Hi Amir

You could also try this paper for a derivation of the complexity of PBMT 
decoding
https://www.aclweb.org/anthology/E/E09/E09-1061v2.pdf

cheers - Barry

On 27/02/17 15:54, Philipp Koehn wrote:
> Hi,
>
> I am not sure if you follow your question - in the formula you cite,
> there are exponential terms: 2^n and T^n.
>
> The Knight paper is worth trying to understand (it's on IBM Models,
> but applies similarly to phrase-based models).
>
> Also keep in mind that limited reordering windows and beam search
> makes actual decoding algorithm implementations linear.
>
> -phi
>
> On Sun, Feb 26, 2017 at 1:16 PM, amir haghighi
> <[email protected]> wrote:
>> Hi all,
>>
>> In the Moses manual and also in SMT textbooks it is mentioned that the
>> decoding complexity for PB-SMT is exponential in the source sentence length.
>> If we have a source sentence with length n, in decoding by hypothesis
>> expansion, we have power(2,n) state, each of them can be reordered in n!
>> orders, and each state can be translated in power(T,n), where T is the
>> number of translation options, right?
>> so the decoder complexity is power(2,n)*n!*power(T,n), so why its mentioned
>> that the complexity is exponential?
>>
>> Could someone please explain for me how the decoder complexity is
>> calculated?
>> I've read the Knight(1999) paper, but I couldn't understand it. Could you
>> please introduce another reference?
>>
>> Thanks
>>
>>
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