří Adámek, Stefan Milius and Jiří Velebil, Base Modules for Parameterized Iterativity, preprint (2005).[12] Jiří Adámek, Stefan Milius and Jiří Velebil, Description of Bases for Parameterized Iterativity, preprint (2005).[13] Jiří Adámek, Stefan Milius and Jiří Velebil, Algebraic Trees Coalgebraically, manuscript (2005).[14] Jiří Adámek, Stefan Milius and Jiří Velebil, How iterative are Iterative Algebras?, submitted.[15] Jon Barwise and Lawrence S. Moss, Vicious Circles, CSLI Publications, Stanford, 1996.[16] Stephen L. Bloom and Calvin C. Elgot, The Existence and Construction of Free Iterative Theories, J. Comput. SystemSci. 12 (1974), 305–318.[17] Stephen L. Bloom and Zoltán Ésik, Iteration Theories: The equational logic of iterative processes, EATCS Monographson Theoretical Computer Science, Berlin: Springer-Verlag (1993).[18] Bruno Courcelle, Fundamental properties of infinite trees, Theoret. Comput. Sci. 25 (1983), no. 2, 95–169.[19] Calvin C. Elgot, Monadic Computation and Iterative Algebraic Theories, in: Logic Colloquium ’73 (eds: H. E. Rose andJ. C. Shepherdson), North-Holland Publishers, Amsterdam, 1975.[20] Calvin C. Elgot, Stephen L. Bloom and Ralph Tindell, On the Algebraic Structure of Rooted Trees, J. Comput. SystemSci. 16 (1978), 361–399.[21] Peter Gabriel and Friedrich Ulmer, Lokal präsentierbare Kategorien, Lecture N. Math. 221, Springer-Verlag, Berlin 1971.[22] Susanna Ginali, Regular trees and the free iterative theory, J. Comput. System Sci. 18 (1979), 228–242.[23] Irène Guessarian, Algebraic Semantics. Lecture Notes in Comput. Sci. 99, Springer, 1981.[24] Hans Peter Gumm, Elements of the General Theory of Coalgebras, LUATCS’99, Rand Africaans University, Johannesburg,South Africa, 1999.[25] Masahito Hasegawa, Recursion from Cyclic Sharing: Traced Monoidal Categories and Models of Cyclic Lambda Calculi,Proc. 3rd International Conference on Typed Lambda Calculi and Applications, Lecture Notes in Comput. Sci. 1210,196–213 Springer-Verlag, Berlin, 1997.[26] A. J. C. Hurkens, Monica McArthur, Yannis N. Moschovakis, Lawrence S. Moss and Glen T. Whitney, The logic of recursiveequations, J. Symbolic Logic 63 (1998), no. 2, 451–478.[27] Bart Jacobs and Jan J. M. M. Rutten, A Tutorial on (Co)Algebras and (Co)Induction, Bull. Eur. Assoc. Theor. Comput.Sci. EATCS 62 (1997), 222–259.[28] André Joyal, Ross Street and Dominic Verity, Traced Monoidal Categories, Math. Proc. Cambridge Philos. Soc. 119 (1996),no. 3, 447–468.[29] F. William Lawvere, Functorial Semantics of Algebraic Theories, PhD thesis, Columbia University, 1963.[30] Michael Makkai and Robert Paré, Accessible categories: the foundation of categorical model theory, Contemp. Math. 104(1989), Amer. Math. Soc., Providence, RI.[31] Ralph Matthes and Tarmo Uustalu, Substitution in Non-Wellfounded Syntax with Variable Binding, Electron.Notes Theor. Comput. Sci. 82 (2003), no. 1, 15 pp.[32] Jay Mersch, Equational Logic of Recursive Program Schemes, in Proceedings of the 1st International Conference on Algebraand Coalgebra in Computer Science (CALCO 2005), Lecture Notes in Comput. Sci. 3629 (2005), 293–312.[33] Stefan Milius, Relations in Categories, master’s thesis, York University, 2000.[34] Stefan Milius, Completely Iterative Algebras and Completely Iterative Monads, Inform. and Comput. 196 (2005), 1–41.[35] Stefan Milius, On Iteratable Endofunctors, Electron. Notes Theor. Comput. Sci. 69 (2002), 18 pp.[36] Stefan Milius, The Iterative Reflection of an Ideal Monad, manuscript (2005).[37] Stefan Milius, Elgot monads, manuscript (2005).[38] Stefan Milius and Lawrence S. Moss, The Category Theoretic Solution of Recursive Program Schemes, extendedabstract, in Proceedings of the 1st International Conference on Algebra and Coalgebra in Computer Science(CALCO 2005), Lecture Notes in Comput. Sci. 3629 (2005), 293–312, full version submitted and available viahttp://www.iti.cs.tu-bs.de/~milius.[39] Robin Milner, Communication and Concurrency, Prentice Hall, 1989.[40] Lawrence S. Moss, Recursion and corecursion have the same equational logic, Theoret. Comput. Sci. 294 (2003), 233–267.[41] Evelyn Nelson, Iterative Algebras, Theoret. Comput. Sci. 25 (1983), 67–94.[42] Jan J. M. M. Rutten, Universal coalgebra, a theory of systems, Theoret. Comput. Sci. 249 (2000), no. 1, 3–80.[43] Jerzy Tiuryn, Unique Fixed Points vs. Least Fixed Points, Theoret. Comput. Sci. 12 (1980), 229–254.[44] Tarmo Uustalu, Generalizing substitution, Theor. Inform. Appl. 37 (2003), no. 4, 315–336.