Efficient and Modular Coalgebraic Partition Refinement - Wißmann, Thorsten; Dorsch, Ulrich; Milius, Stefan; Schröder, Lutz (Logical Methods in Computer Science, 2020)
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 and furthermore to flexibly combine existing system types. Under assumptions on the type functor that allow representing its finite coalgebras in terms of nodes and edges, our algorithm runs in time O(m⋅log⁡n)" role="presentation">(𝑚⋅log𝑛) where n" role="presentation">𝑛 and m" role="presentation">𝑚 are the numbers of nodes and edges, respectively. The generic complexity result and the possibility of combining system types yields a toolbox for efficient partition refinement algorithms. Instances of our generic algorithm match the run-time of the best known algorithms for unlabelled transition systems, Markov chains, deterministic automata (with fixed alphabets), Segala systems, and for color refinement.

Efficient Coalgebraic Partition Refinement - Dorsch, Ulrich; Milius, Stefan; Schröder, Lutz; Wißmann, Thorsten (Proc. 28th International Conference on Concurrency Theory (CONCUR 2017), 2017)

Graded monads and graded logics for the linear time – Branching time spectrum - Dorsch, Ulrich; Milius, Stefan; Schröder, Lutz (Leibniz International Proceedings in Informatics, LIPIcs, 2019)
State-based models of concurrent systems are traditionally considered under a variety of notions of process equivalence. In the case of labelled transition systems, these equivalences range from trace equivalence to (strong) bisimilarity, and are organized in what is known as the linear time – branching time spectrum. A combination of universal coalgebra and graded monads provides a generic framework in which the semantics of concurrency can be parametrized both over the branching type of the underlying transition systems and over the granularity of process equivalence. We show in the present paper that this framework of graded semantics does subsume the most important equivalences from the linear time – branching time spectrum. An important feature of graded semantics is that it allows for the principled extraction of characteristic modal logics. We have established invariance of these graded logics under the given graded semantics in earlier work; in the present paper, we extend the logical framework with an explicit propositional layer and provide a generic expressiveness criterion that generalizes the classical Hennessy-Milner theorem to coarser notions of process equivalence. We extract graded logics for a range of graded semantics on labelled transition systems and probabilistic systems, and give exemplary proofs of their expressiveness based on our generic criterion.
CRIS-Team Scopus Importer:2019-09-17
Keywords: Branching Time; Expressiveness; Linear Time; Modal Logics; Monads; System Equivalences

Predicate Liftings and Functor Presentations in Coalgebraic Expression Languages - Dorsch, Ulrich; Milius, Stefan; Schröder, Lutz; Wißmann, Thorsten (Proc. Coalgebraic Methods in Computer Science (CMCS'18), 2018)