SIAM Journal on Computing
Path-based depth-first search for strong and biconnected components
Information Processing Letters
Minimal cover-automata for finite languages
Theoretical Computer Science
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Hopcroft's Algorithm and Cyclic Automata
Language and Automata Theory and Applications
Economy of description by automata, grammars, and formal systems
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
On the Hopcroft's minimization technique for DFA and DFCA
Theoretical Computer Science
An nlogn Algorithm for Hyper-minimizing States in a (Minimized) Deterministic Automaton
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
Hyper-minimisation Made Efficient
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Finite automata and their decision problems
IBM Journal of Research and Development
On the complexity of hopcroft’s state minimization algorithm
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
Better hyper-minimization: not as fast, but fewer errors
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
On minimising automata with errors
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
The tractability frontier for NFA minimization
Journal of Computer and System Sciences
From equivalence to almost-equivalence, and beyond--minimizing automata with errors
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Hyper-minimization for deterministic tree automata
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
Brzozowski's minimization algorithm: more robust than expected
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
Hyper-optimization for deterministic tree automata
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
Minimization of symbolic automata
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
| Hi-index | 5.23 |
We improve a recent result [A. Badr, Hyper-minimization in O(n^2), Internat. J. Found. Comput. Sci. 20 (4) (2009) 735-746] for hyper-minimized finite automata. Namely, we present an O(nlogn) algorithm that computes for a given deterministic finite automaton (dfa) an almost-equivalent dfa that is as small as possible-such an automaton is called hyper-minimal. Here two finite automata are almost-equivalent if and only if the symmetric difference of their languages is finite. In other words, two almost-equivalent automata disagree on acceptance on finitely many inputs. In this way, we solve an open problem stated in [A. Badr, V. Geffert, I. Shipman, Hyper-minimizing minimized deterministic finite state automata, RAIRO Theor. Inf. Appl. 43 (1) (2009) 69-94] and by Badr. Moreover, we show that minimization linearly reduces to hyper-minimization, which shows that the time-bound O(nlogn) is optimal for hyper-minimization. Independently, similar results were obtained in [P. Gawrychowski, A. Jez, Hyper-minimisation made efficient, in: Proc. 34th Int. Symp. Mathematical Foundations of Computer Science, in: LNCS, vol. 5734, Springer, 2009, pp. 356-368].