Citation Context

...like the composition algorithm, and can thus be given a lazy implementation. 2.3.3. Minimization Any deterministic automaton can be minimized using classical algorithms (Aho, Hopcroft & Ullman, 1974; =-=Revuz, 1992-=-). In the same way, any deterministic weighted automaton A can be minimized using our minimization algorithm (Mohri, 1997). The resulting weighted automaton B is equivalent to the automaton A, and has...

Citation Context

...g to the same 14block of partition P. All decision nodes of the BDD are equivalent. The coarsest stable partition Q ′ that respects P ′ for automaton D can be solved in O(m) worst case time by Revuz =-=[13]-=- and Cai and Paige [6], Sec. 3.4. Finding the equivalence classes of states in Q that point to BDD roots belonging to the same block of Q ′ (i.e., finding the coarsest partition Q that respects P) sol...

Citation Context

...ruction of minimal automata representing finite sets, such as dictionaries in natural language processing. A linear time implementation of such an algorithm for cycle-free automata was given by Revuz =-=[47]-=-. This algorithm has been extended to a more general class of automata by Almeida and Zeitoun [3], namely to automata where all strongly connected components are simple cycles. It has been demonstrate...

Citation Context

...ted automata; finite-state transducers; rational power series; speech recognition. 1 Introduction Finite-state techniques have proven valuable in a variety of natural-language processing applications =-=[5--11,14,16,18,19,29,33,34,37,39,40]-=-. However, speech processing imposes requirements that were not met by any existing finite-state library. In particular, speech recognition requires a general means for managingsuncertainty: all level...

Citation Context

...d acceptor and an unweighted DFA; Equivalence transformations: ffl-elimination, determinization [14, 15] and minimization for unweighted (both the general case [1] and the more efficient acyclic case =-=[20]-=-) and weighted acceptors and transducers [12, 15], removal of inaccessible states and transitions; Search: best path, n-best paths, pruning (remove all states and transitions that occur only on paths ...

Citation Context

...ages. Finite languages are exactly the languages accepted by acyclic finite automata. It has been shown that there is a linear (time) algorithm for the minimization of an acyclic DFA by Revuz in 1992 =-=[15]-=-. However, for the minimization of a general DFA, the best known algorithm has a time complexity O(n log n) by Hopcropt in 1971 [8]. In this article, we compare the state complexity results for finite...

Citation Context

...) in time and space O(jW j). Corollary 5.1.3 For any input W , the minimal deterministic Levenshtein-automaton of degree 1 for W can be computed in time and space O(jW j). Proof. A result by D. Revuz =-=[Rev92]-=- shows that acyclic deterministicsnite state automata can be minimalized in linear time. Since LEV 1 (W ) is deterministic and acyclic the result follows. Example 5.1.4 Figure 5.1 describes the automa...

Citation Context

...algorithm usually credited to Moore (see also [1]) has been improved by Hopcroft [2]. In the special case of finite sets, minimal automata can be constructed and maintained even more efficiently (see =-=[3, 4]-=- and [5] for a recent survey). Extensions to more general situations of Hopcroft’s algorithm are considered in [6, 7, 8]. Hopcroft’s algorithm is known to run in time O(n log n) for an automaton with ...

Citation Context

...t always minimum since it may contain equivalent states. We can minimize it by standard method. In fact, we can do it in linear time with respect to the size of automaton by applying the algorithm in =-=[12]-=-, since our automaton is acyclic except the single error state. In this section, we show that the size of automaton M constructed by our algorithm is at most k! · mmin, where mmin is the size of minim...