7 results
Jiří Adámek ; Stefan Milius ; Lawrence S Moss ; Lurdes Sousa.
For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. The initial algebra consists […]
Published on August 9, 2013
Jiří Adámek ; Mahdie Haddadi ; Stefan Milius.
An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and free algebras. The monad of free corecursive algebras is […]
Published on September 11, 2014
Jiri Adamek ; Stefan Milius ; Jiri Velebil.
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in which the terminals are interpreted as continuous operations. […]
Published on April 1, 2011
Stefan Milius ; Lawrence S Moss ; Daniel Schwencke.
Terminal coalgebras for a functor serve as semantic domains for state-based systems of various types. For example, behaviors of CCS processes, streams, infinite trees, formal languages and non-well-founded sets form terminal coalgebras. We present a uniform account of the semantics of recursive […]
Published on September 30, 2013
Stefan Milius.
The rational fixed point of a set functor is well-known to capture the behaviour of finite coalgebras. In this paper we consider functors on algebraic categories. For them the rational fixed point may no longer be fully abstract, i.e. a subcoalgebra of the final coalgebra. Inspired by \'Esik and […]
Published on September 24, 2018
Jiří Adamek ; Stefan Milius ; Henning Urbat.
The syntactic monoid of a language is generalized to the level of a symmetric monoidal closed category $\mathcal D$. This allows for a uniform treatment of several notions of syntactic algebras known in the literature, including the syntactic monoids of Rabin and Scott ($\mathcal D=$ sets), the […]
Published on May 15, 2018
Thorsten Wißmann ; Stefan Milius ; Lutz Schröder.
We provide a generic algorithm for constructing formulae that distinguish behaviourally inequivalent states in systems of various transition types such as nondeterministic, probabilistic or weighted; genericity over the transition type is achieved by working with coalgebras for a set functor in the […]
Published on November 17, 2022