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
Computing all l-cover automata fast
CIAA'11 Proceedings of the 16th 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
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We consider a problem of hyper-minimisation of an automaton [2,3]: given a DFA M we want to compute a smallest automaton N such that the language L(M) ΔL(N) is finite, where Δ denotes the symmetric difference. We improve the previously known $\mathcal O (|\Sigma|n^2)$ solution by giving an expected $\mathcal O (|\delta|\log n)$ time algorithm for this problem, where |驴| is the size of the (potentially partial) transition function. We also give a slightly slower deterministic $\mathcal O(|\delta|\log^2 n)$ version of the algorithm.Then we introduce a similar problem of k-minimisation: for an automaton M and number k we want to find a smallest automaton N such that L(M) ΔL(N) 驴 Σk , i.e. the languages they recognize differ only on words of length less than k. We characterise such minimal automata and give algorithm with a similar complexity for this problem.