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57
Online Construction of Subsequence Automata for Multiple Texts
, 2000
"... We consider a deterministic finite automaton which accepts all subsequences of a set of texts, called subsequence automaton. We show an online algorithm for constructing subsequence automaton for a set of texts. It runs in O(#(m + k) + N) time using O(#m) space, where # is the size of alphab ..."
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We consider a deterministic finite automaton which accepts all subsequences of a set of texts, called subsequence automaton. We show an online algorithm for constructing subsequence automaton for a set of texts. It runs in O(#(m + k) + N) time using O(#m) space, where # is the size of alphabet, m is the size of the resulting subsequence automaton, k is the number of texts, N is the total length of texts. It can be used to preprocess a given set S of texts in such a way that for any subsequent query w # # # , returns in O(w) time the number of texts in S which contains w as a subsequence. We also show an upper bound of the size of automaton compared to the minimum automaton.
Directed Acyclic Subsequence Graph for multiple texts
, 1999
"... The subsequence matching problem is to decide, for given strings S and T , whether S is a subsequence of T . The string S is called pattern and the string T text. We consider the case of multiple texts and show how to solve the subsequence matching problem in time linear in the length of pattern. ..."
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The subsequence matching problem is to decide, for given strings S and T , whether S is a subsequence of T . The string S is called pattern and the string T text. We consider the case of multiple texts and show how to solve the subsequence matching problem in time linear in the length of pattern. For this purpose we build the automaton that accepts all subsequences of given texts. The automaton is called Directed Acyclic Subsequence Graph (DASG) and we present an algorithm for its building. We also prove upper bound for its number of states. Further, we consider modification of the subsequence matching problem: given a string S and a finite language L, we are to decide whether S is a subsequence of any string in L. We suppose that a finite automaton accepting L is given and present an algorithm for building the DASG for the language L. We also mention applications of DASG to some problems related to subsequences. R'esum'e Le probl`eme de recherche de souss'equence consist...
A Taxonomy of Algorithms for Constructing Minimal Acyclic Deterministic Finite Automata
 Proc. Workshop on Implementing Automata
, 1999
"... this paper, we present a taxonomy of algorithms for constructing minimal acyclic deterministic finite automata (MADFAs). MADFAs represent finite languages and are therefore useful in applications such as storing words for spellchecking, computer and biological virus searching, text indexing and XML ..."
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this paper, we present a taxonomy of algorithms for constructing minimal acyclic deterministic finite automata (MADFAs). MADFAs represent finite languages and are therefore useful in applications such as storing words for spellchecking, computer and biological virus searching, text indexing and XML tag lookup. In such applications, the automata can grow extremely large (with more than 10
Minimization of symbolic automata
 In POPL
, 2014
"... Symbolic Automata extend classical automata by using symbolic alphabets instead of finite ones. Most of the classical automata algorithms rely on the alphabet being finite, and generalizing them to the symbolic setting is not a trivial task. In this paper we study the problem of minimizing symbolic ..."
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Symbolic Automata extend classical automata by using symbolic alphabets instead of finite ones. Most of the classical automata algorithms rely on the alphabet being finite, and generalizing them to the symbolic setting is not a trivial task. In this paper we study the problem of minimizing symbolic automata. We formally define and prove the basic properties of minimality in the symbolic setting, and lift classical minimization algorithms (HuffmanMoore’s and Hopcroft’s algorithms) to symbolic automata. We also introduce a completely new minimization algorithm that takes full advantage of the symbolic representation of the alphabet, and prove its correctness. We provide comprehensive performance evaluation of all the algorithms over large benchmarks and against existing stateoftheart implementations. The experiments show how the new symbolic algorithm is faster than previous implementations. 1.
A Fast Lexically Constrained Viterbi Algorithm for OnLine Handwriting Recognition
 In Proc. 7th International Workshop on Frontiers in Handwriting Recognition
, 2000
"... Abstract: Most online cursive handwriting recognition systems use a lexical constraint to help improve the recognition performance. Traditionally, the vocabulary lexicon is stored in a trie (automaton whose underlying graph is a tree). In this paper, we propose a solution based on a more compact da ..."
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Abstract: Most online cursive handwriting recognition systems use a lexical constraint to help improve the recognition performance. Traditionally, the vocabulary lexicon is stored in a trie (automaton whose underlying graph is a tree). In this paper, we propose a solution based on a more compact data structure, the directed acyclic word graph (DAWG). We show that our solution is equivalent to the traditional system. Moreover, we propose a number of heuristics to reduce the size of the DAWG and present experimental results demonstrating a significant improvement. 1
Incremental construction of compact acyclic NFAs
 IN PROCEEDINGS OF ACL 2001
, 2001
"... This paper presents and analyzes an incremental algorithm for the construction of Acyclic Nondeterministic Finitestate Automata (NFA). Automata of this type are quite useful in computational linguistics, especially for storing lexicons. The proposed algorithm produces compact NFAs, i.e. NFA ..."
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This paper presents and analyzes an incremental algorithm for the construction of Acyclic Nondeterministic Finitestate Automata (NFA). Automata of this type are quite useful in computational linguistics, especially for storing lexicons. The proposed algorithm produces compact NFAs, i.e. NFAs that do not contain equivalent states. Unlike Deterministic Finitestate Automata (DFA), this property is not sufficient to ensure minimality, but still the resulting NFAs are considerably smaller than the minimal DFAs for the same languages.
Complexity of Operations on Cofinite Languages
 9TH LATIN AMERICAN THEORETICAL INFORMATICS SYMPOSIUM (LATIN 2010), OAXACA: MEXICO
, 2010
"... We study the worst case complexity of regular operations on cofinite languages (i.e., languages whose complement is finite) and provide algorithms to compute efficiently the resulting minimal automata. ..."
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We study the worst case complexity of regular operations on cofinite languages (i.e., languages whose complement is finite) and provide algorithms to compute efficiently the resulting minimal automata.
Minimizing local automata
"... Abstract — We design an algorithm that minimizes irreducible deterministic local automata by a sequence of state mergings. Two states can be merged if they have exactly the same outputs. The running time of the algorithm is O(min(m(n −r +1), m log n)), where m is the number of edges, n the number of ..."
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Abstract — We design an algorithm that minimizes irreducible deterministic local automata by a sequence of state mergings. Two states can be merged if they have exactly the same outputs. The running time of the algorithm is O(min(m(n −r +1), m log n)), where m is the number of edges, n the number of states of the automaton, and r the number of states of the minimized automaton. In particular, the algorithm is linear when the automaton is already minimal and contrary to Hopcroft’s minimisation algorithm that has a O(kn log n) running time in this case, where k is the size of the alphabet, and that applies only to complete automata. (Note that kn ≥ m.) While Hopcroft’s algorithm relies on a “negative strategy”, starting from a partition with a single class of all states, and partitioning classes when it is discovered that two states cannot belong to the same class, our algorithm relies on a “positive strategy”, starting from the trivial partition for which each class is a singleton. Two classes are then merged when their leaders have the same outputs. The algorithm applies to irreducible deterministic local automata, where all states are considered both initial and final. These automata, also called covers, recognize symbolic dynamical shifts of finite type. They serve to present a large class of constrained channels, the class of finite memory systems, used for channel coding purposes. The algorithm also applies to irreducible deterministic automata that are leftclosing and have a synchronizing word. These automata present shifts that are called almost of finite type. Almostoffinitetype shifts make a meaningful class of shifts, intermediate between finite type shifts and sofic shifts.