Lecture

CYK Algorithm for Parsing General Grammars

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In course

CS-320: Computer language processing

We teach the fundamental aspects of analyzing and interpreting computer languages, including the techniques to build compilers. You will build a working compiler from an elegant functional language into machine code using a popular backend called LLVM (htt ...

Description

This lecture covers Chomsky's classification of grammars, including type 0, type 1, type 2, and type 3 grammars. It explains the challenges of parsing general grammars, such as ambiguity and the need for dynamic programming. The instructor demonstrates the CYK algorithm for parsing general grammars, focusing on Chomsky Normal Form and the steps involved in the algorithm. The lecture also discusses balanced parentheses grammar and the conversion to Chomsky Normal Form. It concludes with the analysis of the number of parse trees for a given word and the importance of CNF in simplifying grammar rules.

Instructor

Viktor Kuncak

Viktor Kunčak joined EPFL in 2007, after receiving a PhD degree from MIT. Since then has been leading the Laboratory for Automated Reasoning and Analysis and supervised at least 12 completed PhD theses. His works on languages, algorithms and systems for verification and automated reasoning. He served as an initiator and one of the coordinators of a European network (COST action) in the area of automated reasoning, verification, and synthesis. In 2012 he received a 5-year single-investigator European Research Council (ERC) grant of 1.5M EUR. His invited talks include those at Lambda Days, Scala Days, NFM, LOPSTR, SYNT, ICALP, CSL, RV, VMCAI, and SMT. A paper on test generation he co-authored received an ACM SIGSOFT distinguished paper award at ICSE. A PLDI paper he co-authored was published in the Communications of the ACM as a Research Highlight article. His Google Scholar profile reports an over-approximate H-index of 38. He was an associate editor of ACM Transactions on Programming Languages and Systems (TOPLAS) and served as a co-chair of conferences on Computer-Aided Verification (CAV), Formal Methods in Computer Aided Design (FMCAD), Workshop on Synthesis (SYNT), and Verification, Model Checking, and Abstract Interpretation (VMCAI). At EPFL he teaches courses on functional and parallel programming, compilers, and verification. He has co-taught the MOOC "Parallel Programming" that was visited by over 100'000 learners and completed by thousands of students from all over the world.

Official source

Ontological neighbourhood

Computer engineering

Computer programming: Compilers

Related concepts (32)

Earley parser

In computer science, the Earley parser is an algorithm for parsing strings that belong to a given context-free language, though (depending on the variant) it may suffer problems with certain nullable grammars. The algorithm, named after its inventor, Jay Earley, is a chart parser that uses dynamic programming; it is mainly used for parsing in computational linguistics. It was first introduced in his dissertation in 1968 (and later appeared in an abbreviated, more legible, form in a journal).

Parsing

Parsing, syntax analysis, or syntactic analysis is the process of analyzing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar. The term parsing comes from Latin pars (orationis), meaning part (of speech). The term has slightly different meanings in different branches of linguistics and computer science. Traditional sentence parsing is often performed as a method of understanding the exact meaning of a sentence or word, sometimes with the aid of devices such as sentence diagrams.

Context-free language

In formal language theory, a context-free language (CFL) is a language generated by a context-free grammar (CFG). Context-free languages have many applications in programming languages, in particular, most arithmetic expressions are generated by context-free grammars. Different context-free grammars can generate the same context-free language. Intrinsic properties of the language can be distinguished from extrinsic properties of a particular grammar by comparing multiple grammars that describe the language.

Probabilistic context-free grammar

Grammar theory to model symbol strings originated from work in computational linguistics aiming to understand the structure of natural languages. Probabilistic context free grammars (PCFGs) have been applied in probabilistic modeling of RNA structures almost 40 years after they were introduced in computational linguistics. PCFGs extend context-free grammars similar to how hidden Markov models extend regular grammars. Each production is assigned a probability.

Top-down parsing

Top-down parsing in computer science is a parsing strategy where one first looks at the highest level of the parse tree and works down the parse tree by using the rewriting rules of a formal grammar. LL parsers are a type of parser that uses a top-down parsing strategy. Top-down parsing is a strategy of analyzing unknown data relationships by hypothesizing general parse tree structures and then considering whether the known fundamental structures are compatible with the hypothesis.

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Introduction to Grammars

Introduces automata, regular languages limitations, context-free grammars, and balanced parentheses grammars.

Context-Free Grammars: Part 1

Covers context-free grammars, production rules, automata, syntax analysis, and parsing techniques.

Object-Oriented Parser Combinators

Covers object-oriented parser combinators in Scala for building parsers, including JSON parsing and testing.

LL(1) Parsing

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Context-Free Grammars