Inversion Transduction Grammars
Early work on synchronous context free grammars for machine translation made a distinction between lexical mapping rules and purely non-terminal binary rules to make reordering decisions. 
Inversion Transduction Grammars is the main subject of 28 publications. 19 are discussed here.
Publications
Rooted in a finite state machine approach, head automata have been developed that allow for tree representation during the translation process 
 Hiyan Alshawi
Hiyan Alshawi (1996): 
Head Automata and Bilingual Tiling: Translation with Minimal Representations (Invited Talk), Proceedings of the 34th Annual Meeting of the Association for Computational Linguistics (ACL) 
 
  
  
 
@Inproceedings{Alshawi:1996,
author = {Hiyan Alshawi},
title = {Head Automata and Bilingual Tiling: Translation with Minimal Representations (Invited Talk)},
url = {
http://acl.ldc.upenn.edu/P/P96/P96-1023.pdf?origin=publicationDetail},
googlescholar = {11846375422406776920},
booktitle = {Proceedings of the 34th Annual Meeting of the Association for Computational Linguistics (ACL)},
year = 1996
}
; 
 Hiyan Alshawi and Adam L. Buchsbaum and Fei Xia
Hiyan Alshawi and Adam L. Buchsbaum and Fei Xia (1997): 
A Comparison of Head Transducers and Transfer for a Limited Domain Translation Application, Proceedings of the 35th Annual Meeting of the Association for Computational Linguistics (ACL) 
 
  
  
 
@Inproceedings{Alshawi:1997,
author = {Hiyan Alshawi and Adam L. Buchsbaum and Fei Xia},
title = {A Comparison of Head Transducers and Transfer for a Limited Domain Translation Application},
url = {
http://acl.ldc.upenn.edu/P/P97/P97-1046.pdf},
googlescholar = {5948054786386064082},
booktitle = {Proceedings of the 35th Annual Meeting of the Association for Computational Linguistics (ACL)},
year = 1997
}
; 
 Hiyan Alshawi and Srinivas Bangalore and Shona Douglas
Hiyan Alshawi and Srinivas Bangalore and Shona Douglas (1998): 
Automatic Acquisition of Hierarchical Transduction Models for Machine Translation, Proceedings of the 36th Annual Meeting of the Association of Computational Linguistics (ACL) 
 
  
  
 
@Inproceedings{Alshawi:1998,
author = {Hiyan Alshawi and Srinivas Bangalore and Shona Douglas},
title = {Automatic Acquisition of Hierarchical Transduction Models for Machine Translation},
url = {
http://acl.ldc.upenn.edu/C/C98/C98-1006.pdf},
googlescholar = {11495305628758623054},
booktitle = {Proceedings of the 36th Annual Meeting of the Association of Computational Linguistics (ACL)},
year = 1998
}
; 
 Hiyan Alshawi and Srinivas Bangalore and Shona Douglas
Hiyan Alshawi and Srinivas Bangalore and Shona Douglas (2000): 
Learning Dependency Translation Models as Collection of Finite-State Head Transducers, Computational Linguistics 
 
  
  
 
@Article{Alshawi:2000,
author = {Hiyan Alshawi and Srinivas Bangalore and Shona Douglas},
title = {Learning Dependency Translation Models as Collection of Finite-State Head Transducers},
url = {
http://acl.ldc.upenn.edu/J/J00/J00-1004.pdf},
journal = {Computational Linguistics},
volume = {26},
number = {1},
pages = {45--60},
year = 2000
}
. 
 Ye-Yi Wang and Alex Waibel
Ye-Yi Wang and Alex Waibel (1998): 
Modeling with Structures in Statistical Machine translation, Proceedings of the 36th Annual Meeting of the Association of Computational Linguistics (ACL) 
 
  
  
  mentioned in Phrase Based Models and Inversion Transduction Grammars
 mentioned in Phrase Based Models and Inversion Transduction Grammars@Inproceedings{Wang:1998,
author = {Ye-Yi Wang and Alex Waibel},
title = {Modeling with Structures in Statistical Machine translation},
url = {
http://acl.ldc.upenn.edu/P/P98/P98-2221.pdf},
googlescholar = {12385920933414037529},
booktitle = {Proceedings of the 36th Annual Meeting of the Association of Computational Linguistics (ACL)},
year = 1998
}
 also induce hierarchical structures in their statistical machine translation model.
The use of synchronous grammars for statistical machine translation has been pioneered by 
 Dekai Wu
Dekai Wu (1995): 
Trainable Coarse Bilingual Grammars for Parallel Text Bracketing, Proceedings of the Third Workshop on Very Large Corpora (VLC) 
 
  
  
 
@Inproceedings{Wu:1995b,
author = {Dekai Wu},
title = {Trainable Coarse Bilingual Grammars for Parallel Text Bracketing},
url = {
http://acl.ldc.upenn.edu/W/W95/W95-0106.pdf},
googlescholar = {8753937834967775813},
booktitle = {Proceedings of the Third Workshop on Very Large Corpora (VLC)},
year = 1995
}
; 
 Dekai Wu
Dekai Wu (1996): 
A Polynomial-Time Algorithm for Statistical Machine Translation, Proceedings of the 34th Annual Meeting of the Association for Computational Linguistics (ACL) 
 
  
  
 
@Inproceedings{Wu:1996,
author = {Dekai Wu},
title = {A Polynomial-Time Algorithm for Statistical Machine Translation},
url = {
http://acl.ldc.upenn.edu/P/P96/P96-1021.pdf},
googlescholar = {3924641975573530982},
booktitle = {Proceedings of the 34th Annual Meeting of the Association for Computational Linguistics (ACL)},
year = 1996
}
; 
 Dekai Wu
Dekai Wu (1997): 
Stochastic Inversion Transduction Grammars and Bilingual Parsing of Parallel Corpora, Computational Linguistics 
 
  
  
  mentioned in Word Alignment Based On Coocurrence and Inversion Transduction Grammars
 mentioned in Word Alignment Based On Coocurrence and Inversion Transduction Grammars@Article{Wu:1997,
author = {Dekai Wu},
title = {Stochastic Inversion Transduction Grammars and Bilingual Parsing of Parallel Corpora},
url = {
http://acl.ldc.upenn.edu/J/J97/J97-3002.pdf},
googlescholar = {7926725626202301933},
journal = {Computational Linguistics},
volume = {23},
number = {3},
year = 1997
}
; 
 Dekai Wu and Hongsing Wong
Dekai Wu and Hongsing Wong (1998): 
Machine Translation with a Stochastic Grammatical Channel, Proceedings of the 36th Annual Meeting of the Association of Computational Linguistics (ACL) 
 
  
  
 
@Inproceedings{Wu:1998,
author = {Dekai Wu and Hongsing Wong},
title = {Machine Translation with a Stochastic Grammatical Channel},
url = {
http://acl.ldc.upenn.edu/P/P98/P98-2230.pdf},
googlescholar = {17922869678767927043},
booktitle = {Proceedings of the 36th Annual Meeting of the Association of Computational Linguistics (ACL)},
year = 1998
}
 with their work on inversion transduction grammars (ITG) and stochastic bracketing transduction grammars (SBTG). A different formal model are multitext grammars 
 I. Dan Melamed
I. Dan Melamed (2003): 
Multitext grammars and synchronous parsers, Proceedings of the Joint Conference on Human Language Technologies and the Annual Meeting of the North American Chapter of the Association of Computational Linguistics (HLT-NAACL) 
 
  
  
 
@Inproceedings{Melamed:2003,
author = {I. Dan Melamed},
title = {Multitext grammars and synchronous parsers},
url = {
http://acl.ldc.upenn.edu/N/N03/N03-1021.pdf},
googlescholar = {11734294015301744662},
booktitle = {Proceedings of the Joint Conference on Human Language Technologies and the Annual Meeting of the North American Chapter of the Association of Computational Linguistics (HLT-NAACL)},
year = 2003
}
; 
 Melamed, I. Dan
Melamed, I. Dan (2004): 
Statistical Machine Translation by Parsing, Proceedings of the 42nd Meeting of the Association for Computational Linguistics (ACL'04), Main Volume 
 
  
  
 
@inproceedings{Melamed:2004,
author = {Melamed, I. Dan},
title = {Statistical Machine Translation by Parsing},
url = {
http://acl.ldc.upenn.edu/acl2004/main/pdf/113\_pdf\_2-col.pdf},
googlescholar = {10328834082011647315},
booktitle = {Proceedings of the 42nd Meeting of the Association for Computational Linguistics (ACL'04), Main Volume},
month = {July},
address = {Barcelona, Spain},
pages = {653--660},
year = 2004
}
; 
 Melamed, I. Dan  and  Satta, Giorgio  and  Wellington, Benjamin
Melamed, I. Dan  and  Satta, Giorgio  and  Wellington, Benjamin (2004): 
Generalized Multitext Grammars, Proceedings of the 42nd Meeting of the Association for Computational Linguistics (ACL'04), Main Volume 
 
  
  
 
@inproceedings{Melamed:2004b,
author = {Melamed, I. Dan  and  Satta, Giorgio  and  Wellington, Benjamin},
title = {Generalized Multitext Grammars},
url = {
http://acl.ldc.upenn.edu/acl2004/main/pdf/277\_pdf\_2-col.pdf},
googlescholar = {2355681091376158087},
booktitle = {Proceedings of the 42nd Meeting of the Association for Computational Linguistics (ACL'04), Main Volume},
month = {July},
address = {Barcelona, Spain},
pages = {661--668},
year = 2004
}
 and range concatenation grammars 
 Søgaard, Anders
Søgaard, Anders (2008): 
Range Concatenation Grammars for Translation, Coling 2008: Companion volume: Posters and Demonstrations 
 
  
  
 
@InProceedings{sogaard:2008:POSTERS2,
author = {S{\o}gaard, Anders},
title = {Range Concatenation Grammars for Translation},
booktitle = {Coling 2008: Companion volume: Posters and Demonstrations},
month = {August},
address = {Manchester, UK},
publisher = {Coling 2008 Organizing Committee},
pages = {101--104},
url = {
http://www.aclweb.org/anthology/C08-3026},
year = 2008
}
. 
 Zhang, Hao  and  Gildea, Daniel
Zhang, Hao  and  Gildea, Daniel (2005): 
Stochastic Lexicalized Inversion Transduction Grammar for Alignment, Proceedings of the 43rd Annual Meeting of the Association for Computational Linguistics (ACL'05) 
 
  
  
 
@InProceedings{zhang-gildea:2005:ACL,
author = {Zhang, Hao  and  Gildea, Daniel},
title = {Stochastic Lexicalized Inversion Transduction Grammar for Alignment},
booktitle = {Proceedings of the 43rd Annual Meeting of the Association for Computational Linguistics (ACL'05)},
month = {June},
address = {Ann Arbor, Michigan},
publisher = {Association for Computational Linguistics},
pages = {475--482},
url = {
http://www.aclweb.org/anthology/P/P05/P05-1059},
year = 2005
}
 extend the ITG formalism by lexicalizing grammar rules and apply it to a small-scale word alignment task. Armed with an efficient A* algorithm for this formalism 
 Zhang, Hao  and  Gildea, Daniel
Zhang, Hao  and  Gildea, Daniel (2006): 
Efficient Search for Inversion Transduction Grammar, Proceedings of the 2006 Conference on Empirical Methods in Natural Language Processing 
 
  
  
 
@InProceedings{zhang-gildea:2006:EMNLP,
author = {Zhang, Hao  and  Gildea, Daniel},
title = {Efficient Search for Inversion Transduction Grammar},
booktitle = {Proceedings of the 2006 Conference on Empirical Methods in Natural Language Processing},
month = {July},
address = {Sydney, Australia},
publisher = {Association for Computational Linguistics},
pages = {224--231},
url = {
http://www.aclweb.org/anthology/W/W06/W06-1627},
year = 2006
}
, they extend the formalism with rules that are lexicalized in both input and output 
 Zhang, Hao  and  Gildea, Daniel
Zhang, Hao  and  Gildea, Daniel (2006): 
Inducing Word Alignments with Bilexical Synchronous Trees, Proceedings of the COLING/ACL 2006 Main Conference Poster Sessions 
 
  
  
 
@InProceedings{zhang-gildea:2006:POS,
author = {Zhang, Hao  and  Gildea, Daniel},
title = {Inducing Word Alignments with Bilexical Synchronous Trees},
booktitle = {Proceedings of the COLING/ACL 2006 Main Conference Poster Sessions},
month = {July},
address = {Sydney, Australia},
publisher = {Association for Computational Linguistics},
pages = {953--960},
url = {
http://www.aclweb.org/anthology/P/P06/P06-2122},
year = 2006
}
. 
Word alignments generated with ITG may also be used to extract phrase for phrase-based models 
 Joan Andreu Sánchez and José Miguel Benedí
Joan Andreu Sánchez and José Miguel Benedí (2006): 
Obtaining Word Phrases with Stochastic Inversion Translation Grammars for Phrase-based Statistical Machine Translation, Proceedings of the 11th Conference of the European Association for Machine Translation (EAMT) 
 
  
  
 
@InProceedings{Sanchez:2006:EAMT,
author = {Joan Andreu S\'{a}nchez and Jos\'{e} Miguel Bened\'{i}},
title = {Obtaining Word Phrases with Stochastic Inversion Translation Grammars for Phrase-based Statistical Machine Translation},
url = {
http://mt-archive.info/EAMT-2006-Sanchez.pdf},
googlescholar = {16689080566077645608},
booktitle = {Proceedings of the 11th Conference of the European Association for Machine Translation (EAMT)},
month = {June},
address = {Oslo, Norway},
year = 2006
}
; 
 Sánchez, Joan Andreu  and  Benedí, José Miguel
Sánchez, Joan Andreu  and  Benedí, José Miguel (2006): 
Stochastic Inversion Transduction Grammars for Obtaining Word Phrases for Phrase-based Statistical Machine Translation, Proceedings on the Workshop on Statistical Machine Translation 
 
  
  
 
@InProceedings{sanchez-benedi:2006:WMT,
author = {S\'{a}nchez, Joan Andreu  and  Bened\'{i}, Jos\'{e} Miguel},
title = {Stochastic Inversion Transduction Grammars for Obtaining Word Phrases for Phrase-based Statistical Machine Translation},
booktitle = {Proceedings on the Workshop on Statistical Machine Translation},
month = {June},
address = {New York City},
publisher = {Association for Computational Linguistics},
pages = {130--133},
url = {
http://www.aclweb.org/anthology/W/W06/W06-3117},
year = 2006
}
. 
 Zhang, Hao  and  Quirk, Chris  and  Moore, Robert C.  and  Gildea, Daniel
Zhang, Hao  and  Quirk, Chris  and  Moore, Robert C.  and  Gildea, Daniel (2008): 
Bayesian Learning of Non-Compositional Phrases with Synchronous Parsing, Proceedings of ACL-08: HLT 
 
  
  
 
@InProceedings{zhang-EtAl:2008:ACLMain2,
author = {Zhang, Hao  and  Quirk, Chris  and  Moore, Robert C.  and  Gildea, Daniel},
title = {{Bayesian} Learning of Non-Compositional Phrases with Synchronous Parsing},
booktitle = {Proceedings of ACL-08: HLT},
month = {June},
address = {Columbus, Ohio},
publisher = {Association for Computational Linguistics},
pages = {97--105},
url = {
http://www.aclweb.org/anthology/P/P08/P08-1012},
year = 2008
}
 present an efficient ITG phrase alignment algorithm that uses Bayesian learning with priors.
Benchmarks
Discussion
Related Topics
New Publications
 Markus Saers and Dekai Wu Markus Saers and Dekai Wu-  (2013):  Unsupervised learning of bilingual categories in inversion transduction grammar induction- , Proceedings of the International Workshop on Spoken Language Translation (IWSLT)         - @inproceedings{Saers:iwslt:2013, - author = {Markus Saers and Dekai Wu}, - title = {Unsupervised learning of bilingual categories in inversion transduction grammar induction}, - url = { http://www.mt-archive.info/10/IWSLT-2013-Saers.pdf- }, - booktitle = {Proceedings of the International Workshop on Spoken Language Translation (IWSLT)}, - year = 2013 - } 
 Saers, Markus  and  Wu, Dekai Saers, Markus  and  Wu, Dekai-  (2013):  Bayesian Induction of Bracketing Inversion Transduction Grammars- , Proceedings of the Sixth International Joint Conference on Natural Language Processing         - @InProceedings{saers-wu:2013:IJCNLP, - author = {Saers, Markus  and  Wu, Dekai}, - title = {Bayesian Induction of Bracketing Inversion Transduction Grammars}, - booktitle = {Proceedings of the Sixth International Joint Conference on Natural Language Processing}, - month = {October}, - address = {Nagoya, Japan}, - publisher = {Asian Federation of Natural Language Processing}, - pages = {1158--1166}, - url = { http://www.aclweb.org/anthology/I13-1165- }, - year = 2013 - } 
 Anders S\ogaard Anders S\ogaard-  (2011):  A O(|G|n6) time extension of inversion transduction grammars- , Machine Translation       - @article{MTJ:2011:Sogaard,
 author = {Anders S\o{}gaard},
 title = {A O(|G|n6) time extension of inversion transduction grammars},
 pages = {291-315},
 journal = {Machine Translation},
 volume = {25},
 number = {4},
 month = {December},
 year = 2011
 }
 
 Saers, Markus  and  Addanki, Karteek  and  Wu, Dekai Saers, Markus  and  Addanki, Karteek  and  Wu, Dekai-  (2012):  From Finite-State to Inversion Transductions: Toward Unsupervised Bilingual Grammar Induction- , Proceedings of COLING 2012         - @InProceedings{saers-addanki-wu:2012:PAPERS, - author = {Saers, Markus  and  Addanki, Karteek  and  Wu, Dekai}, - title = {From Finite-State to Inversion Transductions: Toward Unsupervised Bilingual Grammar Induction}, - booktitle = {Proceedings of COLING 2012}, - month = {December}, - address = {Mumbai, India}, - publisher = {The COLING 2012 Organizing Committee}, - pages = {2325--2340}, - url = { http://www.aclweb.org/anthology/C12-1142- }, - year = 2012 - } 
 Liu, Shujie  and  Li, Chi-Ho  and  Zhou, Ming Liu, Shujie  and  Li, Chi-Ho  and  Zhou, Ming-  (2010):  Improved Discriminative ITG Alignment using Hierarchical Phrase Pairs and Semi-supervised Training- , Coling 2010: Posters         - @InProceedings{liu-li-zhou:2010:POSTERS, - author = {Liu, Shujie  and  Li, Chi-Ho  and  Zhou, Ming}, - title = {Improved Discriminative ITG Alignment using Hierarchical Phrase Pairs and Semi-supervised Training}, - booktitle = {Coling 2010: Posters}, - month = {August}, - address = {Beijing, China}, - publisher = {Coling 2010 Organizing Committee}, - pages = {730--738}, - url = { http://www.aclweb.org/anthology/C10-2084- }, - year = 2010 - } 
 Li, Peng  and  Liu, Yang  and  Sun, Maosong Li, Peng  and  Liu, Yang  and  Sun, Maosong-  (2012):  A Beam Search Algorithm for ITG Word Alignment- , Proceedings of COLING 2012: Posters         - @InProceedings{li-liu-sun:2012:POSTERS2, - author = {Li, Peng  and  Liu, Yang  and  Sun, Maosong}, - title = {A Beam Search Algorithm for {ITG} Word Alignment}, - booktitle = {Proceedings of COLING 2012: Posters}, - month = {December}, - address = {Mumbai, India}, - publisher = {The COLING 2012 Organizing Committee}, - pages = {673--682}, - url = { http://www.aclweb.org/anthology/C12-2066- }, - year = 2012 - } 
 K. Addanki and C. Lo and M. Saers and D. Wu K. Addanki and C. Lo and M. Saers and D. Wu-  (2012):  LTG vs. ITG Coverage of Cross-Lingual Verb Frame Alternation- , Proceedings of th 16th International Conference of the European Association for Machine Translation (EAMT)         - @inproceedings{EAMT-2012-Addanki, - author = {K. Addanki and C. Lo and M. Saers and D. Wu}, - title = {LTG} vs. {ITG Coverage of Cross-Lingual Verb Frame Alternation}, - url = { http://www.mt-archive.info/EAMT-2012-Addanki- }, - pages = {295-304}, - booktitle = {Proceedings of th 16th International Conference of the European Association for Machine Translation (EAMT)}, - location = {Trento, Italy}, - editor = {Mauro Cettolo and Marcello Federico and Lucia Specia and Andy Way}, - year = 2012 - } 
 Saers, Markus  and  Nivre, Joakim  and  Wu, Dekai Saers, Markus  and  Nivre, Joakim  and  Wu, Dekai-  (2010):  Linear Inversion Transduction Grammar Alignments as a Second Translation Path- , Proceedings of the Joint Fifth Workshop on Statistical Machine Translation and MetricsMATR         - @InProceedings{saers-nivre-wu:2010:WMT, - author = {Saers, Markus  and  Nivre, Joakim  and  Wu, Dekai}, - title = {Linear Inversion Transduction Grammar Alignments as a Second Translation Path}, - booktitle = {Proceedings of the Joint Fifth Workshop on Statistical Machine Translation and MetricsMATR}, - month = {July}, - address = {Uppsala, Sweden}, - publisher = {Association for Computational Linguistics}, - pages = {173--177}, - url = { http://www.aclweb.org/anthology/W10-1725- }, - year = 2010 - } 
 Haghighi, Aria  and  Blitzer, John  and  DeNero, John  and  Klein, Dan Haghighi, Aria  and  Blitzer, John  and  DeNero, John  and  Klein, Dan-  (2009):  Better Word Alignments with Supervised ITG Models- , Proceedings of the Joint Conference of the 47th Annual Meeting of the ACL and the 4th International Joint Conference on Natural Language Processing of the AFNLP         - @InProceedings{haghighi-EtAl:2009:ACLIJCNLP, - author = {Haghighi, Aria  and  Blitzer, John  and  DeNero, John  and  Klein, Dan}, - title = {Better Word Alignments with Supervised ITG Models}, - booktitle = {Proceedings of the Joint Conference of the 47th Annual Meeting of the ACL and the 4th International Joint Conference on Natural Language Processing of the AFNLP}, - month = {August}, - address = {Suntec, Singapore}, - publisher = {Association for Computational Linguistics}, - pages = {923--931}, - url = { http://www.aclweb.org/anthology/P/P09/P09-1104- }, - year = 2009 - }