Some Computational Complexity Results for Synchronous Context-Free Grammars

This paper investigates some computational problems associated with probabilistic translation models that have recently been adopted in the literature on machine translation. These models can be viewed as pairs of probabilistic context-free grammars working in a 'synchronous' way. Two hardness results for the class NP are reported, along with an exponential time lower-bound for certain classes of algorithms that are currently used in the literature.

[1]  Christian N. S. Pedersen,et al.  The consensus string problem and the complexity of comparing hidden Markov models , 2002, J. Comput. Syst. Sci..

[2]  Fred J. Maryanski,et al.  Properties of stochastic syntax-directed translation schemata , 1979, International Journal of Computer & Information Sciences.

[3]  I. Dan Melamed,et al.  Multitext Grammars and Synchronous Parsers , 2003, NAACL.

[4]  C. S. Wetherell,et al.  Probabilistic Languages: A Review and Some Open Questions , 1980, CSUR.

[5]  John Cocke,et al.  A Statistical Approach to Language Translation , 1988, COLING.

[6]  Tadao Kasami,et al.  THE COMPUTATIONAL COMPLEXITY OF THE UNIVERSAL RECOGNITION PROBLEM FOR PARALLEL MULTIPLE CONTEXT‐FREE GRAMMARS , 1994, Comput. Intell..

[7]  Francisco Casacuberta,et al.  Probabilistic finite-state machines - part I , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Giorgio Satta,et al.  Generalized Multitext Grammars , 2004, ACL.

[9]  Daniel Gildea,et al.  Loosely Tree-Based Alignment for Machine Translation , 2003, ACL.

[10]  Kevin Knight,et al.  Decoding Complexity in Word-Replacement Translation Models , 1999, Comput. Linguistics.

[11]  Hermann Ney,et al.  Discriminative Training and Maximum Entropy Models for Statistical Machine Translation , 2002, ACL.

[12]  Dekai Wu,et al.  Machine Translation with a Stochastic Grammatical Channel , 1998, COLING-ACL.

[13]  I. Dan Melamed,et al.  Statistical Machine Translation by Parsing , 2004, ACL.

[14]  Giorgio Satta,et al.  Recognition of Linear Context-Free Rewriting Systems , 1992, ACL.

[15]  Alfred V. Aho,et al.  The Theory of Parsing, Translation, and Compiling , 1972 .

[16]  Aravind K. Joshi,et al.  Evaluating grammar formalisms for applications to natural language processing and biological sequence analysis , 2004 .

[17]  Hermann Ney,et al.  Improved Alignment Models for Statistical Machine Translation , 1999, EMNLP.

[18]  Kevin Knight,et al.  A Syntax-based Statistical Translation Model , 2001, ACL.

[19]  Shankar Kumar,et al.  A Weighted Finite State Transducer Implementation of the Alignment Template Model for Statistical Machine Translation , 2003, NAACL.

[20]  Dekai Wu,et al.  Stochastic Inversion Transduction Grammars and Bilingual Parsing of Parallel Corpora , 1997, CL.

[21]  David Chiang,et al.  A Hierarchical Phrase-Based Model for Statistical Machine Translation , 2005, ACL.

[22]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[23]  Francisco Casacuberta,et al.  Submission to ICGI-2000 Computational complexity of problems on probabilistic grammars and transducers , 2007 .

[24]  Srinivas Bangalore,et al.  Learning Dependency Translation Models as Collections of Finite-State Head Transducers , 2000, Computational Linguistics.