What Are Iteration Theories?
- J. Adámek, Stefan Milius, J. Velebil
- MathematicsInternational Symposium on Mathematical…
- 26 August 2007
We prove that iteration theories can be introduced as algebras for the monad Rat on the category of signatures assigning to every signature Σ the rational-Σ-tree signature. This supports the result…
Infinite trees and completely iterative theories: a coalgebraic view
- P. Aczel, J. Adámek, Stefan Milius, J. Velebil
- MathematicsTheoretical Computer Science
- 7 May 2003
Completely iterative algebras and completely iterative monads
- Stefan Milius
- MathematicsInformation and Computation
- 10 January 2005
A Coalgebraic Perspective on Minimization and Determinization
- J. Adámek, F. Bonchi, Mathias Hülsbusch, B. König, Stefan Milius, Alexandra Silva
- Mathematics, Computer ScienceFoundations of Software Science and Computation…
- 24 March 2012
This paper uses the coalgebraic view on systems to derive, in a uniform way, abstract procedures for checking behavioural equivalence in coalgebras, which perform (a combination of) minimization and determinization.
Recursive coalgebras of finitary functors
- J. Adámek, D. Lücke, Stefan Milius
- MathematicsRAIRO - Theoretical Informatics and Applications
- 1 October 2007
For finitary set functors preserving inverse images, recursive coalgebras A of Paul Taylor are proved to be precisely those for which the system described by A always halts in finitely many steps.
Varieties of Languages in a Category
- J. Adámek, R. Myers, Henning Urbat, Stefan Milius
- Mathematics30th Annual ACM/IEEE Symposium on Logic in…
- 21 January 2015
This work introduces varieties of languages in a category C, and proves that they correspond to pseudovarieties of monoids in a closed monoidal category D, provided that C and D are dual on the level of finite objects.
A Sound and Complete Calculus for Finite Stream Circuits
- Stefan Milius
- Mathematics, Computer Science25th Annual IEEE Symposium on Logic in Computer…
- 11 July 2010
It is proved that a final locally finite (dimensional) coalgebra is, equivalently, an initial iterative algebra of the category of real vector spaces and makes the connection to existing work on the semantics of recursive specifications.
Elgot Algebras
- J. Adámek, Stefan Milius, J. Velebil
- MathematicsLog. Methods Comput. Sci.
- 8 September 2006
It is proved that the category of Elgot algebras is the Eilenberg–Moore category of the monad given by a free iterative theory, and two axioms stem canonically from Elgot’s iterative theories.
Sound and Complete Axiomatizations of Coalgebraic Language Equivalence
- M. Bonsangue, Stefan Milius, Alexandra Silva
- Mathematics, Computer ScienceTOCL
- 14 April 2011
This article investigates under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalized powerset construction that determinizes coalgebras.
Generic Trace Semantics and Graded Monads
- Stefan Milius, D. Pattinson, Lutz Schröder
- Computer ScienceConference on Algebra and Coalgebra in Computer…
- 2015
A notion of graded algebras is introduced and it is shown how they play the role of formulas in trace logics and how they come with a notion of depth that corresponds, e.g., to trace length or bisimulation depth.
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