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31:
237:, which constructs a grammar that may be reducible, i.e., contain repeats, where the entropy-coding cost of "spelling out" the repeats is less than the cost creating and entropy-coding a rule to capture them. (In general, the compression-optimal SLG is not irreducible, and the Smallest Grammar Problem is different from the actual SLG compression problem.)
116:
231:
is a greedy algorithm using the strategy of most-frequent-first substitution. The compressive performance is powerful, although the main memory space requirement is very large.
495:
Conrad, Kennon J.; Wilson, Paul R. (2016). "Grammatical Ziv-Lempel
Compression: Achieving PPM-Class Text Compression Ratios with LZ-Class Decompression Speed".
225:
is a classical grammar compression algorithm that sequentially translates an input text into a CFG, and then the produced CFG is encoded by an arithmetic coder.
180:
156:
136:
202:, and many other new universal lossless compression algorithms. Grammar-based codes are universal in the sense that they can achieve asymptotically the
162:) is known to be NP-hard, so many grammar-transform algorithms are proposed from theoretical and practical viewpoints. Generally, the produced grammar
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Charikar, M.; Lehman, E.; Liu, D.; Panigrahy, R.; Prabharakan, M.; Sahai, A.; Shelat, A. (2005), "The
Smallest Grammar Problem",
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1055:
512:
1208:
410:
Nevill-Manning, C. G.; Witten, I. H. (1997), "Identifying
Hierarchical Structure in Sequences: A linear-time algorithm",
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Kieffer, J. C.; Yang, E.-H. (2000), "Grammar-based codes: A new class of universal lossless source codes",
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1035:
819:
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1556:
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257:
34:
543:
374:
Ziv, J.; Lempel, A. (1978), "Compression of individual sequences via variable rate coding",
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8:
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198:, the multilevel pattern matching (MPM) algorithm, variations of the incremental parsing
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218:
The compression programs of the following are available from external links.
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574:- implementation of Sequitur, Re-Pair, and parallel Re-Pair in Java.
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1509:
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424:
158:. The problem of finding a smallest grammar for an input sequence (
68:(CFG) for the string to be compressed. Examples include universal
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907:
856:
228:
207:
338:"Universal lossless compression via multilevel pattern matching"
947:
1782:
1387:
980:
927:
336:
Kieffer, J. C.; Yang, E.-H.; Nelson, G.; Cosman, P. (2000),
194:
The class of grammar-based codes is very broad. It includes
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30:
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37:(with start symbol Ăź) for the second sentence of the
409:
182:is further compressed by statistical encoders like
174:
150:
130:
110:
1796:
544:Description of grammar-based codes with example
189:
64:algorithms based on the idea of constructing a
593:
461:
607:
494:
412:Journal of Artificial Intelligence Research
275:
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586:
423:
395:
373:
39:United States Declaration of Independence
72:algorithms. To compress a data sequence
29:
213:
14:
1797:
497:2016 Data Compression Conference (DCC)
464:"Offline Dictionary-Based Compression"
581:
462:Larsson, N. J.; Moffat, A. (2000),
111:{\displaystyle x=x_{1}\cdots x_{n}}
27:Lossless data compression algorithm
24:
118:, a grammar-based code transforms
25:
1826:
532:
1774:
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1763:
41:. Each blue character denotes a
210:source with a finite alphabet.
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455:
403:
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329:
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269:
13:
1:
568:a version of Gonzalo Navarro.
263:
49:-compression of the sentence.
190:Examples and characteristics
138:into a context-free grammar
45:; they were obtained from a
7:
241:
10:
1831:
1655:Compressed data structures
977:RLE + BWT + MTF + Huffman
645:Asymmetric numeral systems
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1727:
1645:
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1502:
1493:
1416:
1350:
1341:
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1159:
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1066:
1014:Discrete cosine transform
1004:
995:
944:LZ77 + Huffman + context
897:
807:
737:
625:
616:
539:GLZA discussion and paper
70:lossless data compression
58:Grammar-based compression
1719:Smallest grammar problem
388:10.1109/TIT.1978.1055934
160:smallest grammar problem
1660:Compressed suffix array
1209:Nyquist–Shannon theorem
471:Proceedings of the IEEE
376:IEEE Trans. Inf. Theory
342:IEEE Trans. Inf. Theory
316:10.1109/tit.2005.850116
304:IEEE Trans. Inf. Theory
278:IEEE Trans. Inf. Theory
176:
152:
132:
112:
50:
1689:Kolmogorov complexity
1557:Video characteristics
934:LZ77 + Huffman + ANS
258:Straight-line grammar
177:
153:
133:
113:
35:Straight-line grammar
33:
1779:Compression software
1373:Compression artifact
1329:Psychoacoustic model
505:10.1109/DCC.2016.119
214:Practical algorithms
166:
142:
122:
76:
66:context-free grammar
1769:Compression formats
1408:Texture compression
1403:Standard test image
1219:Silence compression
206:of any stationary,
54:Grammar-based codes
18:Grammar-based codes
1815:Information theory
1677:Information theory
1532:Display resolution
1358:Chroma subsampling
747:Byte pair encoding
692:Shannon–Fano–Elias
554:2008-10-13 at the
397:10338.dmlcz/142945
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148:
128:
108:
51:
43:nonterminal symbol
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1591:Deblocking filter
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991:
990:
514:978-1-5090-1853-6
477:(11): 1722–1732,
354:10.1109/18.850665
290:10.1109/18.841160
253:Grammar induction
184:arithmetic coding
175:{\displaystyle G}
151:{\displaystyle G}
131:{\displaystyle x}
16:(Redirected from
1822:
1805:Data compression
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1596:Lapped transform
1500:
1499:
1378:Image resolution
1363:Coding tree unit
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609:Data compression
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483:10.1109/5.892708
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434:10.1613/jair.374
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348:(4): 1227–1245,
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310:(7): 2554–2576,
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248:Dictionary coder
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1704:Rate–distortion
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1234:Sub-band coding
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1067:Predictive type
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987:
954:LZSS + Huffman
904:LZ77 + Huffman
893:
803:
739:Dictionary type
733:
635:Adaptive coding
612:
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556:Wayback Machine
535:
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499:. p. 586.
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200:Lempel-Ziv code
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1138:Psychoacoustic
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1123:
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1006:Transform type
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572:GrammarViz 2.0
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549:Sequitur codes
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533:External links
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382:(5): 530–536,
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1562:Video quality
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1229:Speech coding
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1224:Sound quality
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1199:Dynamic range
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964:LZ77 + Range
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566:Re-Pair codes
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561:Re-Pair codes
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32:
19:
1735:Hutter Prize
1699:Quantization
1604:Compensation
1398:Quantization
1121:Compensation
851:
687:Shannon–Fano
627:Entropy type
496:
490:
474:
470:
457:
418:(4): 67–82,
415:
411:
405:
379:
375:
369:
345:
341:
331:
307:
303:
297:
281:
277:
271:
217:
204:entropy rate
193:
57:
53:
52:
1694:Prefix code
1547:Frame types
1368:Color space
1194:Convolution
924:LZ77 + ANS
835:Incremental
808:Other types
727:Levenshtein
196:block codes
62:compression
1799:Categories
1751:Mark Adler
1709:Redundancy
1626:Daubechies
1609:Estimation
1542:Frame rate
1464:Daubechies
1424:Chain code
1383:Macroblock
1189:Companding
1126:Estimation
1046:Daubechies
752:Lempel–Ziv
712:Exp-Golomb
640:Arithmetic
442:10289/1186
425:cs/9709102
264:References
1728:Community
1552:Interlace
938:Zstandard
717:Fibonacci
707:Universal
665:Canonical
96:⋯
1714:Symmetry
1682:Timeline
1665:FM-index
1510:Bit rate
1503:Concepts
1351:Concepts
1214:Sampling
1167:Bit rate
1160:Concepts
862:Sequitur
697:Tunstall
670:Modified
660:Adaptive
618:Lossless
552:Archived
242:See also
223:Sequitur
1672:Entropy
1621:Wavelet
1600:Motion
1459:Wavelet
1439:Fractal
1434:Deflate
1417:Methods
1204:Latency
1117:Motion
1041:Wavelet
958:LHA/LZH
908:Deflate
857:Re-Pair
852:Grammar
682:Shannon
655:Huffman
611:methods
523:3116024
450:2957960
362:8191526
324:6900082
229:Re-Pair
208:ergodic
1783:codecs
1744:People
1647:Theory
1614:Vector
1131:Vector
948:Brotli
898:Hybrid
797:Snappy
650:Golomb
521:
511:
448:
360:
322:
1574:parts
1572:Codec
1537:Frame
1495:Video
1479:SPIHT
1388:Pixel
1343:Image
1297:ACELP
1268:ADPCM
1258:ÎĽ-law
1253:A-law
1246:parts
1244:Codec
1152:Audio
1091:ACELP
1079:ADPCM
1056:SPIHT
997:Lossy
981:bzip2
972:LZHAM
928:LZFSE
830:Delta
722:Gamma
702:Unary
677:Range
519:S2CID
467:(PDF)
446:S2CID
420:arXiv
358:S2CID
320:S2CID
1586:DPCM
1393:PSNR
1324:MDCT
1317:WLPC
1302:CELP
1263:DPCM
1111:WLPC
1096:CELP
1074:DPCM
1024:MDCT
968:LZMA
869:LDCT
847:DPCM
792:LZWL
782:LZSS
777:LZRW
767:LZJB
509:ISBN
235:GLZA
60:are
47:gzip
1631:DWT
1581:DCT
1525:VBR
1520:CBR
1515:ABR
1474:EZW
1469:DWT
1454:RLE
1444:KLT
1429:DCT
1312:LSP
1307:LAR
1292:LPC
1285:FFT
1182:VBR
1177:CBR
1172:ABR
1106:LSP
1101:LAR
1086:LPC
1051:DWT
1036:FFT
1031:DST
1019:DCT
918:LZS
913:LZX
889:RLE
884:PPM
879:PAQ
874:MTF
842:DMC
820:CTW
815:BWT
787:LZW
772:LZO
762:LZ4
757:842
501:doi
479:doi
438:hdl
430:doi
392:hdl
384:doi
350:doi
312:doi
286:doi
56:or
1801::
1449:LP
1280:FT
1273:DM
825:CM
517:.
507:.
475:88
473:,
469:,
444:,
436:,
428:,
414:,
390:,
380:24
378:,
356:,
346:46
344:,
340:,
318:,
308:51
306:,
282:46
280:,
186:.
1785:)
1781:(
601:e
594:t
587:v
525:.
503::
481::
440::
432::
422::
416:7
394::
386::
352::
314::
288::
170:G
146:G
126:x
104:n
100:x
91:1
87:x
83:=
80:x
20:)
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