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Better HyperMinimization Not as Fast, but Fewer Errors
"... Abstract. Hyperminimization aims to compute a minimal deterministic finite automaton (dfa) that recognizes the same language as a given dfa up to a finite number of errors. Algorithms for hyperminimization that run in time O(n log n), where n is the number of states of the given dfa, have been rep ..."
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Cited by 3 (1 self)
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Abstract. Hyperminimization aims to compute a minimal deterministic finite automaton (dfa) that recognizes the same language as a given dfa up to a finite number of errors. Algorithms for hyperminimization that run in time O(n log n), where n is the number of states of the given dfa, have been reported recently in [Gawrychowski and Jeż: Hyperminimisation made efficient. Proc. Mfcs, Lncs 5734, 2009] and [Holzer and Maletti: An n log n algorithm for hyperminimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010]. These algorithms are improved to return a hyperminimal dfa that commits the least number of errors. This closes another open problem of [Badr, Geffert, and Shipman: Hyperminimizing minimized deterministic finite state automata. Rairo Theor. Inf. Appl. 43, 2009]. Unfortunately, the time complexity for the obtained algorithm increases to O(n 2). 1
OPTIMAL HYPERMINIMIZATION
, 2011
"... Minimal deterministic finite automata (dfas) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n log n), where n is the number of states of the input dfa, by [Gawrychowski and Je»: Hyperminimisation made ..."
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Cited by 2 (2 self)
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Minimal deterministic finite automata (dfas) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n log n), where n is the number of states of the input dfa, by [Gawrychowski and Je»: Hyperminimisation made e cient. Proc. Mfcs, Lncs 5734, 2009] and [Holzer and Maletti: An n log n algorithm for hyperminimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010]. Both algorithms return a dfa that is as small as possible, while only committing a nite number of errors. These algorithms are further improved to return a dfa that commits the least number of errors at the expense of an increased (quadratic) runtime. This solves an open problem of [Badr, Geffert, and Shipman: Hyperminimizing minimized deterministic finite state automata. Rairo Theor. Inf. Appl. 43, 2009]. In addition, an experimental study on random automata is performed and the effects of the existing algorithms and the new algorithm are reported.
June 8, 2011 22:57 WSPC/INSTRUCTION FILE hyper International Journal of Foundations of Computer Science c ○ World Scientific Publishing Company OPTIMAL HYPERMINIMIZATION ∗
, 2011
"... Communicated by (Michael Domaratzki) Minimal deterministic finite automata (dfas) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n log n), where n is the number of states of the input dfa, by [Gawrychowsk ..."
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Communicated by (Michael Domaratzki) Minimal deterministic finite automata (dfas) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n log n), where n is the number of states of the input dfa, by [Gawrychowski and Jeż: Hyperminimisation made efficient. Proc. Mfcs, Lncs 5734, 2009] and [Holzer and Maletti: An n log n algorithm for hyperminimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010]. Both algorithms return a dfa that is as small as possible, while only committing a finite number of errors. These algorithms are further improved to return a dfa that commits the least number of errors at the expense of an increased (quadratic) runtime. This solves an open problem of [Badr, Geffert, and Shipman: Hyperminimizing minimized deterministic finite state automata. Rairo Theor. Inf. Appl. 43, 2009]. In addition, an experimental study on random automata is performed and the effects of the existing algorithms and the new algorithm are reported.
On minimising automata with errors ⋆ Pawel Gawrychowski1,⋆ ⋆ , Artur Je˙z 1,⋆ ⋆ 2, ⋆ ⋆ ⋆
"... Abstract. The problem of kminimisation 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) △ L(N) ⊆ Σ
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Abstract. The problem of kminimisation 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) △ L(N) ⊆ Σ <k, 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  log 2 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 kminimal 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 NPhard to decide whether there exists a kminimal DFA N with L(M) △ L(N)  ≤ m. A similar result holds for hyperminimisation of DFAs in general: Given a DFA M and numbers s and m, it is NPhard to decide whether there exists a DFA N with at most s states such that L(M) △ L(N)  ≤ m.
HyperMinimization for Deterministic Tree Automata
, 2012
"... Hyperminimization aims to reduce the size of the representation of a language beyond the limits imposed by classical minimization. To this end, the hyperminimal representation can represent a language that has a finite difference to the original language. The first hyperminimization algorithm is ..."
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Hyperminimization aims to reduce the size of the representation of a language beyond the limits imposed by classical minimization. To this end, the hyperminimal representation can represent a language that has a finite difference to the original language. The first hyperminimization algorithm is presented for (bottomup) deterministic tree automata, which represent the recognizable tree languages. It runs in time O(ℓmn), where ℓ is the maximal rank of the input symbols, m is the number of transitions, and n is the number of states of the input tree automaton.
Hyperminimisation of deterministic weighted finite automata . . .
"... Hyperminimisation of deterministic finite automata is a recently introduced state reduction technique that allows a finite change in the recognised language. A generalisation of this lossy compression method to the weighted setting over semifields is presented, which allows the recognised formal po ..."
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Hyperminimisation of deterministic finite automata is a recently introduced state reduction technique that allows a finite change in the recognised language. A generalisation of this lossy compression method to the weighted setting over semifields is presented, which allows the recognised formal power series to differ for finitely many input strings. First, the structure of hyperminimal deterministic weighted finite automata is characterised in a similar way as in classical weighted minimisation and unweighted hyperminimisation. Second, an efficient minimisation algorithm, which runs in time O(n log n), is derived from this characterisation.