Corpus ID: 235421948

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… Expand

Figures from this paper

References

SHOWING 1-10 OF 46 REFERENCES
Coalgebraic Minimization of Automata by Initiality and Finality
  • J. Rot
  • Mathematics, Computer Science
  • MFPS
  • 2016
TLDR
Part of these results are extended to an approach for language equivalence of a general class of systems with branching, such as non-deterministic automata. Expand
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. Expand
A hierarchy of probabilistic system types
TLDR
A new result is exploited that, under mild assumptions on the behaviour functors, a system translation induced by a natural transformation with injective components also reflects bisimilarity. Expand
Efficient Coalgebraic Partition Refinement
TLDR
A generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in reactive verification, and match the runtime of the best known algorithms for unlabelled transition systems, Markov chains, and deterministic automata (with fixed alphabets), and improve the bestknown algorithms for Segala systems. Expand
Universal coalgebra: a theory of systems
  • J. Rutten
  • Mathematics, Computer Science
  • Theor. Comput. Sci.
  • 2000
TLDR
The three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to: coalgebra, homomorphicism of coalgebrAs, and bisimulation, respectively, which are taken as the basic ingredients of a theory called universal coalgebra. Expand
Generic Partition Refinement Algorithms for Coalgebras and an Instantiation to Weighted Automata
TLDR
The aim is to present generic algorithms to decide behavioural equivalence for coalgebras which generalize partition refinement and apply the algorithm to weighted automata over semirings in order to obtain a procedure for checking language equivalences for a large number ofSemirings. Expand
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. Expand
A New Foundation for Finitary Corecursion and Iterative Algebras
TLDR
It is proved that if the given endofunctor preserves monomorphisms then the LFF always exists and is a subcoalgebra of the final coalgebra (unlike the rational fixpoint previously studied by Ad\'amek, Milius, and Velebil). Expand
Generic Trace Theory
TLDR
This paper claims that these various forms of “trace semantics” are instances of a single categorical construction, namely coinduction in a Kleisli category, based on the main technical result that an initial algebra in the category of sets and functions yields a final coalgebra in the Kleislo category. Expand
On Minimal Coalgebras
  • H. Gumm
  • Mathematics, Computer Science
  • Appl. Categorical Struct.
  • 2008
TLDR
The elements of minimal subcoalgebras must correspond uniquely to the formulae of any logic characterizing observational equivalence, and this work gives a straightforward and self-contained account of the coalgebraic logic of D. Pattinson and L. Schröder which it believes is simpler and more direct than the original exposition. Expand
...
1
2
3
4
5
...