Syntax-based statistical translation model

Abstract

A statistical translation model (TM) may receive a parse tree in a source language as an input and separately output a string in a target language. The TM may perform channel operations on the parse tree using model parameters stored in probability tables. The channel operations may include reordering child nodes, inserting extra words at each node (e.g., NULL words) translating leaf words, and reading off leaf words to generate the string in the target language. The TM may assign a translation probability to the string in the target language.

Description

BACKGROUND

Machine translation (MT) concerns the automatic translation of natural language sentences from a first language (e.g., French) into another language (e.g., English). Systems that perform MT techniques are said to “decode” the source language into the target language.

One type of MT decoder is the statistical MT decoder. A statistical MT decoder that translates French sentences into English may include a language model (LM) that assigns a probability P(e) to any English string, a translation model (TM) that assigns a probability P(f|e) to any pair of English and French strings, and a decoder. The decoder may take a previously unseen sentence f and try to find the e that maximizes P(e|f), or equivalently maximizes P(e)·P(f|e).

A TM may not model structural or syntactic aspects of a language. Such a TM may perform adequately for a structurally similar language pair (e.g., English and French), but may not adequately model a language pair with very different word order conventions (e.g., English and Japanese).

SUMMARY

A statistical translation model (TM) may receive a parse tree in a source language as an input and separately output a string in a target language. The TM may perform channel operations on the parse tree using model parameters stored in probability tables. The channel operations may include reordering child nodes, inserting extra words at each node (e.g., NULL words), translating leaf words, and reading off leaf words to generate the string in the target language. The TM may assign a translation probability to the string in the target language.

The reordering operation may be based on a probability corresponding to a sequence of the child node labels. The insertion operation may determine which extra word to insert and an insert position relative to the node.

The TM may be trained using an Expectation Maximization (EM) algorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a statistical translation model (TM) system.

FIG. 2 illustrates channel operations performed on a input parse tree.

FIG. 3 is a flowchart describing channel operations performed by the TM.

FIG. 4 illustrates tables including model parameters used in the channel operations.

FIG. 5 is a graph structure for training the translation model using an Expectation Maximization (EM) algorithm.

DETAILED DESCRIPTION

FIG. 1 illustrates a statistical translation model (TM) system 100. The system may be based on a noisy channel model. A syntactic parser 110 may generate a parse tree from an input sentence. A parse tree 200, such as that shown in FIG. 2, includes a number of nodes, including parent nodes and child nodes. A child node may be a parent to another node (e.g., the VB2 node to the TO and NN nodes). The parent and child nodes have labels corresponding to a part-of-speech (POS) tag for the word or phrase corresponding to the node (e.g., verb (VB), personal pronoun (PP), noun (NN), etc). Leafs 215 of the tree include words in the input string.

The channel 105 accepts the parse tree as an input and performs operations on each node of the parse tree. As shown in FIG. 2, the operations may include reordering child nodes, inserting extra words at each node, translating leaf words, and reading off leafs to generate a string in the target language (e.g., Japanese).

The reorder operation may model translation between languages with different word orders, such as SVO (Subject-Verb-Object)-languages (English or Chinese) and SOV-languages (Japanese or Turkish). The word-insertion operation may capture linguistic differences in specifying syntactic cases. For example, English and French use structural position to specify case, while Japanese and Korean use case-marker particles.

FIG. 3 is a flowchart describing a channel operation 300 according to an embodiment. A string in a source language (e.g., English) may be input to the syntactic parser 110 (block 305). The syntactic parser 110 parses the input string into a parse tree 200 (block 310).

Child nodes on each internal node are stochastically reordered (block 315). A node with N children has N! possible reorderings. The probability of taking a specific reordering may be given by an r-table 405, as shown in FIG. 4. The reordering may be influenced only by the sequence of child nodes. In FIG. 2, the top VB node 205 has a child sequence PRP-VB1-VB2. The probability of reordering it into PRP-VB2-VB1 is 0.723 (from the second row in the r-table 405). The sequence VB-TO may be reordered into TO-VB, and TO-NN into NN-TO. Therefore, the probability of the second tree 220 is 0.7123·0.749·0.8931=0.484.

Next, an extra word may be stochastically inserted at each node (block 320). The word may be inserted either to the left of the node, to the right of the node, or nowhere. The word may be a NULL word 230. In a TM model, a NULL word may be an invisible word in the input sentence that generates output words distributed into random positions. NULL words may be function words, such as “ha” and “no” in Japanese. The position may be decided on the basis of the nodes of the input parse tree.

The insertion probability may be determined by an n-table. The n-table may be split into two tables: a table 410 for insert positions and a table 415 for words to be inserted. The node's label and its parent's label may be used to index the table for insert positions. For example, the PRP node has parent VB 205, thus (parent=VB, node=PRP) is the conditioning index. Using this label pair captures, for example, the regularity of inserting case-marker particles. In an embodiment, no conditioning variable is used when deciding which word to insert. That is, a function word like “ha” is just as likely to be inserted in one place as any other.

In FIG. 2, four NULL words 230 (“ha”, “no”, “ga”, and “desu”) were inserted to create a third tree 225. The top VB node, two TO nodes, and the NN node inserted nothing. Therefore, the probability of obtaining the third tree given the second tree is (0.652·0.219)·(0.252·0.094)·(0.252·0.062)·(0.252·0.0007)·0.735·0.709·0.900·0.800=3.498e−9. A translate operation may be applied to each leaf (block 325). In an embodiment, this operation is dependent only on the word itself and no context is consulted. A t-table 420 may specify the probability for all cases. For the translations shown in the fourth tree 235 of FIG. 2, the probability of the translate operation is 0.9052·0.900·0.038·0.333·01.000=0.0108.

The total probability of the reorder, insert, and translate operations may then be calculated. In this example, the probability is 0.484·3.498e−9·0.0108=1.828e−11. Note that there are many other combinations of such operations that yield the same Japanese sentence. Therefore, the probability of the Japanese sentence given the English parse tree is the sum of all these probabilities.

The channel operations may be modeled mathematically. Assume that an English parse tree is transformed into a French sentence f. Let the English parse tree ε, consist of nodes ε₁, ε₂, . . . , ε_n, and let the output French sentence consist of French words f₁, f₂, . . . , f_m. Three random variables, N, R, and T, are channel operations applied to each node. Insertion N is an operation that inserts a French word just before or after the node. The insertion can be none, left, or right. Insertion N may also decide what French word to insert. Reorder R is an operation that changes the order of the children of the node. If a node has three children, there are 3!=6 ways to reorder them. This operation may apply only to non-terminal nodes in the tree. Translation T is an operation that translates a terminal English leaf word into a French word. This operation applies only to terminal nodes. Note that an English word can be translated into a French NULL word.

The notation θ=<ν,p,τ> stands for a set of values of <N, R, T>. θ₁=<ν₁, p_i,τ₁> is a set of values of random variables associatds with ε_i, and θ=θ₁, θ₂, . . . , θ_n is a set of all random variables associated with a parse tree ε=ε₁, ε₂, . . . , ε_n.

The probability of getting a French sentence f given an English parse tree ε is

$P\left(f|\varepsilon \right)=\sum _{\theta :\mathrm{Str})\theta \left(\varepsilon \right))=f}P\left(\theta |\varepsilon \right)$ where Str(θ(ε)) is the sequence of leaf words of a tree transformed by θ from ε.

The probability of having a particular set of values of random variables in a parse tree isP(θ|ε)=P(θ₁,θ₂, . . . , θ_n|ε₁,ε₂, . . . , ε_n)

$\begin{array}{c}P\left(\theta |\varepsilon \right)=P({\theta }_1,{\theta }_2,\dots ,{\theta }_n|{\varepsilon }_1,{\varepsilon }_2,\dots {\varepsilon }_n)\\ =\prod _{i=1}^{n}P\left({\theta }_i|{\theta }_1,{\theta }_2,\dots ,{\theta }_{i-1},{\varepsilon }_1,{\varepsilon }_2,\dots ,{\varepsilon }_n\right)\end{array}$

Assuming a transform operation is independent from other transform operations, and the random variables of each node are determined only by the node itself, thenP(θ|ε)=P(θ₁,θ₂, . . . , θ_n|ε₁,ε₂, . . . , ε_n)

$\begin{array}{c}P\left(\theta |\varepsilon \right)=P({\theta }_1,{\theta }_2,\dots ,{\theta }_n|{\varepsilon }_1,{\varepsilon }_2,\dots ,{\varepsilon }_n)\\ =\prod _{i=1}^{n}P\left({\theta }_i{\varepsilon }_i\right)\end{array}$

The random variables θ₁=<ν₁,p_i,τ₁> are assumed to be independent of each other. It is also assumed that they are dependent on particular features of the node ε₁. Then,P(θ₁|ε₁)=P(ν_i,ρ_i,τ₁|ε₁)=P(ν₁|ε₁)P(ρ_i|ε_i)P(τ₁|ε₁)=P(ν₁|N(ε₁))P(ρ_i|R(ε₁))P(τ₁|T(ε_i))=n(ν_i|N(ε_i))r(ρ_i|R(ε_i))t(τ_i|T(ε_i))where N, R, and T are the relevant features of N, R, and T, respectively. For example, the parent node label and the node label were used for N, and the syntactic category sequence of children was used for R. The last line in the above formula introduces a change in notation, meaning that those probabilities are the model parameters n(ν|N), r(ρ|R), and t(τ|T), where N, R, and T are the possible values for N, R and T, respectively.

In summary, the probability of getting a French sentence f given an English parse tree ε is

$\begin{array}{c}P\left(f|\varepsilon \right)=\sum _{\theta :\mathrm{Str}\left(\theta \left(\varepsilon \right)\right)=f}P\left(\theta |\varepsilon \right)\\ =\sum _{\theta :\mathrm{Str}\left(\theta \left(\varphi \right)\right)=f}\prod _{i=1}^{n}n\left({\nu }_i|N\left({\varepsilon }_1\right)\right)r\left({\rho }_i|R\left({\varepsilon }_i\right)\right)t({\tau }_iT\left({\varepsilon }_i\right)\end{array}$ where ε=ε₁, ε₂, . . . , ε_n and θ=θ₁, θ₂, . . . , θ_n=<ν₁, ρ₁, τ₁>,<ν₂, ρ₂, τ₂>, . . . , <ν_n, ρ_n, τ_n>.

The model parameters n(ν|N), r(ρ|R), and t(τ|T), that is, the probabilities P(ν|N), P(ρ|R), and P(τ|T), decide the behavior of the translation model. These probabilities may be estimated from a training corpus.

An Expectation Maximization (EM) algorithm may be used to estimate the model parameters (see, e.g., A. Dempster, N. Laird, and D. Rubin. 1977. Maximum likelihood from incomplete data via the em algorithm). The algorithm iteratively updates the model parameters to maximize the likelihood of the training corpus. First, the model parameters are initialized. A uniform distribution may be used or a distribution may be taken from other models. For each iteration, the number of events are counted and weighted by the probabilities of the events. The probabilities of events are calculated from the current model parameters. The model parameters are re-estimated based on the counts, and used for the next iteration. In this case, an event is a pair of a value of random variable (such as ν, ρ, or τ) and a feature value (such as N, R, or T) A separate counter is used for each event. Therefore, the same number of counters c(ν|N), c(ρ|R), and c(τ|T), as the number of entries in the probability tables, n(ν|N), r(ρ|R), and t(τ|T), are needed.

An exemplary training procedure is the following:

1. Initialize all probability tables: n(v|N), r(ρ|R), and t(τ|τ).

2. Reset all counters: c(v,N), c(ρ,R), and c(τ|τ).

3. For each pair <ε,f> in the training corpus,

• • For all θ, such that f=Str(θ(ε)),
    • Let cnt=P(θ|ε/Σ_{θ:Str(θ(ε))=f} P(θ|ε)
    • For i=1 . . . n,c(v_i,N(ε_i))+=cnt c(p_i,R(ε_i))+=cnt c(τ₁,τ(ε₁))+=cnt

4. For each <v,N,>, <p,R>, and <τ,τ>,n(v|N)=c(v,N)/Σ_vc(v,N)r(ρ|R)=c(ρ,R)/Σ_pc(ρ,R)t(τ|τ)=c(τ,τ)/Σ_τc(τ,τ)

5. Repeat steps 2-4 for several iterations.

An EM algorithm for the translation model may implement a graph structure 500 of a pair <ε,f>, as shown in FIG. 5. A graph node is either a major-node 505 or a subnode. A major-node shows a pairing of a subtree of ε and a substring of f. A subnode shows a selection of a value (ν,p,τ) for the subtree-substring pair.

Let f_k^l=f_k . . . f_k+(l−1) be a substring of f from the word f_k with length l. A subtree ε_i is a subtree of ε below ε_i. Assume that a subtree ε₁ is ε.

A major node ν(ε_l,f_k^l) is a pair of a subtree and a substring f_k^l. The root of the graph is ν(ε_l,f_k^l), where L is the length of f. Each major-node connects to several ν-subnodes 510 v(ν;ε₁; f_k^l), showing which value of ν is selected. The arc between ν(ε₁,f_k^l) and v(ν;ε₁; f_k^l) has weight P(ν|ε).

A ν-subnode v(ν;ε₁; f_k^l) connects to a final-node with weight P(τ|ε₁) if ε₁ is a terminal node in ε. If ε_i is a non-terminal node, a ν-subnode connects to several ρ-subnodes v(ρ;ν;ε₁; f_k^l) 515, showing a selection of a value ρ. The weight of the arc is P(ρ|ε_i).

A ρ-subnode 515 is then connected to π-subnodes v(π;ρ;ν;ε₁; f_k^l) 520. The partition variable, π, shows a particular way of partitioning f_k^l.

A π-subnode v(π;ρ;ν;ε₁; f_k^l) is then connected to major-nodes which correspond to the children of ε_i and the substring of f_k^l, decided by <ν, p, τ>. A major-node can be connected from different π-subnodes. The arc weights between ρ-subnodes and major nodes are always 1.0.

This graph structure makes it easy to obtain P(Θ|ε) for a particular Θ and Σ_{θ:Str(θ(ε))=f} P(Θ|ε). A trace starting from the graph root, selecting one of the arcs from major-nodes, ν-subnodes, and ρ-subnodes, and all the arcs from the π-subnodes, corresponds to a particular Θ, and the product of the weight on the trace corresponds to P(Θ|ε). Note that a trace forms a tree, making branches at the π-subnodes.

We define an alpha probability and a beta probability for each major-node, in analogy with the measures used in the inside-outside algorithm for probabilistic context free grammars. The alpha probability (outside probability) is a path probability from the graph root to the node and the side branches of the node. The beta probability (inside probability) is a path probability below the node.

The alpha probability for the graph root, α(ε₁,f₁^L), is 1.0. For other major-nodes,α(ν)=Σ α(Parent_M(s))·{P(ν|ε)Pρ|ε)Πβ(ν′)}

• • εParent_π(ν) ν′εChild_π(s)
    • ν′≠νwhere Parent_π(ν) is a set of π-subnodes which are immediate parents of ν, Child_π(s) is a set of major-nodes which are children of π-subnodes s, and Parent_M(s) is a parent major-node of π-subnodes s (skipping ρ-subnodes, and ν-subnodes). P(ν|ε) and P (ρ|ε) are the arc weights from Parent_M(s) to s.

The beta probability is defined asβ(ν)=β(ε_i,f_k^l) if ε_i is a terminal

$\begin{array}{c}\beta \left(\nu \right)=\beta \left({\varepsilon }_i,f_k^l\right)\mathrm{if}{\varepsilon }_i\mathrm{is}a\mathrm{terminal}\\ =\{\sum ^{P\left(\tau |{\varepsilon }_i\right)}P\left(v|{\varepsilon }_i\right)\sum _{\rho }P\left(\rho |{\varepsilon }_i\right)\sum _{\pi }\underset{j}{\Pi }\beta \left({\varepsilon }_j,f_{k^{\prime }}^{l^{\prime }}\right)\mathrm{if}{\varepsilon }_i\mathrm{is}a\mathrm{non}\text{-}\mathrm{terminal},\end{array}$ non-terminal,where ε_j is a child of ε_i and f_k′^l′is a proper partition of f_k^l.

The counts c(ν, N), c(ρ, R), and c(τ, τ) for each pair <ε, f> are,

$\begin{array}{c}c\left(v,N\right)=\sum _{\underset{{\varepsilon }_i:N\left({\varepsilon }_i\right)=N}{k,l}}\left\{\alpha \left({\varepsilon }_i,f_k^l\right)P\left(v|{\varepsilon }_i\right)\sum _{p}P\left(p|{\varepsilon }_i\right)\sum _{\pi }\underset{j}{\Pi }\beta \left({\varepsilon }_j,f_{k^{\prime }}^{l^{\prime }}\right)\right\}/\beta \left({\varepsilon }_1,f_1^L\right)\\ c\left(\rho ,R\right)=\sum _{\underset{{\varepsilon }_{i}R\left({\varepsilon }_i\right)=R}{k,l}}\left\{\alpha \left({\varepsilon }_i,f_k^l\right)P\left(p|{\varepsilon }_i\right)\sum _{v}P\left(v|{\varepsilon }_i\right)\sum _{\pi }\underset{j}{\Pi }\beta \left({\varepsilon }_j,f_{k^{\prime }}^{l^{\prime }}\right)\right\}/\beta \left({\varepsilon }_1,f_1^L\right)\\ c\left(\tau ,\tau \right)=\sum _{\underset{{\varepsilon }_i:\tau \left({\varepsilon }_i\right)=\tau }{k,l}}\{\alpha \left({\varepsilon }_i,f_k^l\right)P\left(\tau |{\varepsilon }_1,f_1^L\right)\end{array}$

From these definitions,Σ_{θ:Str(θ(ε))=f}P(Θ|ε)=β(ε₁,f₁^L).

The counts c(ν|N), c(ρ|R), and c(τ|T) for each pair <ε, f> are also in FIG. 5. Those formulae replace the step 3 in the training procedure described above for each training pair, and these counts are used in step 4.

The graph structure is generated by expanding the root node ν(ε₁,f_l^L). The beta probability for each node is first calculated bottom-up, then the alpha probability for each node is calculated top-down. Once the alpha and beta probabilities for each node are obtained, the counts are calculated as above and used for updating the parameters.

The complexity of this training algorithm is O(n³|ν∥ρ∥π|). The cube comes from the number of parse tree nodes (n) and the number of possible French substrings (n²).

In an experiment, 2121 translation sentence pairs were extracted from a Japanese-English dictionary. These sentences were mostly short ones. The average sentence length was 6.9 for English and 9.7 for Japanese. However, many rare words were used, which made the task difficult. The vocabulary size was 3463 tokens for English, and 3983 tokens for Japanese, with 2029 tokens for English and 2507 tokens for Japanese occurring only once in the corpus.

A POS tagger (described in E. Brill, Transformation-based error-driven learning and natural language processing: A case study in part of speech tagging. Computational Linguistics, 21(4), 1995) and a parser (described in M. Collins. Head-Driven Statistical Models for Natural Language Parsing. Ph.D. thesis, University of Pennsylvania, 1999.) were used to obtain parse trees for the English side of the corpus. The output of the parser was modified in the following way. First, to reduce the number of parameters in the model, each node was re-labeled with the POS of the node's head word, and some POS labels were collapsed. For example, labels for different verb endings (such as VBD for -ed and VBG for -ing) were changed to the same label VB. There were then 30 different node labels, and 474 unique child label sequences.

Second, a subtree was flattened if the node's head word was the same as the parent's head word. For example, (NN1 (VB NN2)) was flattened to (NN1 VB NN2) if the VB was a head word for both NN1 and NN2. This flattening was motivated by various word orders in different languages. An English SVO structure is translated into SOV in Japanese, or into VSO in Arabic. These differences are easily modeled by the flattened subtree (NN1 VB NN2), rather than (NN1 (VB NN2)).

The training procedure resulted in tables of estimated model parameters. FIG. 4 shows part of those parameters obtained by the training above.

A number of embodiments have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims.

Claims

1. A method for translating natural languages using a statistical translation system, the method comprising: parsing a first string in a first language into a parse tree using a statistical parser included in the statistical machine translation system, the parse tree including a plurality of nodes, one or more of said nodes including one or more leafs, each leaf including a first word in the first language, the nodes including child nodes having labels;determining a plurality of possible reorderings of one or more of said child nodes including one or more of the leafs using the statistical translation system, the reordering performed in response to a probability corresponding to a sequence of the child node labels;determining a probability between 0.0000% and 100.0000%, non-inclusive, of the possible reorderings by the statistical translation system;determining a plurality of possible insertions of one or more words at one or more of said nodes using the statistical translation system;determining a probability between 0.0000% and 100.0000%, non-inclusive, of the possible insertions of one or more words at one or more of said nodes by the statistical translation system;translating the first word at each leaf into a second word corresponding to a possible translation in a second language using the statistical translation system; anddetermining a total probability between 0.0000% and 100.0000%, non-inclusive, based on the reordering, the inserting, and the translating by the statistical translation system.

2. The method of claim 1, wherein said translating comprises translating the first word at each leaf into a second word in the second language in response to a probability of a correct translation.

3. The method of claim 1, wherein said inserting comprises inserting one of a plurality of NULL words at one or more of said nodes.

4. The method of claim 1, wherein said inserting comprises inserting the word at an insert position relative to a node.

5. The method of claim 4, wherein the insert position comprises one of a left position, a right position, and no position.

6. The method of claim 1, wherein the parse tree includes one or more parent nodes and a plurality of child nodes associated with the one or more parent nodes, the parent nodes having parent node labels and the child nodes having child node labels.

7. The method of claim 6, wherein said inserting comprises inserting one of the plurality of words at a child node in response to the child node label and the parent node label.

8. The method of claim 1, further comprising: generating a second string including the second word at each leaf.

9. The method of claim 8, further comprising: assigning a translation probability to the second string.

10. An apparatus for translating natural languages, the apparatus comprising: a reordering module operative to determine a plurality of possible reorderings of nodes in a parse tree, said parse tree including the plurality of possible nodes, one or more of said nodes including a leaf having a first word in a first language, the parse tree including a plurality of parent nodes having labels, each parent node including one or more child nodes having a label, the reordering module including a reorder table having a reordering probability associated with reordering a first child node sequence into a second child node sequence;an insertion module operative to determine a plurality of possible insertions of an additional word at one or more of said nodes and to determine a probability between 0.0000% and 100.0000%, non-inclusive, of the possible insertions of of the additional word;a translation module operative to translate the first word at each leaf into a second word corresponding to a possible translation in a second language;a probability module to determine a plurality of possible reorderings of a probability between 0.0000% and 100.0000%, non-inclusive, of said plurality of possible reorderings of one or more of said nodes and to determine a total probability between 0.0000% and 100.0000%, non-inclusive, based on the reorder, the insertion, and the translation; anda statistical translation system operative to execute the reordering module, the insertion module, the translation module, and the probability module to effectuate functionalities attributed respectively thereto.

11. The apparatus of claim 10, wherein the translation module is further operative to generate an output string including the second word at each leaf.

12. The apparatus of claim 11, wherein the translation module is operative to assign a translation probability to the output string.

13. The apparatus of claim 11, further comprising a training module operative to receive a plurality of translation sentence pairs and train the apparatus using said translation pairs and an Expectation Maximization (EM) algorithm.

14. The apparatus of claim 10, wherein the insertion module includes an insertion table including the probability associated with inserting the additional word in a position relative to one of the child nodes.

15. The apparatus of claim 14, wherein the insertion probability is associated with a label pair including the label of said one or more child node and the label of the parent node associated with said child node.

16. The apparatus of claim 10, wherein the insertion module includes an insertion table including an insertion probability associated with inserting one of a plurality of additional words.

17. The apparatus of claim 16, wherein the additional word comprises a NULL word.

18. An article comprising a non-transitory machine readable medium including machine-executable instructions, the instructions operative to cause a machine to: parse a first string in a first language into a parse tree, the parse tree including a plurality of nodes, one or more of said nodes including one or more leafs, each leaf including a first word in the first language, the nodes including child nodes having labels;determine a plurality of possible reorderings of one or more of said child nodes including one or more of the leafs, the reordering performed in response to a probability corresponding to a sequence of the child node labels;determine a probability between 0.0000% and 100.0000%, non-inclusive, of the plurality of possible reorderings;determining a plurality of possible insertions of one or more words at one or more of said nodes;determine a probability between 0.0000% and 100.0000%, non-inclusive, of the plurality of possible insertions at one or more of said nodes;translate the first word at each leaf into a second word corresponding to a possible translation in a second language; anddetermine a total probability between 0.0000% and 100.0000%, non-inclusive, based on the reordering, the inserting, and the translating, wherein the nodes include child nodes having labels, and wherein said reordering comprises reordering one or more of said child nodes in response to a probability corresponding to a sequence of the child node labels.