Algebra-coalgebra duality in Brzozowski's minimization algorithm

@article{Bonchi2014AlgebracoalgebraDI,
  title={Algebra-coalgebra duality in Brzozowski's minimization algorithm},
  author={Filippo Bonchi and Marcello M. Bonsangue and Helle Hvid Hansen and Prakash Panangaden and Jan J. M. M. Rutten and Alexandra Silva},
  journal={ACM Trans. Comput. Log.},
  year={2014},
  volume={15},
  pages={3:1-3:29}
}
We give a new presentation of Brzozowski's algorithm to minimize finite automata using elementary facts from universal algebra and coalgebra and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. Notably, we derive algorithms to obtain minimal language equivalent automata from Moore nondeterministic and weighted automata. 
29 Citations
10 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 10 references

Canonical regular expressions and minimal state graphs for definite events

  • J. A. BRZOZOWSKI
  • Mathematical Theory of Automata. MRI Symposia…
  • 1962
Highly Influential
6 Excerpts

Adjoint machines, state-behavior machines, and duality

  • M. A. ARBIB, E. G. MANES
  • Journal of Pure and Applied Algebra 6, 3, 313…
  • 1975
Highly Influential
5 Excerpts

Fuzzy machines in a category

  • M. A. ARBIB, E. G. MANES
  • Bulletin of the Australian Mathematical Society…
  • 1975
Highly Influential
4 Excerpts

Minimal realization of machines in closed categories

  • J. GOGUEN
  • Bulletin of the American Mathematical Society 78…
  • 1972
Highly Influential
3 Excerpts

Topics in Mathematical Systems Theory

  • R. E. KALMAN, P. L. FALB, M. A. ARBIB
  • McGraw Hill.
  • 1969
Highly Influential
10 Excerpts

On the general theory of control systems

  • R. KALMAN
  • IRE Transactions on Automatic Control 4, 3, 110…
  • 1959
Highly Influential
10 Excerpts

Similar Papers

Loading similar papers…