Datasets:

WINGNUS
/

ACL-OCL

	{
	"paper_id": "W89-0210",
	"header": {
	"generated_with": "S2ORC 1.0.0",
	"date_generated": "2023-01-19T03:45:19.203562Z"
	},
	"title": "A Sequential Truncation Parsing Algorithm based on the Score Function",
	"authors": [
	{
	"first": "Keh-Ylh",
	"middle": [],
	"last": "Su",
	"suffix": "",
	"affiliation": {},
	"email": ""
	},
	{
	"first": "Jong-Nae",
	"middle": [],
	"last": "Wang",
	"suffix": "",
	"affiliation": {},
	"email": ""
	},
	{
	"first": "Mei-Hul",
	"middle": [],
	"last": "Su",
	"suffix": "",
	"affiliation": {},
	"email": ""
	},
	{
	"first": "Jing-Shin",
	"middle": [],
	"last": "Chang\"'",
	"suffix": "",
	"affiliation": {
	"laboratory": "",
	"institution": "National Tslng Hua University",
	"location": {
	"settlement": "Hslnchu",
	"country": "Taiwan, R.O.C. \""
	}
	},
	"email": ""
	}
	],
	"year": "",
	"venue": null,
	"identifiers": {},
	"abstract": "In a natural language processing system, a large amount o f ambiguity and a large branching factor are hindering factors in obtaining the desired analysis for a given sentence in a short time. In this paper, we are proposing a sequential truncation parsing algorithm to reduce the searching space and thus lowering the parsing time. The algorithm is based on a score function which takes the advantages o f probabilistic characteristics o f syntactic information in the sentences. A preliminary test on this algorithm was conducted with a special version o f our machine translation system, the ARCHTRAN, and an encouraging result was observed. Motivation In a natural language processing system, the number o f possible analyses associated with a given sentence is usually large due to the ambiguous nature o f natural languages. But, it is desirable that only the best one or two analyses are translated and passed to the post-editor in order to reduce the load o f the post-editor. Therefore, in a practical machine translation system, it is important to obtain the best (in probabilistic sense) syntax tree having the best semantic interpretation within a reasonably short time. This is only possible with an intelligent parsing algorithm that can truncate undesirable analyses as early as possible. There are several methods to accelerate the parsing process [Su 88b], one o f which is to decrease the size o f the searching space. This can be accomplished with a scored parsing algorithm that truncates unlikely paths as early as possible [Su 87a, 87b] and hence decreases the parsing time. As for the searching strategy for the scored parsing algorithm, it may be either parallel or sequential. But in our system , a time limit is used to stop the parsing process when a sentence is taking too long to parse because its length or because it has a very com plicated structure. Therefore, the sequential searching strategy is better for us than the parallel approach because-95-International Parsing Workshop '89",
	"pdf_parse": {
	"paper_id": "W89-0210",
	"_pdf_hash": "",
	"abstract": [
	{
	"text": "In a natural language processing system, a large amount o f ambiguity and a large branching factor are hindering factors in obtaining the desired analysis for a given sentence in a short time. In this paper, we are proposing a sequential truncation parsing algorithm to reduce the searching space and thus lowering the parsing time. The algorithm is based on a score function which takes the advantages o f probabilistic characteristics o f syntactic information in the sentences. A preliminary test on this algorithm was conducted with a special version o f our machine translation system, the ARCHTRAN, and an encouraging result was observed. Motivation In a natural language processing system, the number o f possible analyses associated with a given sentence is usually large due to the ambiguous nature o f natural languages. But, it is desirable that only the best one or two analyses are translated and passed to the post-editor in order to reduce the load o f the post-editor. Therefore, in a practical machine translation system, it is important to obtain the best (in probabilistic sense) syntax tree having the best semantic interpretation within a reasonably short time. This is only possible with an intelligent parsing algorithm that can truncate undesirable analyses as early as possible. There are several methods to accelerate the parsing process [Su 88b], one o f which is to decrease the size o f the searching space. This can be accomplished with a scored parsing algorithm that truncates unlikely paths as early as possible [Su 87a, 87b] and hence decreases the parsing time. As for the searching strategy for the scored parsing algorithm, it may be either parallel or sequential. But in our system , a time limit is used to stop the parsing process when a sentence is taking too long to parse because its length or because it has a very com plicated structure. Therefore, the sequential searching strategy is better for us than the parallel approach because-95-International Parsing Workshop '89",
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	"eq_spans": [],
	"section": "Abstract",
	"sec_num": null
	}
	],
	"body_text": [
	{
	"text": "wc arc likely to have some complete syntax trees to work with even if the parsing was suspended abnormally when its time expires. On the other hand, the parallel approach will not have this advantage because none of the on-going paths have traversed to the end.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "",
	"sec_num": null
	},
	{
	"text": "In this paper, we are proposing a sequential truncation algorithm for parsing sentences efficiendy. This algorithm employs the score function we proposed in [Su 88a]. However, this algorithm is different from the one proposed in [Su 87a , 87b], which described a parallel truncation algorithm for scored parsing. Here, we are adopting a sequential truncation method. While we are using this sequential approach, a large speed-up in the parsing time has been .jb served. ",
	"cite_spans": [
	{
	"start": 229,
	"end": 236,
	"text": "[Su 87a",
	"ref_id": null
	}
	],
	"ref_spans": [],
	"eq_spans": [],
	"section": "",
	"sec_num": null
	},
	{
	"text": "where w i to w n stands for the words in the given sentence and the last three product terms are semantic score, syntactic score and lexical score respectively. Since we are using just the syntactic information in our current implementation, we will focus only on the syntactic aspect o f this score function (i.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "S C O R E (Sem ,, S y n j L e x t ) = P ( S e m t' S y n j iL e x k \\ w \\ .. .w n ) = P ( S e m t \\Syrij'L exje w i \" W n) * P (S yrij \|Zexjt(u;i...u;n) * P ( L e x^w i^w n ) ^ ^ = S C O R E atm { S e m i ) * S C O R E syn ( S y n j ) * S C O R E u x ( L e x *) ,",
	"sec_num": null
	},
	{
	"text": ", where V! to v n are the lexical categories corresponding to w i to wn).",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "e. S C O R E jyn(Synj), which can be approximated by S C O R E s y n { S y n j ) \u00ab P ( S y n j \\ L e x k ) = P { S y r i j \\ v i \" v n )",
	"sec_num": null
	},
	{
	"text": "To show the mechanism informally, first refer to the syntax tree in Fig. 1 . ",
	"cite_spans": [],
	"ref_spans": [
	{
	"start": 68,
	"end": 74,
	"text": "Fig. 1",
	"ref_id": null
	}
	],
	"eq_spans": [],
	"section": "e. S C O R E jyn(Synj), which can be approximated by S C O R E s y n { S y n j ) \u00ab P ( S y n j \\ L e x k ) = P { S y r i j \\ v i \" v n )",
	"sec_num": null
	},
	{
	"text": "The syntax score o f the tree in Fig. 1 can be formulated as the following conditional probability equation, where li and r* are the left and right contexts of the reducing symbols:",
	"cite_spans": [],
	"ref_spans": [
	{
	"start": 33,
	"end": 39,
	"text": "Fig. 1",
	"ref_id": null
	}
	],
	"eq_spans": [],
	"section": "96-",
	"sec_num": null
	},
	{
	"text": "S C O R E s y n ( S y n A ) = P .L 2 \\ L \\ ) = P ( L s \\L 7. . L 2 , L \\ ) * P (L j\\L s...L \\) * ... * P ( L 2 \\L \\) ^ ^( {^} \| { h , B , C , r j } ) * P ( { C } \| { l e , F , G , r 6 } ) * ... * P ( { \u00a3 > } \| { ' / l i u ; l f r 1 } )",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "96-",
	"sec_num": null
	},
	{
	"text": "Eq. 2 can be further reduced to the following equation if only one left and one right context symbol are considered where \"0\" is the null symbol.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "96-",
	"sec_num": null
	},
	{
	"text": "EQUATION",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [
	{
	"start": 0,
	"end": 8,
	"text": "EQUATION",
	"ref_id": "EQREF",
	"raw_str": "S C O R E Sy n ( S y n A ) \u00ab P ( {^} \| { 0 , B , C , 0 } ) * P ( { C } \| { B , F , G , 0 } ) * ... * P ( { D } \| { 0 , u , 1 , U ;2 } )",
	"eq_num": "(3)"
	}
	],
	"section": "96-",
	"sec_num": null
	},
	{
	"text": "If we want to calculate the score at the point where a word is just being fetched (compact multiple reductions and one shift into one step), the S C O R E^n f S y r i A ) can also be approximated into the follow ing equation. The parser will use the depth-first strategy to traverse the searching tree. But during the searching process, the parser compares the score o f each path accumulated so far with a running threshold C(ai) (a detailed definition will be given in the follow ing section) at each step i when the next word is fetched. If the score o f the path is less than the running threshold C(ai), it will be truncated, i.e. blocked, and the next path will be tried. This process continues until we get the first com plete parse tree (i.e. when the whole sentence is reduced to a S node). After we obtain the first com plete parse tree, a lower bound for the scores is acquired. The parser w ill continue to traverse other pathes, but from now on, the score o f each path will also be compared with the final accumulated score o f the first complete parse tree in addition to be compared with the running threshold. This additional comparison is similar to the branch and bound strategy em ployed in many A l applications [Wins 84] and it w ill accelerate the parsing process further. The whole process is shown in the flow chart in Fig. 3 . If the test fails in either case, this path w ill be truncated. Continuing in this manner, we may get a second complete parse tree which has a final score higher than the first one. In this case, w e w ill replace the low er bound with the final score o f the second parse tree and repeat the whole process until the end o f the entire searching process.",
	"cite_spans": [],
	"ref_spans": [
	{
	"start": 1344,
	"end": 1350,
	"text": "Fig. 3",
	"ref_id": null
	}
	],
	"eq_spans": [],
	"section": "96-",
	"sec_num": null
	},
	{
	"text": "If all the paths are blocked without arriving at any com plete parse tree, we can adopt one o f two possible strategies. First, we could loosen the running thresholds, i.e. lowering the C (qO, and try the deepest path gone so far again. Second, we can process this sentence in fail-soft mode. The fail-soft mechanism will skip and discard the current state and attempts to continue the parsing at som e later point",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "96-",
	"sec_num": null
	},
	{
	"text": "The effectiveness o f the sequential truncation algorithm depends on the distribution of scores o f the database and the input sentences. As we can see, for each syntax tree can be expressed as the product o f a sequence o f conditional probability as shown in Eq. 4. Each term in the product corresponds to a transition between two ''shift\" actions and is evaluated immediately after a ''shift\". Taking the logarithm on both sides o f Eq. 4, we get the follow ing equation where X* denotes a sequence o f phrase levels at i-th step and L is the length o f the sentence.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "96-",
	"sec_num": null
	},
	{
	"text": "1=1 j If we define yj = ^ log P ( X i \\ X i -\\ ) , then yj denotes the accumulated logarithmic score i= l up to the j-th word which is also the j-th shift of the sentence.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "L log (S C O R E s)l\" ( S y n ) ) = J^lo g P { X ,",
	"sec_num": null
	},
	{
	"text": "Suppose we have M sentences with their correct parse trees in the database. For each parse tree, we can evaluate yj by using the logarithmic score function defined before. So for the k-th sentence in the database, we obtain a sequence y, y , , where ydenotes the accumulated logarithmic score o f the k-th sentence and L denotes the length o f the k-th sentence.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "L log (S C O R E s)l\" ( S y n ) ) = J^lo g P { X ,",
	"sec_num": null
	},
	{
	"text": "If wc regard each parse tree in the database as a sample point in a probability outcome space, we may regard Y* as a random variable which maps each parse tree into an accumulated logarithmic score (note, for a sentence with length L^, it will be associated, with random variables : Vi, V2,...\u00a3\")\u2022 So y, with k from 1 to M, will be the samples o f the random variable Yi. Since each sentence has its own length, the number of samples in the database for different random variable Yi will not be the same.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "L log (S C O R E s)l\" ( S y n ) ) = J^lo g P { X ,",
	"sec_num": null
	},
	{
	"text": "Using the samples in the database, we can draw a histogram for each Yi. We then approximate each histogram by a continuous density function / y ( y ) . To allow a fraction Qi, say 99%, of the best parse trees to pass the test at step i, we can set a constant C(ci) such that P{YX> C ( a t)) = a t . For each path, Yj is the random variable o f the accumulated logarithmic score up to the i-th shift, and C (ai) is the running threshold that we will use to compare with the running accumulated logarithmic score at step i. Those paths with running accumulated logarithmic score yi less than C(ci) would be blocked. Using the notation defined above, the probability o f obtaining the desired parse tree for a sentence with length (1 -f t ) , which is a small portion o f the original searching space generated by a full path searching algorithm. Therefore the efficiency o f parsing is increased. Since f t in Fig. 4a is less than that in Fig. 4b, which correspond to the situation that has a large expectation difference (E[Y,]-E[Zi] ) and a small variance ratio (Var[Yi]/Var{Zi]), the underlying grammar that has the property of Fig. 4b would benefit most from this algorithm. In addition, we can see that if we increase the running threshold C(c*i), we will get a greater fa and a lower aj.",
	"cite_spans": [],
	"ref_spans": [
	{
	"start": 298,
	"end": 412,
	"text": ". For each path, Yj is the random variable o f the accumulated logarithmic score up to the i-th shift, and C (ai)",
	"ref_id": null
	},
	{
	"start": 911,
	"end": 1037,
	"text": "Fig. 4a is less than that in Fig. 4b, which correspond to the situation that has a large expectation difference (E[Y,]-E[Zi]",
	"ref_id": null
	},
	{
	"start": 1134,
	"end": 1141,
	"text": "Fig. 4b",
	"ref_id": null
	}
	],
	"eq_spans": [],
	"section": "L log (S C O R E s)l\" ( S y n ) ) = J^lo g P { X ,",
	"sec_num": null
	},
	{
	"text": "The parsing efficiency w ill thus increase, but the probability (i.e. [ ] a ,) that we will get the \u00bb=i desired parse tree would decrease. How to select a good C(aO to achieve a desired parsing success rate would be discussed in the following section.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "Lk",
	"sec_num": null
	},
	{
	"text": "Using the model given in the last section, the probability that we w ill get the global optimal solution, i.e. the parse tree with the largest probability, for a sentence with length L In this way, we w ill get a more complicated expression for g (a i...a L ) , but it can still be solved in the same way.",
	"cite_spans": [],
	"ref_spans": [
	{
	"start": 185,
	"end": 259,
	"text": "In this way, we w ill get a more complicated expression for g (a i...a L )",
	"ref_id": null
	}
	],
	"eq_spans": [],
	"section": "How to set the running threshold",
	"sec_num": null
	},
	{
	"text": "The running threshold C(o;i) can now be computed off-line by selecting different Kl for different sentence length L. We w ill call this set o f C (a 0 the \"static running threshold\", because once they are computed, they will not be changed during the sentence parsing. However, if we arrive at a complete parse tree with much higher final accumulated running score than the final accumulated running threshold, then even if a path can pass all the accumulated running thresholds it might still be discarded when it is being compared with the final accumulated running score. So, the running threshold should be adjusted to reflect a high final accumulated running score. Therefore, it would be better if the running threshold is changed to C '(ai)= C (ai)+ A C (aj), where A C (a i) is set to 7 * (y* -C ( a ,) ) , where 0< 7<1",
	"cite_spans": [],
	"ref_spans": [
	{
	"start": 795,
	"end": 810,
	"text": "* (y* -C ( a ,)",
	"ref_id": null
	}
	],
	"eq_spans": [],
	"section": "How to set the running threshold",
	"sec_num": null
	},
	{
	"text": "and y* is the accumulated logarithmic score o f the current best parse tree at the i-th step, and 7 is a tunning constant pre-selected by the system designer. C'(aj) is then the \"dynamic running threshold\". Using the dynamic running threshold, the efficiency o f parsing would be further improved.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "How to set the running threshold",
	"sec_num": null
	},
	{
	"text": "If it so happen that all the pathes are blocked before any complete parse tree is formed, we can find the deepest path (let us assuming it to be at the j-th step) among the blocked ones and continue it with a lowered running threshold o f C'(aj)=y'] , where y' is the score o f this path at the j-th step. Since the procedure to lower the running threshold is quite complicated and uses up memory space in run time, it might be better just invoke the fail-soft mechanism for sentences whose paths are all blocked.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "How to set the running threshold",
	"sec_num": null
	},
	{
	"text": "We com pleted two preliminary testings of truncation algorithm with special versions of our English-Chinese MT system and a database o f 1430 sentences.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "Testing",
	"sec_num": null
	},
	{
	"text": "In the first experiment, the sentence parsing time needed by a charted parser that uses bottom-up parsing with top-down filtering is compared with the time needed by the same charted parser with truncation mechanism. From the test, we found that the average sentence parsing time by the charted parser with truncation is improved by a factor o f four. For some sentences, the improvement can go as high as a factor o f twenty. This result is encouraging because m inim izing parsing *time is critical to a practical MT system. Nevertheless, we noted that our output quality has degraded slightly. B y this, we mean that the best selected tree produced by the charted parser with no truncation is not among the trees produced by the charted parser with truncation. Exploring this problem further, we discovered that the chart [Wino 83] used during parsing is in conflict with the truncation mechanism. The reason for having chart is to be able to store all subtrees that were parsed in previous path traversal. So, when we backtrack to the next path and arrive at the same range o f inputs, the same subtrees can be used again without reparsing. However, the idea behind the truncation mechanism is to discard subtree in the context in which it has low probability. Therefore, if w e adopt the truncation mechanism during parsing, not every subtree between a string o f inputs is successfully constructed and stored into the chart. For exam ple, in One solution to this incompatibility problem is to mark the sections o f the chart that are complete. Hence, if an incomplete subchart is encountered again, it w ill be reparsed. On the other hand, if a com plete set o f chart is encountered, the subtrees can be copied directly from the chart. Another solution is to suspend the truncation mechanism when a set is being tried the first time. And if subtrees are copied directly from the chart, the truncation mechanism resumes its normal function. In this way, it is guaranteed that every subchart in the chart is complete. Both o f these solutions increase our sentence parsing time as the overhead. This compromise, however, is unavoidable if the advantages o f using chart are to be maintained.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "Testing",
	"sec_num": null
	},
	{
	"text": "In the second experiment, we converted the charted parser for the first experiment into one with sequential searching strategy and without the use o f the chart. Similar sentence parsing test is conducted for this chartless parser but with a smaller analyses grammar. The result shows that the total parsing time for this parser with truncation mechanism added is better than the same parser without truncation by the factor o f three. ",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "Testing",
	"sec_num": null
	},
	{
	"text": "In a natural language processing system, it is important to arrive at a good analysis for a sentence in a relatively short time. One way to achieve this is to decrease the parsing time by reducing the searching space. We have proposed a sequential truncation algorithm with a score function to achieve this goal.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "Conclusion",
	"sec_num": null
	},
	{
	"text": "In this sequential truncation strategy, a sequence o f running thresholds are used to bound the searching space during each step o f the scored parsing. In addition, a path can also be blocked by the branch-and-bound mechanism if its accumulated score is lower than that o f an already completed parse tree. There are several reasons for adopting this strategy. First, the first parse tree with a moderate quality can be found quickly and easily. Second, the running threshold serves to truncate part of the path that is quite unlikely to lead to the best analysis, and thus greatly reduces the searching space.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "Conclusion",
	"sec_num": null
	},
	{
	"text": "We have made a pilot test on the truncation mechanism with a charted parser that adopts bottom-up parsing with top-down '\"tering. With a database of 1430 sentences, the result indicates an average improvement ir le sentence parsing time by the factor o f four (for some sentences the improvement goes as . gh as a factor o f twenty). However, we also discovered an incompatibility problem between the use o f chart and the truncation mechanism. In another pilot test we conducted on the truncation mechanism, the sentence parsing time is tested for a chartless parser that adopts sequential parsing strategy. The result shows an improvement in parsing time by a factor o f three for the inclusion of the truncation mechanism. These encouraging results demonstrate a great promise for the sequential truncation strategy.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "Conclusion",
	"sec_num": null
	},
	{
	"text": "As our current research topic, we shall resolve the incompatibility problem between the chart and the truncation algorithm and include the solution into our working MT system, the ARCHTRAN.",
	"cite_spans": [],
	"ref_spans": [],
	"eq_spans": [],
	"section": "Conclusion",
	"sec_num": null
	}
	],
	"back_matter": [],
	"bib_entries": {
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	"FIGREF0": {
	"uris": null,
	"type_str": "figure",
	"text": "system, the best analysis is selected base on its score. Several scoring mechanisms have been proposed in the literatures [Robi 83, Benn 85, Gars 87, Su 88a]. The one we adopt is the score function based on the conditional probability we proposed in [Su 88a]. How to select the best analysis o f a sentence is now convened into the problem o f finding the semantic interpretation (Semi), the syntactic structure (Synj) and the lexical categories (LeXk) that maximize the conditional probability o f the following equation,",
	"num": null
	},
	"FIGREF2": {
	"uris": null,
	"type_str": "figure",
	"text": "^8,\u00a37,\u00a361^5,\u00a34...\u00a31) * P (\u00a351^4,\u00a33...\u00a31) * P (LitLz\\L2,L\\) * P(Ij2\\Li) (4) * P(LsL7 L6 \\L5) P(Ls\\L<) P(L<Lz\\L2 ) P(L2 \\L1) P ( L s \\L 5) * P ( L s \\L<) * P ( L < \\ L 2 ) * P ( L 2III) Two assumptions were made in formulating Eq. 2 -4 . First, it is assumed that the forming o f phrase level i is only dependent on its immediate lower phrase level, since most information percolated from other lower levels is contained in that level. And second, a reduction is only locally context sensitive to its left or right context at each phrase level. This assumption is also supported in other systems as w ell [Marc 80, Gars 87]. A simulation based solely on this syntactic score was conducted and reported in [Su 88a] with a full-path searching algorithm. The result shows that the correct syntactic structures o f over 85% o f the test sentences were successfully picked when a total o f three local left and right context sym bols were consulted. The Sequential Truncation Algorithm Using the score function defined in the previous section, we w ill present the idea of sequential truncation algorithm with Fig. The searching tree Each path in Fig. 2 corresponds to a possible derivation of a given sentence.",
	"num": null
	},
	"FIGREF3": {
	"uris": null,
	"type_str": "figure",
	"text": "be Yi a \u00bb* \u00bb= i If we set Zi as the random variable which maps all the possible paths o f all the sentences we want to parse into the accumulated logarithmic score at i-th word, then all the paths, whether they can reach the final state o f the searching tree or not, w ill have a set of running accumulated logarithmic scores. Fig. 4 shows the relation between the density function ( 2) o f running score o f the input text and the density function f y (y) of cumulative score o f the database. In the figure, the dashed lines are the means o f the density functions. Since the step-wise cumulative score in the database is evaluated using the correct parse tree that we have selected, we would expect that the expectation value o f Yi w ill be greater than that o f Zi, that is, E[Yi] > E[Zi]; and the variance of Yi is less than that o f Zi, that is Var[Yi]<Var[Relationship between the running sccre cf the inpU text and the cumrnulative score of the database Let f t denotes F'z (C(cti))y whereF'z (z)is the cumulated distribution function o f Zi, then f t is the probability that a path w ill be truncated at the i-th step o f the searching tree. By using this sequential truncation method, the searching space would then be approximately reduced to",
	"num": null
	},
	"FIGREF4": {
	"uris": null,
	"type_str": "figure",
	"text": "is K l = [ ] <\" where K l is a constant pre-selected by the system designer as a compromise between the parsing time and the post-editing time. Assuming that the average branching factor for each path at each stage is a constant N, then the average total number of paths we have to try is : 9 ( < i = N + N * (1 -fa) * N + N * (1 -fix) * N * (1 -h ) * N + -= N * ( \\ + N * h (a \\) + N 2 * h ( a i ) * h (012) + ...) in order to minimize the path number, the relation h ( a \\) < h (0:2) ... < h (a^) must holds because h(aj) has a larger coefficient than h(ai+i). The problem o f selecting an appropriate running threshold C(aO is now converted into one o f minim izing g(ai...a:L) under the constraint o f a{ = K l-Taking the logarithm on 1=1 L both sides, we get \u00a3 log a t = log K l . Then the Lagrange multiplier A is used to get 1=1 L g* ^ * Y j \u00b09 a \u00ab-Taldng the partial derivative o f g* with respects 1=1 to a i...a L , we w ill get the follow ing equations : l) variables, which are a i...a L , and A, and (L + l) equations. So, can be solved by the numerical method. Since a* is usually very close to 1, we can linearize the function h (ai) in the region around <*=1 and approximate by h ( a ,) % a a,-+ b. In this way, w e can substitute h(aj) in the above equation by a * a* -I-b to sim plify the calculation.During our derivation, we have assumed that the average branching factor at each stage is a constant N. This constraint can be relaxed by assuming the average branching factor at i-th stage to be N*.",
	"num": null
	},
	"FIGREF5": {
	"uris": null,
	"type_str": "figure",
	"text": "there are two possible subtrees between b and c when the pathes in the block A are expanded.Lj R2 c a t ext Chart with truncation mechanismInFig. 5, one o f the subtrees is discarded and the other is stored into the chart. There are two reasons why a subtree may be discarded. First, it might be caused by a natural language's constraints on the context dependency. Second, a subtree might be discarded because o f its small running accumulated score (and thus truncated by the truncation mechanism.) Either will leave us a chart with incomplete subchart. So, this will result in the best possible tree being missing as a side-effect o f using this chart. For instance, inFig. 5, the best tree might be the second subtree with the left context o f L 2 and with the right context o f R2 (i.e., its probability is the highest.) But, since the path expansion starting from the left context o f Li has the second subtree discarded because its probability under the context o f Li and Ri is small, the best tree w ill never be formed. Therefore, with a chart having incomplete subcharts, the possibility o f obtaining the best tree is determined by the pathes traversed before.",
	"num": null
	},
	"FIGREF6": {
	"uris": null,
	"type_str": "figure",
	"text": "the positive results o f the above two experiments, we have shown the inclusion o f the sequential truncation algorithm is advantageous for a MT system. In addition, w e have also shown the feasibility o f harmonize the use o f chart and the truncation algorithm. Currently, we are in the process o f resolving the incompatibility problem between the chart and the truncation mechanism and constructing a working system with this solution.",
	"num": null
	}
	}
	}
	}