This operation computes the composition of two transducers. If `A`

transduces string `x`

to `y`

with weight `a`

and `B`

transduces `y`

to `z`

with weight `b`

, then their composition transduces
string `x`

to `z`

with weight `a ⊗ b`

.

The output labels of the first transducer or the input labels of the second transducer must be sorted (or the FSTs otherwise support appropriate
matchers).
The weights need to form a commutative semiring (valid for `TropicalWeight`

and `LogWeight`

for instance).

Versions of this operation (not all shown here) accept options that allow choosing the matcher, composition filter, state table and, when delayed, the caching behavior used by composition.

`A`

:

`B`

:

`A o B`

:

Compose(A, B, &C); ComposeFst<Arc>(A, B); fstcompose a.fst b.fst out.fst

Assuming the first FST is unsorted and the second is sorted:

`Compose`

:

- Time:
*O(V*_{1}V_{2}D_{1}(log D_{2}+ M_{2})) - Space:
*O(V*_{1}V_{2}D_{1}M_{2})

`ComposeFst`

:

- TIme:
*O(v*,_{1}v_{2}d_{1}(log d_{2}+ m_{2})) - Space:
*O(v*_{1}v_{2})

`Compose`

and `fstcompose`

trim their output, `ComposeFst`

does not (since it is a delayed operation).

The efficiency of composition can be strongly affected by several factors:

- the choice of which transducer is sorted
- prefer sorting the FST that has the greater average out-degree
- sorting both transducers allows composition to automatically select the best transducer to match against (per state pair)
- note stored sort properties of the FSTs are first checked in constant time followed by the minimum number of linear-time sort tests necessary to discover one sorted FST; thus composition may be unaware that both FSTs are sorted when those properties are not stored.

- the amount of non-determinism
- the presence and location of epsilon transitions - avoid epsilon transitions on the output side of the first transducer or the input side of the second transducer or prefer placing them later in a path since they delay matching and can introduce non-coaccessible states and transitions

See here for more discussion on efficient usage.

I | Attachment | History | Action | Size | Date | Who | Comment |
---|---|---|---|---|---|---|---|

jpg | compose1.jpg | r2 r1 | manage | 11.7 K | 2007-06-30 - 21:47 | MichaelRiley | |

jpg | compose2.jpg | r7 r6 r5 r4 r3 | manage | 11.2 K | 2007-06-30 - 21:47 | MichaelRiley | |

jpg | compose3.jpg | r6 r5 r4 r3 r2 | manage | 14.8 K | 2007-06-30 - 21:47 | MichaelRiley |

Topic revision: r23 - 2014-04-23 - MichaelRiley

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