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On the Complexity of Grammar-Based Compression over Fixed Alphabets

Katrin Casel, Henning Fernau, Serge Gaspers, Benjamin Gras, Markus L. Schmid, Marc Herbstritt
2016 International Colloquium on Automata, Languages and Programming  
the complexity of the shortest-grammar problem).  ...  It is shown that the shortest-grammar problem remains NP-complete if the alphabet is fixed and has a size of at least 24 (which settles an open question).  ...  122:13 this is possible, it seems that deeper combinatorial insights with respect to grammar-based compression are necessary.  ... 
doi:10.4230/lipics.icalp.2016.122 dblp:conf/icalp/CaselFGGS16 fatcat:g4g7dthkube2xkgnlw63stysjy

Page 716 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
The model is based on the novelty that errors can be expressed as strings over an alphabet of basic er- ror symbols.  ...  Summary: “We investigate a type of lossless source code called a grammar-based code, which, in response to any input data string x over a fixed finite alphabet, selects a context-free grammar G, representing  ... 

Universal lossless data compression with side information by using a conditional MPM grammar transform

En-Hui Yang, A. Kaltchenko, J.C. Kieffer
2001 IEEE Transactions on Information Theory  
Arithmetic Encoder In any grammar-based code, the original sequence is compressed indirectly by compressing the transformed grammar .  ...  Based on the CMPM grammar transform, a universal lossless data compression algorithm with side information is developed, which can achieve asymptotically the conditional entropy rate of any stationary,  ... 
doi:10.1109/18.945239 fatcat:pjlujgndwnes7mgvjfzsgq3wsi

Tree Automata and XPath on Compressed Trees [chapter]

Markus Lohrey, Sebastian Maneth
2006 Lecture Notes in Computer Science  
Finally, the complexity of the XPath evaluation problem on trees that are compressed via straight-line context-free tree grammars is investigated.  ...  The complexity of various membership problems for tree automata on compressed trees is analyzed.  ...  In this paper we investigate the computational complexity of algorithmic problems on compressed trees.  ... 
doi:10.1007/11605157_19 fatcat:gh5klilhfrel7cspgmwpk5psxq

Grammar-based codes: a new class of universal lossless source codes

J.C. Kieffer, En-Hui Yang
2000 IEEE Transactions on Information Theory  
We investigate a type of lossless source code called a grammar-based code, which, in response to any input data string over a fixed finite alphabet, selects a context-free grammar representing in the sense  ...  Lossless compression of takes place indirectly via compression of the production rules of the grammar .  ...  with respect to the family of finite-state information sources on a fixed finite alphabet.  ... 
doi:10.1109/18.841160 fatcat:omffhh552vgppjvo4rflne4svm

Algorithmics on SLP-compressed strings: A survey

Markus Lohrey
2012 Groups - Complexity - Cryptology  
Among others, we study pattern matching for compressed strings, membership problems for compressed strings in various kinds of formal languages, and the problem of querying compressed strings.  ...  A straight-line program is a context-free grammar that generates exactly one string. In this way, exponential compression rates can be achieved.  ...  version of this paper.  ... 
doi:10.1515/gcc-2012-0016 fatcat:o7lrrx3cgvhqrhmf4bsulc7rsa

The complexity of tree automata and XPath on grammar-compressed trees

Markus Lohrey, Sebastian Maneth
2006 Theoretical Computer Science  
The complexity of various membership problems for tree automata on compressed trees is analyzed.  ...  Finally, the complexity of the evaluation problem for (structural) XPath queries on trees that are compressed via straight-line context-free tree grammars is investigated.  ...  In this paper, we investigate the computational complexity of algorithmic problems on compressed trees.  ... 
doi:10.1016/j.tcs.2006.07.024 fatcat:43l2bclzzzatxpfdzw2bj2hlou

Complexity of Equations over Sets of Natural Numbers

Artur Jeż, Alexander Okhotin
2009 Theory of Computing Systems  
Among the consequences of the result is EXPTIME-completeness of the compressed membership problem for conjunctive grammars.  ...  Systems of equations of the form X i = ϕ i (X 1 , . . . , Xn) (1 i n) are considered, in which the unknowns are sets of natural numbers.  ...  Implications on conjunctive grammars The complexity of equations over sets of numbers established above has direct implications on the complexity of conjunctive grammars over a one-letter alphabet.  ... 
doi:10.1007/s00224-009-9246-y fatcat:ehvbpe7jnfcudbq7ayegs3xuxm

On the Complexity of the Smallest Grammar Problem over Fixed Alphabets

Katrin Casel, Henning Fernau, Serge Gaspers, Benjamin Gras, Markus L. Schmid
2020 Theory of Computing Systems  
depth" of grammars on the complexity of the smallest grammar problem.  ...  More precisely, it is shown that the smallest grammar problem remains NP-complete (and its optimisation version is APX-hard), even if the alphabet is fixed and has size of at least 17.  ...  We thank Gabriele Fici for pointing us to the "rule number" variant of the smallest grammar problem that we discussed at the end of Section 3.3.  ... 
doi:10.1007/s00224-020-10013-w fatcat:bfszfw3afrclbbzmqrt33tttcm

A Space-Saving Approximation Algorithm for Grammar-Based Compression

Hiroshi SAKAMOTO, Shirou MARUYAMA, Takuya KIDA, Shinichi SHIMOZONO
2009 IEICE transactions on information and systems  
Hiroshi SAKAMOTO †a) , Member, Shirou MARUYAMA † †b) , Takuya KIDA † † †c) , and Shinichi SHIMOZONO †d) , Nonmembers SUMMARY A space-efficient approximation algorithm for the grammar-based compression  ...  While g depends on the string, it is known that g = Ω(log n) and g = O n log k n for strings from k-letter alphabet [12] .  ...  On the other hand, various practical algorithms for the grammar-based compression have been devised so far.  ... 
doi:10.1587/transinf.e92.d.158 fatcat:aj43d6v2zvb2pbganpte7dpfzi

Ensemble Grammar Induction For Detecting Anomalies in Time Series [article]

Yifeng Gao, Jessica Lin, Constantin Brif
2020 arXiv   pre-print
Instead of using a particular choice of parameter values for anomaly detection, the method generates the final result based on a set of results obtained using different parameter values.  ...  To address this limitation, previously, a linear time anomaly detection algorithm based on grammar induction has been proposed.  ...  , Inc., for the U.S.  ... 
arXiv:2001.11102v1 fatcat:y64nb4okjzchxfr2ur2nc6snti

A Space-Saving Linear-Time Algorithm for Grammar-Based Compression [chapter]

Hiroshi Sakamoto, Takuya Kida, Shinichi Shimozono
2004 Lecture Notes in Computer Science  
A space-efficient linear-time approximation algorithm for the grammar-based compression problem, which requests for a given string to find a smallest context-free grammar deriving the string, is presented  ...  The algorithm consumes only O(g * log g * ) space and achieves the worstcase approximation ratio O(log g * log n), with the size n of an input and the optimum grammar size g * .  ...  On the other hand, various practical algorithms for the grammar-based compression have been devised so far.  ... 
doi:10.1007/978-3-540-30213-1_33 fatcat:3wl2lys6azg63jzwiy63lo7tn4

The smallest grammar problem revisited [article]

Hideo Bannai, Momoko Hirayama, Danny Hucke, Shunsuke Inenaga, Artur Jez, Markus Lohrey, Carl Philipp Reh
2019 arXiv   pre-print
Finally, results of Arpe and Reischuk relating grammar-based compression for arbitrary alphabets and binary alphabets are improved.  ...  In a seminal paper of Charikar et al. on the smallest grammar problem, the authors derive upper and lower bounds on the approximation ratios for several grammar-based compressors, but in all cases there  ...  Grammar-based compression. The idea of grammar-based compression is based on the fact that in many cases a word w can be succinctly represented by a context-free grammar that produces exactly w.  ... 
arXiv:1908.06428v1 fatcat:mtor27f2w5ed3h5cwhzmnswzm4

Efficient universal lossless data compression algorithms based on a greedy sequential grammar transform. I. Without context models

En-Hui Yang, J.C. Kieffer
2000 IEEE Transactions on Information Theory  
Simulation results show that the proposed algorithms outperform the Unix Compress and Gzip algorithms, which are based on LZ78 and LZ77, respectively.  ...  Based on this grammar transform, three universal lossless data compression algorithms, a sequential algorithm, an improved sequential algorithm, and a hierarchical algorithm, are then developed.  ...  than Unix Compress, which is based on LZ78.  ... 
doi:10.1109/18.841161 fatcat:6mwq5kmq3jckxkoxlmlsw6b4t4

Regular Expression Search on Compressed Text

Pierre Ganty, Pedro Valero
2019 2019 Data Compression Conference (DCC)  
The algorithm reports the number of matching lines in the uncompressed text in time linear in the size of its compressed version.  ...  We define efficient data structures that yield nearly optimal complexity bounds and provide a sequential implementation -zearch-that requires up to 25% less time than the state of the art. 2 Interpreted  ...  For repair-compressed text, the indexes of the alphabet sym bols are 0,1,..., 255 (Σ is fixed 7 ) and the indexes of the variables are 256 .. .p+256.  ... 
doi:10.1109/dcc.2019.00061 dblp:conf/dcc/Ganty019 fatcat:vv6xqbvzsza47i4n6zuzgoywku
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