Journal ArticleDOI
Lower bounds for context-free grammars
Reads0
Chats0
TLDR
Ellul, Krawetz, Shallit and Wang prove an exponential lower bound on the size of any context-free grammar generating the language of all permutations over some alphabet, and obtain exponential lower bounds for many other languages.About:
This article is published in Information Processing Letters.The article was published on 2011-09-01. It has received 19 citations till now. The article focuses on the topics: Context-sensitive grammar & Upper and lower bounds.read more
Citations
More filters
Journal ArticleDOI
On the Complexity of the Smallest Grammar Problem over Fixed Alphabets
TL;DR: It is shown that the smallest grammar problem remains N P -complete (and its optimisation version is A P X -hard), even if the alphabet is fixed and has size of at least 17, and an O ( 3 ∣ w ∣ ) exact exponential-time algorithm is presented, based on dynamic programming.
Book ChapterDOI
On Minimal Grammar Problems for Finite Languages
TL;DR: It is shown that the language of all cubes of a given length requires an exponential number of context-free productions and the upper and lower bounds on the complexity of the operations union and concatenation for finite languages are investigated.
Proceedings ArticleDOI
Notes on counting with finite machines
TL;DR: The descriptional complexity of recognizing languages {1^n} and {1^{t n} : t = 0, 1, 2, ...} with state-based finite machines of various kinds is determined.
Journal ArticleDOI
Developing a policy management algorithm for ship provision: a Delphi Technique Integrated with Hesitant Fuzzy Set (DTIHFS) approach
TL;DR: A policy management algorithm framework integrating the Delphi Technique and the Hesitant Fuzzy Set approach was established and it was found that it would be possible to reduce daily provision cost per crew from $10.36 to $8.24 and from $16.16 to $11.64 within 453 and 470 days for given ships.
Book ChapterDOI
A Language-Theoretic View on Network Protocols
TL;DR: The first line of defense against malformed or malicious inputs as mentioned in this paper is to ensure that the validator (which is often part of the parser) is free of bugs in the parser.
References
More filters
Journal ArticleDOI
The smallest grammar problem
TL;DR: This paper shows that every efficient algorithm for the smallest grammar problem has approximation ratio at least 8569/8568 unless P=NP, and bound approximation ratios for several of the best known grammar-based compression algorithms, including LZ78, B ISECTION, SEQUENTIAL, LONGEST MATCH, GREEDY, and RE-PAIR.
Proceedings Article
Regular expressions: new results and open problems
TL;DR: In this paper, the authors sketch some new results and discuss what remains to be solved about regular expressions' descriptive capabilities. But they do not discuss the specific problems that arise when using regular expressions.
Regular Expressions: New Results and Open Problems.
TL;DR: Regular expressions have been studied for nearly 50 years, yet many intriguing problems about their descriptive capabilities remain open and some new results are sketches.
Journal ArticleDOI
Complexity of normal form grammars
TL;DR: Greibach normal form Grammars and position restricted grammars will be investigated from the point of view of descriptional complexity of context-free languages.
Journal ArticleDOI
Generating all permutations by context-free grammars in Chomsky normal form
TL;DR: In this paper, the authors consider context-free grammars in the normal form that generate a finite language of all n! strings that are permutations of n different symbols (n ≥ 1).