Minimality Notions via Factorization Systems

@article{Wimann2021MinimalityNV,
  title={Minimality Notions via Factorization Systems},
  author={Thorsten Wi{\ss}mann},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.07233}
}
For the minimization of state-based systems (i.e. the reduction of the number of states while retaining the system’s semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the system. In the present article, we relate the two aspects on coalgebras by defining an abstract notion of minimality. The abstract notion minimality and minimization live in a general category with a factorization system. We will find criteria on the category… 
1 Citations

Figures from this paper

Minimality Notions via Factorization Systems and Examples

TLDR
The two minimization aspects on coalgebras are related by defining an abstract notion of minimality and it is seen how the two aspects of minimization interact and under which criteria they can be sequenced in any order, like in automata minimization.

References

SHOWING 1-10 OF 51 REFERENCES

Bisimulation by Partitioning Is Ω((m+n)log n)

TLDR
It is shown, exploiting the concept of an oracle, that the approach of Paige, Tarjan, and Bonic is not of help to develop a generic algorithm for deciding bisimilarity on labeled transition systems that is faster than the established lowerbound of Ω((m+n) logn).

On Rational Fixpoints of Endofunctors on Nominal Sets

Nominal sets provide a framework to study key notions of syntax and semantics such as fresh names, variable binding and α-equivalence on a conveniently abstract categorical level. Coalgebras for

A coalgebraic view on reachability

TLDR
This work provides an iterative construction of the reachable part of a given pointed coalgebra that is inspired by and resembles the standard breadth-first search procedure to compute the Reachable partof a graph.

Coalgebra Learning via Duality

TLDR
This paper generalises learning to the theory of coalgebras using the use of logical formulas as tests, based on a dual adjunction between states and logical theories.

Path category for free - Open morphisms from coalgebras with non-deterministic branching

TLDR
The above construction provides path-categories and trace semantics for free for different flavours of transition systems: non-deterministic tree automata, regular nondeterministic nominal automata (RNNA), an expressive automata notion living in nominal sets and multisorted transition systems.

Efficient and Modular Coalgebraic Partition Refinement

TLDR
A generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification, and yields a toolbox for efficient partition refinement algorithms.

Simple O(m logn) Time Markov Chain Lumping

TLDR
This article presents an algorithm for sorting weights with a combination of the so-called possible majority candidate algorithm with any O(k logk) sorting algorithm, which works because the weights consist of two groups, one of which is sufficiently small and all weights in the other group have the same value.

A Final Coalgebra Theorem

We prove that every set-based functor on the category of classes has a final coalgebra. This result strengthens the final coalgebra theorem announced in the book “Non-well-founded Sets”, by the first
...