Thesis, and Concatenation (∙), Alternation (+), and Kleene Star (*) Operators
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Implementation of Recursively Enumerable Languages Using Universal Turing Machine in JFLAP
International Journal of Information and Computation Technology. ISSN 0974-2239 Volume 4, Number 1 (2014), pp. 79-84 © International Research Publications House http://www. irphouse.com /ijict.htm Implementation of Recursively Enumerable Languages using Universal Turing Machine in JFLAP Ankur Singh1 and Jainendra Singh2 1Department of Computer Science, IEC College of Engineering, Greater Noida, INDIA. 2 Department of Computer Science, Maharaja Surajmal Institute, C-4, Janakpuri, New Delhi, INDIA. Abstract This paper presents the implementation of recursively enumerable language using Universal Turing machine for JFLAP platform. Automata play a major role in compiler design and parsing. The class of formal languages that work for the most complex problems belongs to the set of Recursively Enumerable Language (REL).RELs are accepted by the type of automata as Turing Machine. Turing Machines are the most powerful computational machines and are the theoretical basis for modern computers. Turing Machine works for all classes of languages including regular language, Context Free Languages as well as Recursive Enumerable Languages. Still it is a tedious task to create and maintain Turing Machines for all problems. The Universal Turing Machine (UTM) is a solution to this problem. A UTM simulates any other TM, thus providing a single model and solution for all the computational problems. Universal Turing Machine is used to implementation of RELs for JFLAP platform. JFLAP is most successful and widely used tool for visualizing and simulating all types of automata. Keywords: Automata; Compiler; Turing Machine; TM; JFLAP; PDA. 1. Introduction An automaton is a mathematical model for a finite state machine (FSM). A FSM is a machine that has a set of input symbols and transitions and jumps through a series of states according to a transition function. -
The Earley Algorithm Is to Avoid This, by Only Building Constituents That Are Compatible with the Input Read So Far
Earley Parsing Informatics 2A: Lecture 21 Shay Cohen 3 November 2017 1 / 31 1 The CYK chart as a graph What's wrong with CYK Adding Prediction to the Chart 2 The Earley Parsing Algorithm The Predictor Operator The Scanner Operator The Completer Operator Earley parsing: example Comparing Earley and CYK 2 / 31 We would have to split a given span into all possible subspans according to the length of the RHS. What is the complexity of such algorithm? Still O(n2) charts, but now it takes O(nk−1) time to process each cell, where k is the maximal length of an RHS. Therefore: O(nk+1). For CYK, k = 2. Can we do better than that? Note about CYK The CYK algorithm parses input strings in Chomsky normal form. Can you see how to change it to an algorithm with an arbitrary RHS length (of only nonterminals)? 3 / 31 Still O(n2) charts, but now it takes O(nk−1) time to process each cell, where k is the maximal length of an RHS. Therefore: O(nk+1). For CYK, k = 2. Can we do better than that? Note about CYK The CYK algorithm parses input strings in Chomsky normal form. Can you see how to change it to an algorithm with an arbitrary RHS length (of only nonterminals)? We would have to split a given span into all possible subspans according to the length of the RHS. What is the complexity of such algorithm? 3 / 31 Note about CYK The CYK algorithm parses input strings in Chomsky normal form. -
LATE Ain't Earley: a Faster Parallel Earley Parser
LATE Ain’T Earley: A Faster Parallel Earley Parser Peter Ahrens John Feser Joseph Hui [email protected] [email protected] [email protected] July 18, 2018 Abstract We present the LATE algorithm, an asynchronous variant of the Earley algorithm for pars- ing context-free grammars. The Earley algorithm is naturally task-based, but is difficult to parallelize because of dependencies between the tasks. We present the LATE algorithm, which uses additional data structures to maintain information about the state of the parse so that work items may be processed in any order. This property allows the LATE algorithm to be sped up using task parallelism. We show that the LATE algorithm can achieve a 120x speedup over the Earley algorithm on a natural language task. 1 Introduction Improvements in the efficiency of parsers for context-free grammars (CFGs) have the potential to speed up applications in software development, computational linguistics, and human-computer interaction. The Earley parser has an asymptotic complexity that scales with the complexity of the CFG, a unique, desirable trait among parsers for arbitrary CFGs. However, while the more commonly used Cocke-Younger-Kasami (CYK) [2, 5, 12] parser has been successfully parallelized [1, 7], the Earley algorithm has seen relatively few attempts at parallelization. Our research objectives were to understand when there exists parallelism in the Earley algorithm, and to explore methods for exploiting this parallelism. We first tried to naively parallelize the Earley algorithm by processing the Earley items in each Earley set in parallel. We found that this approach does not produce any speedup, because the dependencies between Earley items force much of the work to be performed sequentially. -
JFLAP – an Interactive Formal Languages and Automata Package
JFLAP – An Interactive Formal Languages and Automata Package Susan H. Rodger Thomas W. Finley Duke University Cornell University October 18, 2005 ii To Thomas, Erich, and Markus — S. H. Rodger KYHDKIKINKOIIAGKTIYKD BLGKLGFAROADGINIRJREL MRJHKDIARARATALYMFTKY DRNERKTMATSKHWGOBBKRY RDUNDFFKCKALAAKBUTCIO MIOIAJSAIDMJEWRYRKOKF WFYUSCIYETEGAUDNMULWG NFUCRYJJTYNYHTEOJHMAM NUEWNCCTHKTYMGFDEEFUN AULWSBTYMUAIYKHONJNHJ TRRLLYEMNHBGTRTDGBCMS RYHKTGAIERFYABNCRFCLJ NLFFNKAULONGYTMBYLWLU SRAUEEYWELKCSIBMOUKDW MEHOHUGNIGNEMNLKKHMEH CNUSCNEYNIIOMANWGAWNI MTAUMKAREUSHMTSAWRSNW EWJRWFEEEBAOKGOAEEWAN FHJDWKLAUMEIAOMGIEGBH IEUSNWHISDADCOGTDRWTB WFCSCDOINCNOELTEIUBGL — T. W. Finley Contents Preface ix JFLAP Startup xiv 1 Finite Automata 1 1.1 A Simple Finite Automaton . 1 1.1.1 Create States . 2 1.1.2 Define the Initial State and the Final State . 2 1.1.3 Creating Transitions . 2 1.1.4 Deleting States and Transitions . 3 1.1.5 Attribute Editor Tool . 3 1.2 Simulation of Input . 5 1.2.1 Stepping Simulation . 5 1.2.2 Fast Simulation . 7 1.2.3 Multiple Simulation . 8 1.3 Nondeterminism . 9 1.3.1 Creating Nondeterministic Finite Automata . 9 1.3.2 Simulation . 10 1.4 Simple Analysis Operators . 12 1.4.1 Compare Equivalence . 13 1.4.2 Highlight Nondeterminism . 13 1.4.3 Highlight λ-Transitions . 13 1.5 Alternative Multiple Character Transitions∗ ....................... 13 1.6 Definition of FA in JFLAP . 14 1.7 Summary . 15 1.8 Exercises . 15 2 NFA to DFA to Minimal DFA 19 2.1 NFA to DFA . 19 iii iv CONTENTS 2.1.1 Idea for the Conversion . 19 2.1.2 Conversion Example . 20 2.1.3 Algorithm to Convert NFA M to DFA M 0 .................... 22 2.2 DFA to Minimal DFA . 23 2.2.1 Idea for the Conversion . 23 2.2.2 Conversion Example . -
Lecture 10: CYK and Earley Parsers Alvin Cheung Building Parse Trees Maaz Ahmad CYK and Earley Algorithms Talia Ringer More Disambiguation
Hack Your Language! CSE401 Winter 2016 Introduction to Compiler Construction Ras Bodik Lecture 10: CYK and Earley Parsers Alvin Cheung Building Parse Trees Maaz Ahmad CYK and Earley algorithms Talia Ringer More Disambiguation Ben Tebbs 1 Announcements • HW3 due Sunday • Project proposals due tonight – No late days • Review session this Sunday 6-7pm EEB 115 2 Outline • Last time we saw how to construct AST from parse tree • We will now discuss algorithms for generating parse trees from input strings 3 Today CYK parser builds the parse tree bottom up More Disambiguation Forcing the parser to select the desired parse tree Earley parser solves CYK’s inefficiency 4 CYK parser Parser Motivation • Given a grammar G and an input string s, we need an algorithm to: – Decide whether s is in L(G) – If so, generate a parse tree for s • We will see two algorithms for doing this today – Many others are available – Each with different tradeoffs in time and space 6 CYK Algorithm • Parsing algorithm for context-free grammars • Invented by John Cocke, Daniel Younger, and Tadao Kasami • Basic idea given string s with n tokens: 1. Find production rules that cover 1 token in s 2. Use 1. to find rules that cover 2 tokens in s 3. Use 2. to find rules that cover 3 tokens in s 4. … N. Use N-1. to find rules that cover n tokens in s. If succeeds then s is in L(G), else it is not 7 A graphical way to visualize CYK Initial graph: the input (terminals) Repeat: add non-terminal edges until no more can be added. -
Animating the Conversion of Nondeterministic Finite State
ANIMATING THE CONVERSION OF NONDETERMINISTIC FINITE STATE AUTOMATA TO DETERMINISTIC FINITE STATE AUTOMATA by William Patrick Merryman A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Computer Science MONTANA STATE UNIVERSITY Bozeman, Montana January 2007 ©COPYRIGHT by William Patrick Merryman 2007 All Rights Reserved ii APPROVAL of a thesis submitted by William Patrick Merryman This thesis has been read by each member of the thesis committee and has been found to be satisfactory regarding content, English usage, format, citations, bibliographic content, and consistency, and is ready for submission to the Division of Graduate Education. Dr. Rockford Ross Approved for the Department of Computer Science Dr. Michael Oudshoorn Approved for the Division of Graduate Education Dr. Carl A. Fox iii STATEMENT OF PERMISSION TO USE In presenting this thesis in partial fulfillment of the requirements for a Master’s degree at Montana State University, I agree that the Library shall make it available to borrowers under rules of the Library. If I have indicated my intention to copyright this thesis by including a copyright notice page, copying is allowable only for scholarly purposes, consistent with “fair use” as prescribed in the U.S. Copyright Law. Requests for permission for extended quotation from or reproduction of this thesis in whole or in parts may be granted only by the copyright holder. William Patrick Merryman January, 2007 iv TABLE OF CONTENTS 1. INTRODUCTION ........................................................................................ -
A Mobile App for Teaching Formal Languages and Automata
Received: 21 December 2017 | Accepted: 19 March 2018 DOI: 10.1002/cae.21944 SPECIAL ISSUE ARTICLE A mobile app for teaching formal languages and automata Carlos H. Pereira | Ricardo Terra Department of Computer Science, Federal University of Lavras, Lavras, Brazil Abstract Formal Languages and Automata (FLA) address mathematical models able to Correspondence Ricardo Terra, Department of Computer specify and recognize languages, their properties and characteristics. Although Science, Federal University of Lavras, solid knowledge of FLA is extremely important for a B.Sc. degree in Computer Postal Code 3037, Lavras, Brazil. Science and similar fields, the algorithms and techniques covered in the course Email: [email protected] are complex and difficult to assimilate. Therefore, this article presents FLApp, Funding information a mobile application—which we consider the new way to reach students—for FAPEMIG (Fundação de Amparo à teaching FLA. The application—developed for mobile phones and tablets Pesquisa do Estado de Minas Gerais) running Android—provides students not only with answers to problems involving Regular, Context-free, Context-Sensitive, and Recursively Enumer- able Languages, but also an Educational environment that describes and illustrates each step of the algorithms to support students in the learning process. KEYWORDS automata, education, formal languages, mobile application 1 | INTRODUCTION In this article, we present FLApp (Formal Languages and Automata Application), a mobile application for teaching FLA Formal Languages and Automata (FLA) is an important area that helps students by solving problems involving Regular, of Computer Science that approaches mathematical models Context-free, Context-Sensitive, and Recursively Enumerable able to specify and recognize languages, their properties and Languages (levels 3 to 0, respectively), in addition to create an characteristics [14]. -
An Earley Parsing Algorithm for Range Concatenation Grammars
An Earley Parsing Algorithm for Range Concatenation Grammars Laura Kallmeyer Wolfgang Maier Yannick Parmentier SFB 441 SFB 441 CNRS - LORIA Universitat¨ Tubingen¨ Universitat¨ Tubingen¨ Nancy Universite´ 72074 Tubingen,¨ Germany 72074 Tubingen,¨ Germany 54506 Vandœuvre, France [email protected] [email protected] [email protected] Abstract class of LCFRS has received more attention con- cerning parsing (Villemonte de la Clergerie, 2002; We present a CYK and an Earley-style Burden and Ljunglof,¨ 2005). This article proposes algorithm for parsing Range Concatena- new CYK and Earley parsers for RCG, formulat- tion Grammar (RCG), using the deduc- ing them in the framework of parsing as deduction tive parsing framework. The characteris- (Shieber et al., 1995). The second section intro- tic property of the Earley parser is that we duces necessary definitions. Section 3 presents a use a technique of range boundary con- CYK-style algorithm and Section 4 extends this straint propagation to compute the yields with an Earley-style prediction. of non-terminals as late as possible. Ex- periments show that, compared to previ- 2 Preliminaries ous approaches, the constraint propagation The rules (clauses) of RCGs1 rewrite predicates helps to considerably decrease the number ranging over parts of the input by other predicates. of items in the chart. E.g., a clause S(aXb) S(X) signifies that S is → 1 Introduction true for a part of the input if this part starts with an a, ends with a b, and if, furthermore, S is also true RCGs (Boullier, 2000) have recently received a for the part between a and b. -
Principles and Implementation of Deductive Parsing
Principles and implementation of deductive parsing The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Stuart M. Shieber, Yves Schabes, and Fernando C. N. Pereira. Principles and implementation of deductive parsing. Journal of Logic Programming, 24(1-2):3-36, July-August 1995. Also available as cmp-lg/9404008. Published Version http://dx.doi.org/10.1016/0743-1066(95)00035-I Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:2031716 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA J. LOGIC PROGRAMMING 1995:24(1{2):3{36 3 PRINCIPLES AND IMPLEMENTATION OF DEDUCTIVE PARSING STUART M. SHIEBER, YVES SCHABES, ∗ AND FERNANDO C. N. PEREIRAy £ We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such de- duction systems so as to implement the corresponding parser. The method generalizes easily to parsers for augmented phrase structure formalisms, such as definite-clause grammars and other logic grammar formalisms, and has been used for rapid prototyping of parsing algorithms for a variety of formalisms including variants of tree-adjoining grammars, categorial gram- mars, and lexicalized context-free grammars. ¡ 1. INTRODUCTION Parsing can be viewed as a deductive process that seeks to prove claims about the grammatical status of a string from assumptions describing the grammatical properties of the string's elements and the linear order between them. -
Using Jflap in Academics to Understand Automata Theory in a Better Way
International Journal of Advances in Electronics and Computer Science, ISSN: 2393-2835 Volume-5, Issue-5, May.-2018 http://iraj.in USING JFLAP IN ACADEMICS TO UNDERSTAND AUTOMATA THEORY IN A BETTER WAY KAVITA TEWANI Assistant Professor, Institute of Technology, Nirma University E-mail: [email protected] Abstract - As it is been observed that the things get much easier once we visualize it and hence this paper is just a step towards it. Usually many subjects in computer engineering curriculum like algorithms, data structures, and theory of computation are taught theoretically however it lacks the visualization that may help students to understand the concepts in a better way. The paper shows some of the practices on tool called JFLAP (Java Formal Languages and Automata Package) and the statistics on how it affected the students to learn the concepts easily. The diagrammatic representation is used to help the theory mentioned. Keywords - Automata, JFLAP, Grammar, Chomsky Heirarchy , Turing Machine, DFA, NFA I. INTRODUCTION visualization and interaction in the course is enhanced through the popular software tools[6,7]. The proper The theory of computation is a basic course in use of JFLAP and instructions are provided in the computer engineering discipline. It is the subject manual “JFLAP activities for Formal Languages and which is been taught theoretically and hands-on Automata” by Peter Linz and Susan Rodger. It problems are given to the students to enhance the includes the theoretical approach and their understanding but it lacks the programming implementation in JFLAP. [10] assignment. However the subject is the base for creation of compilers and therefore should be given III. -
Analysis of Cocke-Younger-Kasami and Earley Algorithms on Probabilistic Context-Free Grammar
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 10 | Oct 2019 www.irjet.net p-ISSN: 2395-0072 Analysis of Cocke-Younger-Kasami and Earley Algorithms on Probabilistic Context-Free Grammar Palash Anjania1, Shrushti Gangar2, Krina Bhimani3, Lynette D’mello4 1,2,3Student, Dept. of Computer Engineering, Dwarkadas J. Sanghvi College, Maharashtra India 4Lynette D’Mello, Professor, Dept. of Computer Engineering, Dwarkadas J. Sanghvi College, Maharashtra India ---------------------------------------------------------------------***---------------------------------------------------------------------- Abstract - Programming parsers are generally based on 2. LITERATURE REVIEW context-free grammar. The study of such grammars are of great importance around the world, out of which the CYK 2.1. CYK Algorithm and the Earley are the well-known algorithms. In this paper, we have done a comparative study on the above 2.1.1 Introduction: Cocke-Younger-Kasami algorithm two algorithms. We applied these algorithms on also known CYK or CKY algorithm is a membership probabilistic context-free grammar (PCFG) and tried to algorithm which works only on context-free grammar in analyses their results and obtained their time Chomsky Normal form (CNF). It is a Bottom-Up Dynamic complexities. The results obtained show that the Earley programming approach and is more data driven. algorithm have proved to be better than the CYK Probabilistic CYK recovers the most probable parse algorithm. given the probabilities of all productions and used to decide whether the string belongs to the grammar or Key Words: Cocke-Younger-Kasami algorithm, Earley not. In Context-free Grammar the right-hand side of each algorithm, Probabilistic Context-free grammar, production can have either one terminal or two non- terminals. -
Syntactic Parsing: Introduction, CYK Algorithm
Introduction Syntax Context-Free Grammars CYK Algorithm Syntactic Parsing: Introduction, CYK Algorithm M. Rajman & J.-C. Chappelier Laboratoire d’Intelligence Artificielle Faculté I&C ©EPFL M. Rajman & J.-C. Chappelier Syntactic parsing: Introduction & CYK Algorithm – 1 / 47 Introduction Syntax Objectives of this lecture Context-Free Grammars CYK Algorithm ¯ Introduce syntactic level of NLP ¯ Present its two components: formal grammars and parsing algorithms Contents: I Introduction I Formal Grammars I Context-Free Grammars I CYK Algorithm ©EPFL M. Rajman & J.-C. Chappelier Syntactic parsing: Introduction & CYK Algorithm – 2 / 47 Introduction Syntax Syntactic level Syntactic level and Parsing Syntactic acceptability Formalisms Context-Free Analysis of the sentence structure Grammars CYK Algorithm i.e. "grammatical" analysis (in the linguistic sense) Automatic natural language processing requires formal grammars (ressource) and parsing algorithms Two separated/complementary aspects: procedural declarative generic algorithms data parsing algorithm formal grammar ©EPFL M. Rajman & J.-C. Chappelier Syntactic parsing: Introduction & CYK Algorithm – 3 / 47 Introduction Syntax Parsing Syntactic level and Parsing Syntactic acceptability Formalisms Context-Free Grammars Parsing can be seen as: CYK Algorithm I RECOGNIZING a sequence of words ¯ Is a given sentence correct or not? or as I ANALYZING a sequence of words ¯ For a syntactically correct sentence, give the set of all its possible interpretations (i.e. associated structures). (Returns the