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State Complexity of Basic Operations on Nondeterministic Finite Automata
 In Implementation and Application of Automata (CIAA ’02), LNCS 2608
, 2001
"... The state complexities of basic operations on nondeterministic finite automata (NFA) are investigated. In particular, we consider Boolean operations, catenation operations  concatenation, iteration, free iteration  and the reversal on NFAs that accept finite and infinite languages over arbitrar ..."
Abstract

Cited by 28 (3 self)
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The state complexities of basic operations on nondeterministic finite automata (NFA) are investigated. In particular, we consider Boolean operations, catenation operations  concatenation, iteration, free iteration  and the reversal on NFAs that accept finite and infinite languages over arbitrary alphabets. Most of the shown bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. For the intersection of finite languages and the complementation tight bounds in the order of magnitude are proved.
On the Determinization of Weighted Finite Automata
 SIAM J. Comput
, 1998
"... . We study determinization of weighted finitestate automata (WFAs), which has important applications in automatic speech recognition (ASR). We provide the first polynomialtime algorithm to test for the twins property, which determines if a WFA admits a deterministic equivalent. We also provide ..."
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Cited by 16 (0 self)
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. We study determinization of weighted finitestate automata (WFAs), which has important applications in automatic speech recognition (ASR). We provide the first polynomialtime algorithm to test for the twins property, which determines if a WFA admits a deterministic equivalent. We also provide a rigorous analysis of a determinization algorithm of Mohri, with tight bounds for acyclic WFAs. Given that WFAs can expand exponentially when determinized, we explore why those used in ASR tend to shrink. The folklore explanation is that ASR WFAs have an acyclic, multipartite structure. We show, however, that there exist such WFAs that always incur exponential expansion when determinized. We then introduce a class of WFAs, also with this structure, whose expansion depends on the weights: some weightings cause them to shrink, while others, including random weightings, cause them to expand exponentially. We provide experimental evidence that ASR WFAs exhibit this weight dependence. ...
The Topological Approach to the Limitedness Problem on Distance Automata
, 1998
"... this paper, we present the topological approach to the limitedness problem on distance automata. Our techniques has been improved so that the Brown's result is no longer needed. The main mathematical tools used are the local structure theory for nite semigroup [13] and some basic topological ideas. ..."
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Cited by 8 (1 self)
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this paper, we present the topological approach to the limitedness problem on distance automata. Our techniques has been improved so that the Brown's result is no longer needed. The main mathematical tools used are the local structure theory for nite semigroup [13] and some basic topological ideas. Most of the technical results in this paper except Lemma 3.9 and Lemma 3.10 were obtained in ([14], [15]). Besides for the sake of completeness, we include all the proofs because many of them have been reworked for better presentations