Cycle-aware minimization of acyclic deterministic finite-state automata

Bubenzer, Johannes

doi:10.1016/j.dam.2013.08.003

Cited by 5 publications

(7 citation statements)

References 7 publications

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“…In this comparison, the impact of the intermediate structures required for the DAWG/ADFA construction is analyzed. In [32], the author presents a linear-time algorithm O(Q) for the minimization of acyclic deterministic finite-state automata (DAWG/ADFA). In [33], the author presents an algorithm that directly (i.e.…”

Section: Related Workmentioning

confidence: 99%

MergedTrie: Efficient textual indexing

Ferrández

Peral

2019

PLoS ONE

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The accessing and processing of textual information (i.e. the storing and querying of a set of strings) is especially important for many current applications (e.g. information retrieval and social networks), especially when working in the fields of Big Data or IoT, which require the handling of very large string dictionaries. Typical data structures for textual indexing are Hash Tables and some variants of Tries such as the Double Trie (DT). In this paper, we propose an extension of the DT that we have called MergedTrie . It improves the DT compression by merging both Tries into a single and by segmenting the indexed term into two fixed length parts in order to balance the new Trie. Thus, a higher overlapping of both prefixes and suffixes is obtained. Moreover, we propose a new implementation of Tries that achieves better compression rates than the Double-Array representation usually chosen for implementing Tries. Our proposal also overcomes the limitation of static implementations that does not allow insertions and updates in their compact representations. Finally, our MergedTrie implementation experimentally improves the efficiency of the Hash Tables, the DTs, the Double-Array, the Crit-bit, the Directed Acyclic Word Graphs (DAWG), and the Acyclic Deterministic Finite Automata (ADFA) data structures, requiring less space than the original text to be indexed.

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Section: Related Workmentioning

confidence: 99%

MergedTrie: Efficient textual indexing

Ferrández

Peral

2019

PLoS ONE

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“…Minimization of NFAs is PSPACE-complete [10] and remains NP-hard even for restricted subclasses of acyclic NFAs [1]. A linear time minimization algorithm for acyclic DFAs is given by Bubenzer [2] and incremental minimization techniques for acyclic NFAs have been considered e.g. by Lamperti et al [17].…”

Section: Resultsmentioning

confidence: 99%

Branching Measures and Nearly Acyclic NFAs

Keeler

Salomaa

2019

Int. J. Found. Comput. Sci.

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To get a more comprehensive understanding of the amount of branching in computations of a nondeterministic finite automaton (NFA), we introduce and study the string path width and depth path width measures. For a given NFA, the string path width on a string [Formula: see text] counts the number of all complete computations on [Formula: see text], and the depth path width on an integer [Formula: see text] counts the number of complete computations on all strings of length [Formula: see text]. We give an algorithm to decide the finiteness of the depth path width of an NFA. Deciding finiteness of string path width can be reduced to the corresponding question on ambiguity. An NFA is nearly acyclic if any computation can pass through at most one cycle. The class of nearly acyclic NFAs consists of exactly all NFAs with finite depth path width. Using this characterization we show that the finite depth path width of an [Formula: see text]-state NFA over a [Formula: see text]-letter alphabet is at most [Formula: see text] and that this bound is tight. The nearly acyclic NFAs recognize exactly the class of constant density regular languages.

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“…Minimization of NFAs is PSPACE-complete [9] and remains NP-hard even for restricted subclasses of acyclic NFAs [1]. A linear time minimization algorithm for acyclic DFAs is given by Bubenzer [2] and incremental minimization techniques for acyclic NFAs have been considered e.g. by Lamperti et al [14].…”

Section: Resultsmentioning

confidence: 99%

Branching Measures and Nearly Acyclic NFAs

Keeler

Salomaa

2017

Descriptional Complexity of Formal Systems

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To get a more comprehensive understanding of the branching complexity of nondeterministic finite automata (NFA), we introduce and study the string path width and depth path width measures. The string path width on a string w counts the number of all complete computations on w, and the depth path width on an integer counts the number of complete computations on all strings of length. We give an algorithm to decide the finiteness of the depth path width of an NFA. Deciding finiteness of string path width can be reduced to the corresponding question on ambiguity. An NFA is nearly acyclic if any computation can pass through at most one cycle. The class of nearly acyclic NFAs consists of exactly all NFAs with finite depth path width. Using this characterization we show that the finite depth path width of an m-state NFA over a k-letter alphabet is at most (k + 1) m−1 and that this bound is tight. The nearly acyclic NFAs recognize exactly the class of constant density regular languages.

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Cycle-aware minimization of acyclic deterministic finite-state automata

Cited by 5 publications

References 7 publications

MergedTrie: Efficient textual indexing

MergedTrie: Efficient textual indexing

Branching Measures and Nearly Acyclic NFAs

Branching Measures and Nearly Acyclic NFAs

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