Journal of Algorithms
Dynamic ordered sets with exponential search trees
Journal of the ACM (JACM)
Hopcroft's Algorithm and Cyclic Automata
Language and Automata Theory and Applications
Hyper-minimisation Made Efficient
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
An nlogn algorithm for hyper-minimizing a (minimized) deterministic automaton
Theoretical Computer Science
Better hyper-minimization: not as fast, but fewer errors
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
From equivalence to almost-equivalence, and beyond--minimizing automata with errors
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
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
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The problem of k-minimisation for a DFA M is the computation of a smallest DFA N (where the size |M| of a DFA M is the size of the domain of the transition function) such that L(M) Δ L(N) ⊆ Σk, which means that their recognized languages differ only on words of length less than k. The previously best algorithm, which runs in time O(|M| log2 n) where n is the number of states, is extended to DFAs with partial transition functions. Moreover, a faster O(|M| log n) algorithm for DFAs that recognise finite languages is presented. In comparison to the previous algorithm for total DFAs, the new algorithm is much simpler and allows the calculation of a k-minimal DFA for each k in parallel. Secondly, it is demonstrated that calculating the least number of introduced errors is hard: Given a DFA M and numbers k and m, it is NP-hard to decide whether there exists a k-minimal DFA N with |L(M)ΔL(N)| ≤ m. A similar result holds for hyper-minimisation of DFAs in general: Given a DFA M and numbers s and m, it is NP-hard to decide whether there exists a DFA N with at most s states such that |L(M)ΔL(N)| ≤ m.