From iterative algebras to iterative theories

Electronic Notes in Theoretical Computer Science

Volumn 107, Issue 1-4 SPEC. ISS., 2004, Pages 3-24

  Adámek, Jiří ^a   Milius, Stefan ^a   Velebil, Jiří ^b  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

Coalgebra; Free iterative theory; Rational monad

Indexed keywords

CODES (SYMBOLS); FINITE ELEMENT METHOD; ITERATIVE METHODS; POLYNOMIALS; SET THEORY; TREES (MATHEMATICS); ALGEBRA; BINARY CODES; COMPUTATION THEORY;

COALGEBRA; FREE ITERATIVE THEORY; RATIONAL MONAD; ITERATIVE ALGEBRAS;

ALGEBRA; ITERATIVE METHODS;

EID: 10444235086     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.entcs.2004.02.033     Document Type: Conference Paper

References (17)

1. P. Aczel, J. Adámek, S. Milius and J. Velebil, Infinite Trees and Completely Iterative Theories: A Coalgebraic View, Theoret. Comput. Sci. 300 (2003), 1-45.
2. J. Adámek, On a description of terminal coalgebras and iterative theories, Electron. Notes Theor. Comput. Sci. 82.1 (2003).
3. J. Adámek, S. Milius and J. Velebil. Free Iterative Theories - A Coalgebraic View, Math. Structures Comput. Sci. 13 (2003), 259-320.
4. J. Adámek, S. Milius and J. Velebil, On Rational Monads and Free Iterative Theories, Electron. Notes Theor. Comput. Sci. 69 (2003).
5. J. Adámek, S. Milius and J. Velebil, From Iterative Algebras to Iterative Theories, full version, available via http://www.iti.cs.tu-bs.de/~milius/
6. J. Adámek and J. Rosický, Locally presentable and accessible categories, Cambridge University Press, 1994.
7. S. Bloom and C. C. Elgot, The Existence and Construction of Free Iterative Theories, J. Comput. System Sci. 12 (1974), 305-318.
8. B. Courcelle, Fundamental Properties of Infinite Trees, Theoret. Comput. Science 25 (1983), 95-169.
9. C. C. Elgot, Monadic Computation and Iterative Algebraic Theories, in: Logic Colloquium '73 (eds: H. E. Rose and J. C. Shepherdson), North-Holland Publishers, Amsterdam, 1975.
10. C. C. Elgot, S. L. Bloom and R. Tindell, On the Algebraic Structure of Rooted Trees, J. Comput. System Sci. 16 (1978), 361-399.
11. P. Gabriel and F. Ulmer, Lokal präsentierbare Kategorien, Lecture N. Math 221, Springer-Verlag, Berlin 1971.
12. N. Ghani, C. Lüth and F. De Marchi, Electron. Notes Theor. Comput. Sci 65(1), 2002.
13. S. Ginali, Regular trees and the free iterative theory, J. Comput. System Sci. 18 (1979), 228-242.
14. J. Lambek, A fixpoint theorem for complete categories, Math. Z. 103 (1968), 151-161.
15. S. Milius, On Iteratable Endofunctors, Electron. Notes Theor. Comput. Sci 69 (2003).
16. E. Nelson, Iterative Algebras, Theoret. Comput. Science 25 (1983), 67-94.
17. J. Tiuryn, Unique Fixed Points vs. Least Fixed Points, Theoret. Comput. Sci. 12 (1980), 229-254.