2019
DOI: 10.23638/lmcs-15(2:6)2019
|View full text |Cite
|
Sign up to set email alerts
|

The height of piecewise-testable languages and the complexity of the logic of subwords

Abstract: The height of a piecewise-testable language L is the maximum length of the words needed to define L by excluding and requiring given subwords. The height of L is an important descriptive complexity measure that has not yet been investigated in a systematic way. This article develops a series of new techniques for bounding the height of finite languages and of languages obtained by taking closures by subwords, superwords and related operations.As an application of these results, we show that FO 2 pA ˚, Ďq, the … Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

0
6
0

Year Published

2019
2019
2022
2022

Publication Types

Select...
2
2

Relationship

0
4

Authors

Journals

citations
Cited by 4 publications
(6 citation statements)
references
References 42 publications
0
6
0
Order By: Relevance
“…The notion of k-universality coincides to that of k-richness introduced in [36,37]. We use the name k-universality rather than k-richness, as richness of words is also used with other meanings, see, e. g., [19,45].…”
Section: Universalitymentioning
confidence: 99%
See 1 more Smart Citation
“…The notion of k-universality coincides to that of k-richness introduced in [36,37]. We use the name k-universality rather than k-richness, as richness of words is also used with other meanings, see, e. g., [19,45].…”
Section: Universalitymentioning
confidence: 99%
“…The concept of subsequences is employed in many different areas of computer science. Subsequences appear in areas of theoretical computer science such as, for instance, in formal languages and logics (e. g., where they are used in relation to piecewise testable languages [54,55,35,36,37], or to define the subword order and downward closures [31,41,40,60]) or in combinatorics on words, where they are used to define the notions of binomial equivalence and binomial complexity, or to introduce the notion of subword histories, [49,23,43,42,51,47,50]; however, subsequences are also used in more applied settings, e. g., for modelling concurrency [48,52,13], or in database theory (especially event stream processing [5,30,61]). Moreover, many classical algorithmic problems are based on subsequences, e. g., longest common subsequence [6] or shortest common supersequence [46], and, in particular, such problems have recently regained interest in the context of fine-grained complexity (see [11,12,1,2]).…”
Section: Introductionmentioning
confidence: 99%
“…Subsequences are also a heavily investigated topic in the area of word combinatorics, string algorithms, and combinatorial pattern matching, and are connected to other areas of computer science (see, e.g., in the Chapter Subwords by J. Sakarovitch and I. Simon of the standard textbook [123] or the survey [107] and the references therein). In theoretical computer science, one can often encounter subsequences and their generalizations; for instance, in logic of automata theory, subsequences are used in the context of piecewise testability [156,157], in particular, to the height of piecewise testable languages [94,95,96], subword order [84,113,112], or downward closures [167]. In combinatorics on words, many concepts were developed around the idea of counting the occurrences of particular subsequences of a word, such as the k-binomial equivalence [144,68,119,117], subword histories [153], and Parikh matrices [130,146].…”
Section: Word Equationsmentioning
confidence: 99%
“…Two strings w 1 and w 2 are k-Simon congruent (w 1 ∼ k w 2 ), iff S k (w 1 ) = S k (w 2 ). Simon's congruence, which was originally introduced to study piecewise testable events, is now established in the study of piecewise testable languages, a special class of regular languages with applications in learning theory, databases theory, or linguistics (see, e.g., [96] and the references therein). More information and a broad overview of the work of Imre Simon can be found in the two survey papers [140,141] Next to many interesting combinatorial properties, Simon's congruence is a string similarity measure.…”
Section: Word Equationsmentioning
confidence: 99%
See 1 more Smart Citation