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 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 Tunnel Parsing with counted repetitions

2020 ◽  
Vol 21 (4) ◽  
Author(s):  
Nikolay Handzhiyski ◽  
Elena Somova
Keyword(s):  
Efficient Algorithm ◽  
Time Complexity ◽  
Linear Time ◽  
Domain Specific Languages ◽  
Context Free Grammar ◽  
Syntax Tree ◽  
Domain Specific ◽  
Concrete Syntax ◽  
Parsing Algorithm ◽  
Context Free

The article describes a new and efficient algorithm for parsing, called Tunnel Parsing, that parses from left to right on the basis of a context-free grammar without left recursion and rules that recognize empty words. The algorithm is applicable mostly for domain-specific languages. In the article, particular attention is paid to the parsing of grammar element repetitions. As a result of the parsing, a statically typed concrete syntax tree is built from top to bottom, that accurately reflects the grammar. The parsing is not done through a recursion, but through an iteration. The Tunnel Parsing algorithm uses the grammars directly without a prior refactoring and is with a linear time complexity for deterministic context-free grammars.

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.

Framework for rare event detection using Artificial Neural Network based context free grammar

2020 ◽  
Vol 39 (6) ◽  
pp. 8463-8475
Author(s):  
Palanivel Srinivasan ◽  
Manivannan Doraipandian
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Event Detection ◽  
Performance Metrics ◽  
Rare Events ◽  
Rare Event ◽  
Video Stream ◽  
Context Free Grammar ◽  
Artificial Neural ◽  
Context Free

Rare event detections are performed using spatial domain and frequency domain-based procedures. Omnipresent surveillance camera footages are increasing exponentially due course the time. Monitoring all the events manually is an insignificant and more time-consuming process. Therefore, an automated rare event detection contrivance is required to make this process manageable. In this work, a Context-Free Grammar (CFG) is developed for detecting rare events from a video stream and Artificial Neural Network (ANN) is used to train CFG. A set of dedicated algorithms are used to perform frame split process, edge detection, background subtraction and convert the processed data into CFG. The developed CFG is converted into nodes and edges to form a graph. The graph is given to the input layer of an ANN to classify normal and rare event classes. Graph derived from CFG using input video stream is used to train ANN Further the performance of developed Artificial Neural Network Based Context-Free Grammar – Rare Event Detection (ACFG-RED) is compared with other existing techniques and performance metrics such as accuracy, precision, sensitivity, recall, average processing time and average processing power are used for performance estimation and analyzed. Better performance metrics values have been observed for the ANN-CFG model compared with other techniques. The developed model will provide a better solution in detecting rare events using video streams.

scholarly journals Searching for universal model of amyloid signaling motifs using probabilistic context-free grammars

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Witold Dyrka ◽  
Marlena Gąsior-Głogowska ◽  
Monika Szefczyk ◽  
Natalia Szulc
Keyword(s):  
Functional Relationship ◽  
High Sensitivity ◽  
Alternative Methods ◽  
Discriminative Power ◽  
Context Free Grammar ◽  
Protein Motifs ◽  
Functional Features ◽  
Universal Grammars ◽  
Context Free ◽  
Probabilistic Context

Abstract Background Amyloid signaling motifs are a class of protein motifs which share basic structural and functional features despite the lack of clear sequence homology. They are hard to detect in large sequence databases either with the alignment-based profile methods (due to short length and diversity) or with generic amyloid- and prion-finding tools (due to insufficient discriminative power). We propose to address the challenge with a machine learning grammatical model capable of generalizing over diverse collections of unaligned yet related motifs. Results First, we introduce and test improvements to our probabilistic context-free grammar framework for protein sequences that allow for inferring more sophisticated models achieving high sensitivity at low false positive rates. Then, we infer universal grammars for a collection of recently identified bacterial amyloid signaling motifs and demonstrate that the method is capable of generalizing by successfully searching for related motifs in fungi. The results are compared to available alternative methods. Finally, we conduct spectroscopy and staining analyses of selected peptides to verify their structural and functional relationship. Conclusions While the profile HMMs remain the method of choice for modeling homologous sets of sequences, PCFGs seem more suitable for building meta-family descriptors and extrapolating beyond the seed sample.

A generalization of the concept of a context-free grammar

Cybernetics ◽  
1974 ◽  
Vol 8 (3) ◽  
pp. 349-351
Author(s):  
A. A. Letichevskii
Keyword(s):  
Context Free Grammar ◽  
Context Free

scholarly journals Knowledge Sources for Constituent Parsing of German, a Morphologically Rich and Less-Configurational Language

2013 ◽  
Vol 39 (1) ◽  
pp. 57-85 ◽  
Author(s):  
Alexander Fraser ◽  
Helmut Schmid ◽  
Richárd Farkas ◽  
Renjing Wang ◽  
Hinrich Schütze
Keyword(s):  
State Of The Art ◽  
Lessons Learned ◽  
Knowledge Sources ◽  
Lexical Knowledge ◽  
Context Free Grammar ◽  
The Impact ◽  
Context Free ◽  
Probabilistic Context

We study constituent parsing of German, a morphologically rich and less-configurational language. We use a probabilistic context-free grammar treebank grammar that has been adapted to the morphologically rich properties of German by markovization and special features added to its productions. We evaluate the impact of adding lexical knowledge. Then we examine both monolingual and bilingual approaches to parse reranking. Our reranking parser is the new state of the art in constituency parsing of the TIGER Treebank. We perform an analysis, concluding with lessons learned, which apply to parsing other morphologically rich and less-configurational languages.

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.

WHEN CHURCH-ROSSER BECOMES CONTEXT FREE

2007 ◽  
Vol 18 (06) ◽  
pp. 1293-1302 ◽  
Author(s):  
MARTIN KUTRIB ◽  
ANDREAS MALCHER
Keyword(s):  
Linear Time ◽  
Membership Problem ◽  
Closure Properties ◽  
Context Free Language ◽  
Arithmetic Hierarchy ◽  
Context Free ◽  
Free Language

We investigate the intersection of Church-Rosser languages and (strongly) context-free languages. The intersection is still a proper superset of the deterministic context-free languages as well as of their reversals, while its membership problem is solvable in linear time. For the problem whether a given Church-Rosser or context-free language belongs to the intersection we show completeness for the second level of the arithmetic hierarchy. The equivalence of Church-Rosser and context-free languages is Π1-complete. It is proved that all considered intersections are pairwise incomparable. Finally, closure properties under several operations are investigated.

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