Syntactic Minimization of Nondeterministic Finite Automata

@inproceedings{Myers2021SyntacticMO,
  title={Syntactic Minimization of Nondeterministic Finite Automata},
  author={Robert S. R. Myers and Henning Urbat},
  booktitle={MFCS},
  year={2021}
}
Nondeterministic automata may be viewed as succinct programs implementing deterministic automata, i.e. complete specifications. Converting a given deterministic automaton into a small nondeterministic one is known to be computationally very hard; in fact, the ensuing decision problem is PSPACE-complete. This paper stands in stark contrast to the status quo. We restrict attention to subatomic nondeterministic automata, whose individual states accept unions of syntactic congruence classes. They… Expand

Tables from this paper

References

SHOWING 1-10 OF 37 REFERENCES
Nondeterministic Syntactic Complexity
We introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the ‘canonical boolean representation’ of the syntacticExpand
Mathematical foundations of automata theory
  • Available at http://www.liafa. jussieu.fr/~jep/PDF/MPRI/MPRI.pdf,
  • 2020
∞-Categories for the Working Mathematician
homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition,Expand
A relational category of formal contexts
  • 2016
A relational category of formal contexts (preprint)
  • 2016
A relational category of formal contexts (preprint), 2016
  • 2016
New Interpretation and Generalization of the Kameda-Weiner Method
TLDR
This work presents a reinterpretation of the Kameda-Weiner method of finding a minimal nondeterministic finite automaton (NFA) of a language, in terms of atoms of the language, and provides a unified view of the construction of several known NFAs. Expand
Coalgebraic constructions of canonical nondeterministic automata
TLDR
This work recovers three well-studied canonical nfas and obtains a new canonical nfa called the distromaton by taking V = distributive lattices, which is shown to be minimal relative to a suitable measure. Expand
On Continuous Nondeterminism and State Minimality
TLDR
It is proved that for each regular language L there is a unique minimal nondeterministic closure automaton whose underlying nfa accepts L, and in the important case where the closure operator of this machine is topological, its underlying nFA is shown to be state-minimal. Expand
Theory of átomata
We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call "atomaton", whose states are the "atoms" of the language, that is, non-empty intersectionsExpand
...
1
2
3
4
...