Search

• < Previous
• 1
• Next >

---

Well-Pointed Coalgebras

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&nbsp;[&hellip;]

---

Abstract GSOS Rules and a Modular Treatment of Recursive Definitions

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&nbsp;[&hellip;]

---

Efficient and Modular Coalgebraic Partition Refinement

Thorsten Wißmann ; Ulrich Dorsch ; Stefan Milius ; Lutz Schröder.

We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical relational systems but also, e.g. various forms of weighted systems&nbsp;[&hellip;]

---

Proper Functors and Fixed Points for Finite Behaviour

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&nbsp;[&hellip;]

---

Elgot Algebras

Jiri Adamek ; Stefan Milius ; Jiri Velebil.

Denotational semantics can be based on algebras with additional structure (order, metric, etc.) which makes it possible to interpret recursive specifications. It was the idea of Elgot to base denotational semantics on iterative theories instead, i.e., theories in which abstract recursive&nbsp;[&hellip;]

---

A Categorical Approach to Syntactic Monoids

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&nbsp;[&hellip;]

---