scholarly journals Grammatical compression: compressed equivalence and other problems

2010 ◽  
Vol Vol. 12 no. 4 ◽  
Author(s):  
Alberto Bertoni ◽  
Roberto Radicioni
Keyword(s):  
Strategic Games ◽  
Special Issue ◽  
Ability To Work ◽  
Inclusion Problems ◽  
Polynomial Time Algorithms ◽  
Straight Line ◽  
International Audience ◽  
Context Free ◽  
Compressed Data ◽  
Straight Line Programs

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications International audience In this work, we focus our attention to algorithmic solutions for problems where the instances are presented as straight-line programs on a given algebra. In our exposition, we try to survey general results by presenting some meaningful examples; moreover, where possible, we outline the proofs in order to give an insight of the methods and the techniques. We recall some recent results for the problem PosSLP, consisting of deciding if the integer defined by a straight-line program on the ring Z is greater than zero; we discuss some implications in the areas of numerical analysis and strategic games. Furthermore, we propose some methods for reducing Compressed Word Problem from an algebra to another; reductions from trace monoids to the semiring of nonnegative integers are exhibited and polynomial time algorithms for compressed equivalence in monoids related to Dyck reductions are shown. Finally, we consider inclusion problems for context-free languages, proving how in some cases efficient algorithms for these problems benefit from the ability to work with compressed data.

scholarly journals Balancing Straight-line Programs

2021 ◽  
Vol 68 (4) ◽  
pp. 1-40
Author(s):  
Moses Ganardi ◽  
Artur Jeż ◽  
Markus Lohrey
Keyword(s):  
Linear Time ◽  
Base Property ◽  
Context Free Grammar ◽  
Tree Compression ◽  
Straight Line ◽  
Finite Base ◽  
Single String ◽  
The Cost ◽  
Context Free ◽  
Straight Line Programs

We show that a context-free grammar of size that produces a single string of length (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for of size , whose unique derivation tree has depth . This solves an open problem in the area of grammar-based compression, improves many results in this area, and greatly simplifies many existing constructions. Similar results are shown for two formalisms for grammar-based tree compression: top dags and forest straight-line programs. These balancing results can be all deduced from a single meta-theorem stating that the depth of an algebraic circuit over an algebra with a certain finite base property can be reduced to with the cost of a constant multiplicative size increase. Here, refers to the size of the unfolding (or unravelling) of the circuit. In particular, this results applies to standard arithmetic circuits over (noncommutative) semirings.

scholarly journals COMPRESSED MEMBERSHIP PROBLEMS FOR REGULAR EXPRESSIONS AND HIERARCHICAL AUTOMATA

2010 ◽  
Vol 21 (05) ◽  
pp. 817-841 ◽  
Author(s):  
MARKUS LOHREY
Keyword(s):  
Open Problem ◽  
Regular Languages ◽  
Regular Expressions ◽  
Membership Problem ◽  
Complexity Bounds ◽  
Straight Line ◽  
Membership Problems ◽  
Context Free ◽  
Straight Line Programs ◽  
Extended Regular Expressions

Membership problems for compressed strings in regular languages are investigated. Strings are represented by straight-line programs, i.e., context-free grammars that generate exactly one string. For the representation of regular languages, various formalisms with different degrees of succinctness (e.g., suitably extended regular expressions, hierarchical automata) are considered. Precise complexity bounds are derived. Among other results, it is shown that the compressed membership problem for regular expressions with intersection is PSPACE-complete. This solves an open problem of Plandowski and Rytter.

scholarly journals A NEW LINEAR GENETIC PROGRAMMING APPROACH BASED ON STRAIGHT LINE PROGRAMS: SOME THEORETICAL AND EXPERIMENTAL ASPECTS

2009 ◽  
Vol 18 (05) ◽  
pp. 757-781 ◽  
Author(s):  
CÉSAR L. ALONSO ◽  
JOSÉ LUIS MONTAÑA ◽  
JORGE PUENTE ◽  
CRUZ ENRIQUE BORGES
Keyword(s):  
Data Structure ◽  
Genetic Programming ◽  
Computer Programs ◽  
Symbolic Regression ◽  
Programming Approach ◽  
Linear Genetic Programming ◽  
Straight Line ◽  
Structured Representations ◽  
Regression Problems ◽  
Straight Line Programs

Tree encodings of programs are well known for their representative power and are used very often in Genetic Programming. In this paper we experiment with a new data structure, named straight line program (slp), to represent computer programs. The main features of this structure are described, new recombination operators for GP related to slp's are introduced and a study of the Vapnik-Chervonenkis dimension of families of slp's is done. Experiments have been performed on symbolic regression problems. Results are encouraging and suggest that the GP approach based on slp's consistently outperforms conventional GP based on tree structured representations.

On the average-case complexity of underdetermined functions

2018 ◽  
Vol 28 (4) ◽  
pp. 201-221
Author(s):  
Aleksandr V. Chashkin
Keyword(s):  
Boolean Functions ◽  
Correct Order ◽  
Average Case ◽  
Case Complexity ◽  
Average Case Complexity ◽  
Straight Line ◽  
Straight Line Programs

Abstract The average-case complexity of computation of underdetermined functions by straight-line programs with conditional stop over the basis of all at most two-place Boolean functions is considered. Correct order estimates of the average-case complexity of functions with maximum average-case complexity among all underdetermined functions are derived depending on the degree of their determinacy, the size of their domain, and the size of their support.

scholarly journals Special Issue on Visualisations in Historical Linguistics: Introduction

2020 ◽  
Vol Special issue on... ◽  
Author(s):  
Benjamin Molineaux ◽  
Bettelou Los ◽  
Martti Mäkinen
Keyword(s):  
Historical Linguistics ◽  
Data Visualisation ◽  
Complex Materials ◽  
Special Issue ◽  
The Core ◽  
Methodological Research ◽  
International Audience ◽  
Introductory Paper ◽  
The Individual ◽  
Historical Periods

International audience The advent of ever-larger and more diverse historical corpora for different historical periods and linguistic varieties has led to the impossibility of obtaining simple, direct-and yet balancedrepresentations of the core patterns in the data. In order to draw insights from heterogeneous and complex materials of this type, historical linguists have begun to reach for a growing number of data visualisation techniques, from the statistical, to the cartographical, the network-based and beyond. An exploration of the state of this art was the objective of a workshop at the 2018 International Conference on English Historical Linguistics, from whence most of the materials of this Special Issue are drawn. This brief introductory paper outlines the background and relevance of this line of methodological research and presents a summary of the individual papers that make up the collection.

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