5 results
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 […]
Published on November 8, 2006
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
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
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
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 […]
Published on January 31, 2020