Largest common prefix of a regular tree language

2021 ◽  
Vol 115 ◽  
pp. 235-245
Author(s):  
Markus Lohrey ◽  
Sebastian Maneth
Keyword(s):  
Tree Language ◽  
Regular Tree ◽  
Common Prefix

PROPERTIES OF QUASI-RELABELING TREE BIMORPHISMS

2010 ◽  
Vol 21 (03) ◽  
pp. 257-276 ◽  
Author(s):  
ANDREAS MALETTI ◽  
CĂTĂLIN IONUŢ TÎRNĂUCĂ
Keyword(s):  
Cartesian Product ◽  
Canonical Representation ◽  
Finite Union ◽  
Top Down ◽  
Tree Language ◽  
Regular Tree ◽  
Fundamental Properties ◽  
Tree Transducers ◽  
Tree Languages ◽  
Context Free

The fundamental properties of the class QUASI of quasi-relabeling relations are investigated. A quasi-relabeling relation is a tree relation that is defined by a tree bimorphism (φ, L, ψ), where φ and ψ are quasi-relabeling tree homomorphisms and L is a regular tree language. Such relations admit a canonical representation, which immediately also yields that QUASI is closed under finite union. However, QUASI is not closed under intersection and complement. In addition, many standard relations on trees (e.g., branches, subtrees, v-product, v-quotient, and f-top-catenation) are not quasi-relabeling relations. If quasi-relabeling relations are considered as string relations (by taking the yields of the trees), then every Cartesian product of two context-free string languages is a quasi-relabeling relation. Finally, the connections between quasi-relabeling relations, alphabetic relations, and classes of tree relations defined by several types of top-down tree transducers are presented. These connections yield that quasi-relabeling relations preserve the regular and algebraic tree languages.

State Complexity of Regular Tree Languages for Tree Matching

2016 ◽  
Vol 27 (08) ◽  
pp. 965-979
Author(s):  
Sang-Ki Ko ◽  
Ha-Rim Lee ◽  
Yo-Sub Han
Keyword(s):  
The State ◽  
Top Down ◽  
Matching Problem ◽  
Tree Language ◽  
State Complexity ◽  
Regular Tree ◽  
Language L ◽  
Different Types ◽  
Tree Languages

We study the state complexity of regular tree languages for tree matching problem. Given a tree t and a set of pattern trees L, we can decide whether or not there exists a subtree occurrence of trees in L from the tree t by considering the new language L′ which accepts all trees containing trees in L as subtrees. We consider the case when we are given a set of pattern trees as a regular tree language and investigate the state complexity. Based on the sequential and parallel tree concatenation, we define three types of tree languages for deciding the existence of different types of subtree occurrences. We also study the deterministic top-down state complexity of path-closed languages for the same problem.

Operational State Complexity of Subtree-Free Regular Tree Languages

2016 ◽  
Vol 27 (06) ◽  
pp. 705-724
Author(s):  
Sang-Ki Ko ◽  
Hae-Sung Eom ◽  
Yo-Sub Han
Keyword(s):  
The State ◽  
Tree Automaton ◽  
Top Down ◽  
Tree Language ◽  
Worst Case ◽  
Bottom Up ◽  
State Complexity ◽  
Regular Tree ◽  
Tree Languages

We introduce subtree-free regular tree languages that are closely related to XML schemas and investigate the state complexity of basic operations on subtree-free regular tree languages. The state complexity of an operation for regular tree languages is the number of states that are sufficient and necessary in the worst-case for the minimal deterministic ranked tree automaton that accepts the tree language obtained from the operation. We establish the precise state complexity of (sequential, parallel) concatenation, (bottom-up, top-down) star, intersection and union for subtree-free regular tree languages.

Regular Approximation of Weighted Linear Context-Free Tree Languages

2017 ◽  
Vol 28 (05) ◽  
pp. 523-542
Author(s):  
Markus Teichmann
Keyword(s):  
Tree Language ◽  
Regular Tree ◽  
Tree Grammar ◽  
Regular Approximation ◽  
Leibler Divergence ◽  
Tree Languages ◽  
Free Tree ◽  
Context Free

We show how to train a weighted regular tree grammar such that it best approximates a weighted linear context-free tree grammar concerning the Kullback–Leibler divergence between both grammars. Furthermore, we construct a regular tree grammar that approximates the tree language induced by a context-free tree grammar.

scholarly journals A Unified Framework to Compute over Tree Synchronized Grammars and Primal Grammars

2002 ◽  
Vol Vol. 5 ◽  
Author(s):  
Frédéric Saubion ◽  
Igor Stéphan
Keyword(s):  
Proof System ◽  
Unified Framework ◽  
Tree Language ◽  
Control Structures ◽  
Regular Tree ◽  
Unification Theory ◽  
Tree Languages ◽  
International Audience ◽  
Regular Sets ◽  
Specific Control

International audience Tree languages are powerful tools for the representation and schematization of infinite sets of terms for various purposes (unification theory, verification and specification ...). In order to extend the regular tree language framework, more complex formalisms have been developed. In this paper, we focus on Tree Synchronized Grammars and Primal Grammars which introduce specific control structures to represent non regular sets of terms. We propose a common unified framework in order to achieve the membership test for these particular languages. Thanks to a proof system, we provide a full operational framework, that allows us to transform tree grammars into Prolog programs (as it already exists for word grammars with DCG) whose goal is to recognize terms of the corresponding language.

scholarly journals ALGEBRAIC CHARACTERIZATION OF LOGICALLY DEFINED TREE LANGUAGES

2010 ◽  
Vol 20 (02) ◽  
pp. 195-239 ◽  
Author(s):  
ZOLTÁN ÉSIK ◽  
PASCAL WEIL
Keyword(s):  
Algebraic Structure ◽  
Algebraic Characterization ◽  
Tree Language ◽  
Regular Tree ◽  
First Order ◽  
Product Operation ◽  
Finite Word ◽  
Tree Languages ◽  
Block Product

We give an algebraic characterization of the tree languages that are defined by logical formulas using certain Lindström quantifiers. An important instance of our result concerns first-order definable tree languages. Our characterization relies on the usage of preclones, an algebraic structure introduced by the authors in a previous paper, and of the block product operation on preclones. Our results generalize analogous results on finite word languages, but it must be noted that, as they stand, they do not yield an algorithm to decide whether a given regular tree language is first-order definable.

An Efficient Tool for Searching Maximal and Super Maximal Repeats in Large DNA/Protein Sequences via Induced-Enhanced Suffix Array

2019 ◽  
Vol 12 (2) ◽  
pp. 128-134
Author(s):  
Sanjeev Kumar ◽  
Suneeta Agarwal ◽  
Ranvijay
Keyword(s):  
Protein Sequences ◽  
Input Sequence ◽  
Suffix Array ◽  
Secondary Memory ◽  
Time And Space ◽  
Efficient Tool ◽  
Frequency Distributions ◽  
Alignment Algorithms ◽  
Common Prefix ◽  
Art Works

Background: DNA and Protein sequences of an organism contain a variety of repeated structures of various types. These repeated structures play an important role in Molecular biology as they are related to genetic backgrounds of inherited diseases. They also serve as a marker for DNA mapping and DNA fingerprinting. Efficient searching of maximal and super maximal repeats in DNA/Protein sequences can lead to many other applications in the area of genomics. Moreover, these repeats can also be used for identification of critical diseases by finding the similarity between frequency distributions of repeats in viruses and genomes (without using alignment algorithms). Objective: The study aims to develop an efficient tool for searching maximal and super maximal repeats in large DNA/Protein sequences. Methods: The proposed tool uses a newly introduced data structure Induced Enhanced Suffix Array (IESA). IESA is an extension of enhanced suffix array. It uses induced suffix array instead of classical suffix array. IESA consists of Induced Suffix Array (ISA) and an additional array-Longest Common Prefix (LCP) array. ISA is an array of all sorted suffixes of the input sequence while LCP array stores the lengths of the longest common prefixes between all pairs of consecutive suffixes in an induced suffix array. IESA is known to be efficient w.r.t. both time and space. It facilitates the use of secondary memory for constructing the large suffix-array. Results: An open source standalone tool named MSR-IESA for searching maximal and super maximal repeats in DNA/Protein sequences is provided at https://github.com/sanjeevalg/MSRIESA. Experimental results show that the proposed algorithm outperforms other state of the art works w.r.t. to both time and space. Conclusion: The proposed tool MSR-IESA is remarkably efficient for the analysis of DNA/Protein sequences, having maximal and super maximal repeats of any length. It can be used for identification of well-known diseases.

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