Abstract:
A system for assigning part-of-speech tags to English text includes an improved contextual tagger which utilizes a deterministic finite state transducer to improve tagging speed such that large documents can have its sentences accurately tagged as to parts of speech to permit fast grammar checking, spell checking, information retrieval, text indexing and optical character recognition. The subject system performs by first acquiring a set of rules by examining a training corpus of tagged text. Then, these rules are transformed into a deterministic finite-state transducer through the utilization of non-deterministic transducers, a composer and a determiniser. In order to tag an input sentence, the sentence is initially tagged by first assigning each word in the sentence with its most likely part of speech tag regardless of the surrounding words in the sentences. The deterministic finite-state transducer is then applied on the resulting sequence of part of speech tags using the surrounding words and obtains the final part of speech tags. The Subject System requires an amount of time to compute the part-of-speech tags which is proportional to the number of words in the input sentence and which is independent of the number of rules it has applied.

Description:
FIELD OF INVENTION 
     This invention relates to a system that computes the parts of speech tags of English text and more particularly to a part-of-speech tagger utilizing a deterministic finite state transducer whose rules are automatically learned from a training corpus. 
     BACKGROUND OF THE INVENTION 
     English words are ambiguous with respect to their parts-of-speech. For instance a given word can function as a noun, a verb in past tense, and a verb in past participle. For example, the word &#34;left&#34; can be an adjective, as in &#34;I took a left turn&#34;; a noun, as in &#34;He is on my left&#34;; as the past tense of the verb &#34;leave&#34;, as in &#34;He left yesterday&#34;; and as the past participle of the verb leave (as in &#34;He has left&#34;). However in context English words are not ambiguous. Most applications dealing with English text need to assign the correct part-of-speech to each word in the context it appears. This problem is called part-of-speech tagging. 
     The ability to detect the sequence of parts-of-speech as they exist in a given sentence is of paramount importance for many applications involving English text such as grammar checkers, spell checkers, text retrieval, speech recognition, hand writing recognition devices, character recognition devices and text compression devices. The result of having derived parts-of-speech is a part-of-speech sequence such as &#34;PRONOUN, VERB, DETERMINER, NOUN, VERB&#34; for an input sentence &#34;I heard this band play&#34;. 
     Previous methods for assigning part-of-speech tags to English text consist of either statistically based methods or rule-based methods. Examples of statistically-based methods are the method of Kenneth Church&#39;s Stochastic Parts Program published as &#34;A Stochastic Parts Program and Noun Phrase Parser for Unrestricted Text&#34; in the Proceedings of the Second Conference on Applied Natural Language Processing, Austin Tex., 1988, or the one of Charniak, Eugene, Curtis Hendrickson, Neil Jacobson, and Mike Perkowitz published as &#34;Equations for part-of-speech tagging&#34; in the Proceedings of the AAAI 93, Ninth National Conference on Artificial Intelligence 1993, or the method of Julian Kupiec published as &#34;Robust part-of-speech tagging using a hidden markov model&#34; in the journal of Computer Speech and Language volume 6 in 1992 or the one of Ralph Weischedel, Marie Meteer, Richard Schwartz, Lance Ramshaw, and Jeff Palmucci published as &#34;Coping with ambiguity and unknown words through probabilistic models&#34; in the journal of Computation Linguistics volume 18, number 2 in 1993. An example of a rule-based method is the method of Eric Brill published as &#34;A simple rule-based part of speech tagger&#34; in the proceedings of the Third Conference on Applied Natural Language Processing in 1992. 
     Prior art methods for assigning part of speech tags are very slow since the time required to assign part of speech tags is related to the number of words in the input sentence and also to the number of rules they use. This makes the prior art systems inapplicable to very large English texts such as the contents of a library. 
     Recently, as indicated above, Brill described a rule-based tagger which performs as well as taggers based upon probabilistic models and which overcomes the limitations common in rule-based approaches to language processing. It is robust and the rules are automatically acquired. In addition, the tagger requires drastically less space than stochastic taggers. However, current implementations of Brill&#39;s tagger are considerably slower than the ones based on probabilistic models since it may require RCn elementary steps to tag an input of n words with R rules requiring at most C words of context. 
     In Brill, as an example, 200 contextual tagging rules are used, one-by-one for each word to obtain the part of speech tag. This is relatively slow because each of the rules is applied individually on each word and because the output of one rule may be changed by the output of a later rule. One reason for the relatively slowness of the Brill system is his non-deterministic approach in which the output of one rule may be changed by the output of another rule. On the other hand, a deterministic system is desireable to increase speed in which after each word is read only one part of speech choice is made; and this without requiring more than one pass on the input sentence. 
     Note that Brill&#39;s tagger is comprised of three parts, each of which is inferred from a training corpus: a lexical tagger, an unknown word tagger and a contextual tagger. For the purpose of exposition, the discussion of the unknown word tagger is postponed and the focus of the following discussion is mainly the contextual rule tagger. 
     The notation for part-of-speech tags is as follows: &#34;pps&#34; stands for third singular nominative pronoun, &#34;vbd&#34; for verb in past tense, &#34;np&#34; for proper noun, &#34;vbn&#34; for verb in past participle form, &#34;by&#34; for the word &#34;by&#34;, &#34;at&#34; for determiner, &#34;nn&#34; for singular noun and &#34;bedz&#34; tbr the word &#34;was&#34;. 
     By way of background, the lexical tagger used by Brill initially tags by assigning each word its most likely tag, estimated by examining a large tagged corpus, without regard to context. For example, assuming that &#34;vbn&#34; is the most likely tag for the word &#34;killed&#34; and &#34;vbd&#34; for &#34;shot&#34;, the lexical tagger might assign the following part-of-speech tags: 
     (1) Chapman/np killed/vbn John/np Lenon/np 
     (2) John/np Lenon/np was/bedz shot/vbd by/by Chapman/np 
     (3) He/pps witnessed/vbd Lenon/np killed/vbn by/by Chapman/np 
     Since the lexical tagger used by Brill does not use any contextual information, many words can be wrongly tagged. For example, in (1) the word &#34;killed&#34; is erroneously tagged as a verb in past participle form, and in (2) &#34;shot&#34; is incorrectly tagged as a verb in past tense. Given the initial tagging obtained by the lexical tagger, in the Subject System a contextual tagger applies a sequence of rules in order and attempts to remedy the errors made by the initial tagging. For example, the rules below might be found in a contextual tagger. 
     rule 1: vbn vbd PREVTAG np 
     rule 2: vbd vbn NEXTTAG by 
     The first rule says to change tag &#34;vbn&#34; to &#34;vbd&#34; if the previous tag is &#34;np&#34;. The second rule says to change &#34;vbd&#34; to tag &#34;vbn&#34; ff the next tag is &#34;by&#34;. Once the first rule is applied, the tag for &#34;killed&#34; in (1) and (3) is changed from &#34;vbn&#34; to &#34;vbd&#34; and the following tagged sentences are obtained: 
     (4) Chapman/np killed/vbd John/np Lenon/np 
     (5) John/np Lenon/np was/bedz shot/vbd by/by Chapman/np 
     (6) He/pps witnessed/vbd Lenon/np killed/vbd by/by Chapman/np 
     And once the second rule is applied, the tag for &#34;shot&#34; in (5) is changed from &#34;vbd&#34; to &#34;vbn&#34; resulting (8) and the tag for &#34;killed&#34; in (6) is changed back from &#34;vbd&#34; to &#34;vbn&#34; resulting (9): 
     (7) Chapman/np killed/vbd John/np Lenon/np 
     (8) John/np Lenon/np was/bedz shot/vbn by/by Chapman/np 
     (9) He/pps witnessed/vbd Lenon/np killed/vbn by/by Chapman/np 
     In Brill, the sequence of contextual rules is automatically inferred from a training corpus. A list of tagging errors, with their counts, is compiled by comparing the output of the lexical tagger to the correct part-of-speech assignment. Then, for each error, it is determined which instantiation of a set of rule templates results in the greatest error reduction. Then the set of new errors caused by applying the rule is computed and the process is reiterated until the error reduction drops below a given threshold. The following Table illustrates a set of contextual rule templates. 
     
                       TABLE I______________________________________A   B     PREVTAG        C    change A to B if previous                         tag is CA   B     PREV1OR2OR3TAG C    change A to B if previous                         one or two or three tag is CA   B     PREV1OR2TAG    C    change A to B if previous                         one or two tag is CA   B     NEXT1OR2TAG    C    change A to B if next one                         or two tag is CA   B     NEXTTAG        C    change A to B if next tag                         is CA   B     SURROUNDTAG    C D  change A to B if surround-                         ing tags are C and DA   B     NEXTBIGRAM     C D  change A to B if next two                         tags are C and DA   B     PREVBIGRAM     C D  change A to B if previous                         two tags are C and D______________________________________ 
    
     After training the set of contextual rule templates described in Table I, 280 contextual rules are obtained. The resulting rule-based tagger performs as well as the state of the art taggers based upon probabilistic models and overcomes the limitations common in rule-based approaches to language processing: it is robust and the rules are automatically acquired. In addition, the tagger requires drastically less space than stochastic taggers. However, Brill&#39;s tagger is inherently slow. 
     Once the lexical assignment is performed, Brill&#39;s algorithm applies each contextual rule acquired during the training phase, one by one, to each sentence to be tagged. For each individual rule, the algorithm scans the input from left to right while attempting to trigger the rule. This simple algorithm is computationally inefficient for two reasons. 
     The first reason for inefficiency is the fact that an individual rule is attempted on each token of the input regardless of the fact that some of the current tokens may have been previously examined by attempting to apply the same rule at a previous position. The algorithm works as if each rule is a template of tags that is being slided next to the input. Consider, for example, the rule A B PREVBIGRAM C C that changes tag A to tag B if the previous two tags are C. When applied to the input C D C C A, three alignments are attempted and at each step no record of previous partial matches or mismatches are recorded, as can be seen from the following tables. ##STR1## 
     In this example, the second alignment could have been skipped by using the information from the first alignment. 
     The second reason for inefficiency is the potential interaction between rules. For example, when the rule 1 and rule 2 are applied to sentence 
     &#34;He/pps witnessed/vbd Lenon/np killed/vbn by/by Chapman/np&#34; the first rule results in the change: 
     &#34;He/pps witnessed/vbd Lenon/np killed/vbd by/by Chapman/np&#34;which is undone by the second rule resulting in 
     &#34;He/pps witnessed/vbd Lenon/np killed/vbn by/by Chapman/np&#34; 
     The algorithm may therefore perform unnecessary computation. In summary, Brill&#39;s algorithm for implementing the contextual tagger may require RCn elementary steps to tag an input of n words with R contextual rules requiring at most C tokens of context. 
     SUMMARY OF THE INVENTION 
     In contradistinction to Brill, the tagger to be described requires n steps to tag a sentence of length n, independently of the number of rules and the length of the context they require. 
     Note that each rule in Brill&#39;s tagger can be viewed as a non-deterministic finite state transducer, with the application of all rules in Brill&#39;s tagger being obtained by combining each of these non-deterministic transducers into one non-deterministic transducer. 
     On the other hand, the Subject Tagger rejects the use of this non-deterministic transducer approach in favor of a deterministic transducer in which a sentence is tagged both in accordance with context and in a single pass. In order to accomplish this, the deterministic transducer memorizes the relevant context and converts it into a finite set of states. The term &#34;finite state&#34; refers to the capability of the transducer to remember only a finite number of contexts of the input sentence, when the input sentence is read from left to right. Thus a finite state transducer transforms an input sentence to a tagged output sentence while utilizing at each point only a finite number of words of the part of the input sentence it has already read. 
     Adding the deterministic quality further limits the transduction so that for each input word only one tagging choice is made. The subject deterministic finite state transducer operates by postponing any choice until enough context is read, meaning that the choice is made only after it has been ascertained that one choice among the possible choices is correct. 
     The resulting deterministic transducer is a part-of-speech tagger which operates in optimal time in the sense that the time to assign tags to a sentence corresponds to the time required to deterministically tag following a single path in this finite state machine. The lexicon used by the Subject System is also optimally encoded using a finite state machine. 
     In one emodiment, in order to construct a system that assigns part of speech tags to English text, the Subject System first acquires a set of tagging rules by examining a training corpus of tagged text. During this training phase, each word in the dictionary is associated to its most likely part of speech in the training corpus. For example, the part of speech &#34;VERB-PAST-TENSE&#34; is associated with the word &#34;left&#34;. This same word could also be &#34;ADJECTIVE&#34; but this part of speech tag is less likely for the word &#34;left&#34; and it is not recorded. Tagging text according to this dictionary leads to numerous errors such as for a sentence like &#34;Turn left at the light&#34;. This initial tagging is corrected by applying a sequence of contextual rules acquired automatically from the training corpus. An example of such rule is &#34;CHANGE VERB-PAST-TENSE TO ADJECTIVE IF THE PREVIOUS TAG IS VERB&#34;. These rules are automatically acquired by compiling a list of tagging errors with their counts obtained by comparing the first output to the correct part-of-speech assignment. 
     Then, for each error, it is determined which instantiation of a set of rule templates results in the greatest error reduction. Thereafter the set of new errors caused by applying the rule is computed and the process is reiterated until the error reduction drops below a specified number or threshold. After training a set of contextual rule templates on a corpus of thirty thousand sentences associated with their correct parts-of-speech, two hundred and eighty contextual rules are obtained. These rules are then transformed into a compact device called a deterministic finite-state transducer which functions as the contextual tagger. A finite-state transducer is a finite-state automaton whose transitions are labeled by pairs of symbols. The first symbol is the input and the second is the output. Applying a finite-state transducer to an input consists in following a path according to the input symbols while storing the output symbols, the result being the sequence of output symbols stored. 
     Given a set of rules, the Subject Tagger is constructed in four steps. The first step consists in turning each contextual rule found into a finite-state transducer called a Rule to Transduce transformer. Each of the contextual rules is defined locally, that is the transformation it describes must be applied at each position of the input sequence. For instance, the rule &#34;A B PREV1OR2TAG C&#34;, that changes the part-of-speech tag A into B if the previous tag or the one before is C, must be applied twice on C A A, resulting in the output C B B. The second step consists in turning the transducers produced by the preceding step into transducers that operate globally on the input in one pass. This is accomplished by a local extension transformer. The third step uses a composer to combine all transducers into one single transducer. This corresponds to the formal operation of composition defined on transducers. The transducer obtained in the previous step is still not optimal since it may contain some non-determinism. The fourth and final step consists in transforming the finite-state transducer obtained in the previous step into an equivalent deterministic transducer using a determiniser. The resulting finite-state transducer is the contextual part-of-speech tagger that operates on an initially tagged sentence, tagged with a lexical tagger and an unknown word tagger, in linear time independently of the number of rules and of the length of the context. The subject tagger is thus optimized to operate faster than any other existing system. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other features of the Subject Invention will be better understood taken into conjunction with the Detailed Description in conjunction with the Drawings of which: 
     FIG. 1 is a block diagram illustrating the construction of the finite state transducer implementing the contextual rules used by the part of speech tagger which consists in transforming the sequence of contextual rules into a sequence of finite state transducers and then transforming to their local extensions, followed by composing them together to produce a non-deterministic transducer which is then determinised; 
     FIG. 2 is a diagram illustrating the finite state transducer for the contextual rule which changes &#34;vbn&#34; to &#34;vbd&#34; if the previous tag is &#34;np&#34;; 
     FIG. 3 is a diagram illustrating the local extension of the finite state transducer shown in FIG. 2; 
     FIG. 4 is a diagram illustrating the finite state transducer for the contextual rule which changes &#34;vbd&#34; to &#34;vbn&#34; if the next tag is &#34;by&#34;. 
     FIG. 5 is a diagram illustrating the local extension of the finite state transducer shown in FIG. 4; 
     FIG. 6 is a diagram illustrating the composition of the finite state transducers shown in FIG. 3 and FIG. 5; 
     FIG. 7 is a diagram illustrating the determinisation of the finite state transducer shown in FIG. 6; 
     FIG. 8 is a block diagram of a complete part of speech tagger illustrating the use of a lexical tagger which produces a partially tagged sentence which is then processed by an unknown word tagger which produces an initial tagger sentence which is then corrected by a contextual tagger which produces the final part of speech tags for the input sentence; 
     FIG. 9 is a diagram illustrating the encoding of a lexicon by with a finite state automaton; 
     FIG. 10 is a diagram illustrating an example of finite state transducer defined locally that transforms &#34;ab&#34; into &#34;bc&#34; and &#34;b&#34; into &#34;d&#34;. 
     FIG. 11 is a diagram illustrating a finite state transducer defined globally equivalent to the one on FIG. 10 defined locally; 
     FIG. 12 is a diagram illustrating an example of finite state transducer which is not deterministic; and, 
     FIG. 13 is a diagram illustrating the deterministic finite state transducer which is equivalent to the non-deterministic finite state transducer of FIG. 12. 
    
    
     DETAILED DESCRIPTION 
     a) Construction of the Contextual Tagger 
     As to the construction of the subject Contextual Tagger which is used to improve on an initially tagged sentence referring now to FIG. 1, a method 10 for producing a contextual tagger 11 which is a finite-state transducer, also referred to as a deterministic transducer, utilizes a Rule-to-Transducer transformer 12, the input to which is a sequence of contextual rules 13. The output 14 of Rule-to-Transducer transformer 12 actually constitutes a contextual tagger, but is excessively slow because of non-deterministic choices involved in the transduction and because of the necessity of applying the transducer to each position of the input sentence. 
     In order to improve the speed of such a contextual tagger, the output of transformer 12 which is a sequence of transducers 14 is coupled to a local extension transducer 15 which permits applying the transducer only once on the input, as opposed to applying it iteratively on each suffix of the input sentence if this is accomplished through the utilization of a specialized algorithm described hereinafter. 
     The output of transformer 15 is a sequence of non-deterministic transducers 16, in which the term &#34;non-deterministic&#34; refers to multiple choices taken at each position of the input sentence. The result of applying the specialized algorithm is a contextual tagger which is somewhat faster than the contextual tagger corresponding to transducer 12 but which is still relatively slow because there are many transducers to apply to the input sentence, and because each one of them is non-deterministic. 
     In order to further increase the speed of the contextual tagger, the output of Local Extension Transformer 15 is applied to a composer 17 which merges all the non-deterministic transducers into one omnibus non-deterministic transducer 18. In this case, the result is a contextual tagger in which one omnibus transducer is applied to the sentence. 
     While omnibus non-deterministic transducer 18 provides a much improved contextual tagger in the sense of the speed with which an input sentence can be tagged, the transducer is nonetheless non-deterministic. Thus when analyzing parts of speech, the tagger must proceed down multiple paths before it can determine whether the path leads to a solution or not. Going down blind paths is time consuming, requiring a system for optimizing the process such that the determination of the part-of-speech of a word is recognized without the necessity of multiple paths of computation. 
     In order to eliminate the problems associated with non-deterministic transducers, the output of the omnibus non-deterministic transducer 18 is applied to a determiniser 19 which postpones decisions as to which path to compute until enough information about the input sentence is provided in order to make a correct choice. When the determiniser sees two paths, decisions are postponed until a following word indicates which of the paths will lead to a solution. Thus the determiniser looks at a following word or words in the sentence to ascertain which path will lead to a solution, at which point that path is chosen. The output of determiniser 19 thus constitutes a deterministic transducer such as tagger 11. Thus contextual tagger 11, unlike Brill&#39;s contextual tagger, utilizes a deterministic finite-state transducer. 
     Note that the function represented by each contextual rule can be represented as a non-deterministic finite state transduction and the sequential application of each contextual rule also corresponds to a non-deterministic finite state transduction which is the result of the composition of each individual transduction. This representation allows one to turn the non-deterministic transducer to a deterministic transducer. The resulting part-of-speech tagger operates in linear time independently of the number of rules and of the length of the context. The new tagger operates in optimal time in the sense that the time to assign tags to a sentence corresponds to the time required to deterministically follow a single path in the resulting finite state machine. 
     The Subject System relies on two central notions: the notion of finite-state transducer and the notion of sequential transducer. As defined herein, a finite-state transducer is a finite-state automaton whose transitions are labeled by pairs of symbols. The first symbol is the input and the second is the output. Applying a finite-state transducer to an input consists in following a path according to the input symbols while storing the output symbols, the result being the sequence of output symbols stored. 
     For the present purpose, when pictorially describing a finite-state transducer: final states are doubly circled; E represents the empty string; on a transition from state i to state j, a/b indicates a transition on input symbol a and output symbol(s) b; the question mark(?) in an arc transition (for example labeled ?/b) originating at state i stands for any input symbol that is not referred as input symbol in any other outgoing arcs from i. 
     Specifically, given a sequence of contextual rule 2, the sequence of contextual rules is turned into a sequence of finite-state transducers by a rule-to-transducer transformer. For example, the functionality of the rule &#34;vbn vbd PREVTAG np&#34; is turned into the transducer shown in FIG. 2. 
     Each of the contextual rules is defined locally, that is the transformation it describes must be applied at each position of the input sequence. For instance, the rule A B PREV1OR2TAG C, that changes A into B if the previous tag or the one before is C, must be applied twice on C A A (resulting the output C B B). We now improve this aspect. 
     Speed is improved by turning the sequence of transducers previously produced into a sequence of transducers via a local extension transformer that operates globally on the input in one pass. Given a function f1 that transforms, for instance, a into b (i.e. f1 (a)=b), one wants to extend it to a function f2 such that f2(w)=w0 where w0 is the word built from the word w where each occurrence of a has been replaced by b. One says that f2 is the local extension of f1 and one writes f2=LocExt(f1). 
     The local extension of the transducer for the rule &#34;vbn vbd PREVTAG np&#34; is shown in FIG. 3. Similarly, the transducer for the contextual rule &#34;vbd vbn NEXTrAG by&#34; and its local extension are shown in FIGS. 4 and 5. 
     The sequence of transducers obtained above still needs to be applied one after the other. These transducers are combined all transducers into one single transducer by a Composer. This corresponds to the formal operation of composition defined on transducers. For example, the transducer obtained by composing the local extension of T2 of FIG. 3 with the local extension of T1 of FIG. 5 is shown in FIG. 6. 
     The final transducers is obtained by transforming the finite-state transducer previously described into an equivalent deterministic transducer by a Determiniser. 
     For example, the transducer illustrated in FIG. 6 is non-deterministic since it has some non-deterministic paths. For instance, from state 0 on input symbol vbd two possible emissions are possible, vbn, from 0 to 2, and vbd, from 0 to 3. This non-determinism is due to the rule &#34;vbd vbd NEXTTAG by&#34; since this rule requires to read the second symbol before it can know which symbol must be emitted. The deterministic version of the transducer T3 is shown in FIG. 7. Whenever non-determinism arises in T3, in the deterministic machine the empty symbol E is emitted and the emission of the output symbol is postponed. For example, from the start state 0 the empty string is emitted on input vbd, while the current state is set to 2. If the following word is &#34;by&#34;, the two token string &#34;vbn by&#34; is emitted, from 2 to 0, otherwise &#34;vbd&#34; is emitted, depending on the input from 2 to 2 or from 2 to 0. 
     The resulting transducer 11 is a part-of-speech tagger that operates in linear time independently of the number of rules and of the length of the context. The Subject System therefore operates in optimal time. 
     Referring now to FIG. 8, the contextual tagger 11 The process of tagging requires an input sentence 26 in which a lexical tagger 28 looks up each word in a dictionary and assigns the most likely tag to each word in the sentence to provide a partially tagged sentence 30. The output of lexical tagger 28 is a partially tagged sentence since some words may be not found in the dictionary. The words left untagged in the partially tagged sentence 30 are tagged by an unknown word tagger 32 which guesses tags by looking at the last three letters of the unknown words. The output of the unknown word tagger 32 is the initial tagged sentence 34. The contextual tagger as constructed in FIG. 1 as deterministic transducer 11 is applied to the initial tagged sentence 34 to produce the final tagged sentence 36. 
     Since the dictionary is the largest part of the tagger in term of space, a compact representation is crucial. Moreover, the lookup process has to be very fast too, otherwise the improvement of the speed of the contextual manipulations would be of little practical interest. To achieve high speed for this procedure, the dictionary is represented by a deterministic finite-state automaton with both fast access and small storage space. The algorithm, as described by Revuz, Dominique in 1991 as &#34;Dictionnaires et Lexiques, Methodes et Algorithmes&#34;, Ph.D.thesis, Universite Paris 7, consists in first building a tree whose branches are labeled by letters and whose leaves are labeled by a list of tags (such as nn vb) and then reducing it the minimum directed acyclic graph (DAG). 
     For example, the DAG of FIG. 9 encodes the following words and part of speech tags: ads nns; the word &#34;bag&#34; which can be a noun &#34;nn&#34; and a verb &#34;vb&#34;; the word &#34;bagged&#34; which can be the past participle &#34;vbn&#34; or the past tense &#34;vbd&#34;; the word &#34;bayed&#34; which can be the past participle &#34;vbn&#34; or the past tense &#34;vbd&#34;; and the &#34;bids&#34; which can be a plural noun &#34;nns&#34;. 
     When a dictionary is represented by a DAG, looking up a word in it consists simply in following one path in the DAG. The complexity of the lookup procedure depends only on the length of the word and is, in particular, independent of the size of the dictionary. 
     The Subject System operates after all the known words, that is the words listed in the dictionary, have been tagged by a module by their most frequent tag and before the set of contextual rules is applied. This module guesses a tag for a word according to its suffix (e.g. a word of with an &#34;ing&#34; suffix is likely to be a verb), its prefix (e.g. a word starting with an uppercase character is likely to be a proper noun) and other relevant properties. This module basically follows the same techniques as the ones used to implement the lexicon. 
     The Subject System tagger has an accuracy comparable to the accuracy of statistical-based methods. However it runs at a much higher speed. The Subject System tagger runs nearly ten times faster than the fastest of the other systems. Moreover, the finite-state tagger inherits from the rule-based system its compactness compared to a statistical-based tagger. In fact, whereas statistical-based taggers have to store words, bigrams and trigrams probabilities, the rule-based tagger and therefore the finite-state tagger, only has to store a small number of rules, e.g. between 200 and 300. 
     The Subject System was empirically compared with Eric Brill&#39;s implementation of his tagger, and with a trigram tagger adapted from the work of Church known as &#34;A stochastic parts program and noun phrase parser for unrestricted text&#34; described in 1998 in the Second Conference on Applied Natural Language Processing. The three programs were run on large files 
     Table I summarizes our experiments. All taggers were trained on a portion of the brown corpus. The experiments were run on a HP720 with 32Mbytes of memory. All three taggers have approximately the same precision (95% of the tags are correct). By design, the finite-state tagger produces the same output as the rule- based tagger. 
     
                       TABLE V______________________________________Statistical-Based          Rule-BasedTagger         Tagger      Subject System______________________________________Speed 1200 words/sec              500 words/sec                          10800 words/secSpace 2200 KB      379 KB      815 KB______________________________________ 
    
     It will be appreciated that the Subject System runs much faster than any previously existing system. This is of paramount importance when tagging large amounts of text such as the text contained in an electronic library. 
     b) Local-Extension Transformer 
     What is now more precisely described is the notion and the implementation of Local-Extension. The idea is to transform a function that is defined locally into a function defined globally. In other words, suppose one has the function T1 of FIG. 10, this function transforms the word &#34;ab&#34; into &#34;bc&#34; by applying first the transition 40 from the state 42 to the state 44 to the first input letter &#34;a&#34;. This emits &#34;b&#34;, and then when applying the transition 46 from the state 44 to the state 48 on the second input letter &#34;b&#34;, &#34;c&#34; is emitted. In the same way, T1 also transforms the word &#34;b&#34; into the word &#34;d&#34; through the transition 50. Thus T1 also defines locally the function T2 that takes any word as an input and outputs the same word, where all occurrences of &#34;ab&#34; and &#34;b&#34;, the possible inputs of T1, have respectively been transformed into &#34;bc&#34; and &#34;d&#34;. For instance, T2 takes the word &#34;bbbbccccccabcccabccc&#34; and transforms it into &#34;ddddccccccbccccbcccc&#34;. 
     To compute this transformation as fast as possible, the best way is to precompile the representation of T1 of FIG. 10 into the representation of T2 of FIG. 11. The method is the following: the states of T2 are indexed by a set of states of T1 and by a type that is either transduction or identity. Thus states can either be of the transduction type or the identity type. 
     For instance, the state 0 as illustrated at 52 of FIG. 10 is indexed by the set of states {0} and is associated with the type identity. The type identity means that the input is kept unchanged, for instance the letter &#34;c&#34; of the input is never transformed. The transitions as illustrated at 58 and at 59 reflect this fact. The type transducer means that the function applies a modification of T1 as in the state illustrated at 54 where &#34;a&#34; has been transformed into &#34;b&#34; through the transition illustrated at 56 from the state illustrated at 52. This transition correspond to the transition illustrated at 40 of T1 from the state illustrated at 42 to the state illustrated at 44 in FIG. 10. From the initial state 52 one also has to consider the fact that an input letter &#34;a&#34; might be kept unchanged (has in the word &#34;aa&#34;) and thus build the transition illustrated at 60 labeled &#34;a/a&#34;. This transition points to the state illustrated at 61 whose type is identity, which indicates that the input has been kept unchanged up to this point. The state illustrated at 61 corresponds to the state 1 illustrated at 44 of T1 in FIG. 10 and also to the initial state 0 illustrated at 42 of T1 in FIG. 10. Hence, the state 1 illustrated at 61 in FIG. 11 is labeled by the set of states {0,1} and is associated with the type identity. The other transitions and states are built in the same way with the exception of the state illustrated at 64 in FIG. 11 which refers to the state 2 of T1 illustrated at 48 which is a final state. Final states are depicted with a double circle. Being at a final state means that a transformation has been completed and that it is thus possible to return to the initial state. This is expressed by the transition illustrated at 62 labeled by &#34;ε/ε&#34; in FIG. 11. This means that one can go from state illustrated at 64 to the state illustrated at 52 by reading the empty string ε and by emitting the empty string ε. 
     c) Determiniser 
     Having a Finite-State Transducer, one wants an equivalent Finite-State transducer that can be applied deterministically. In fact, one has a Finite-State Transducer such as T3 in FIG. 12. This transducer is not deterministic, in fact, suppose one wants to apply the input word &#34;ad&#34;, the first input letter is &#34;a&#34;, we thus start at the state 66 with two possibilities, the first one consists in going to state 68 by reading &#34;a&#34; and emitting &#34;b&#34; and the other consists in going to the state 70 by reading &#34;a&#34; too but emitting &#34;c&#34;. Reading the second letter of the input, that is &#34;d&#34;, shows that only the first choice was relevant to the actual input and that the final output is &#34;bd&#34;. Having to handle this kind of choice coast a tremendous amount of time spending which shows the need for finite-state transducer for which one never has to choose between alternative propositions. Such Finite-State transducers are called deterministic. Building a deterministic transducer is done according to the following method. Suppose one has to deal with the transducer T3 described in FIG. 12, one builds the deterministic transducer T4 of FIG. 13 in the following way. One first builds the initial state 72 by saying that it contains the pair (O,ε) in which 0 refers to the state 0 of T3 and ε to the fact that nothing, i.e. the empty word ε, is to be emitted at this point. The only input symbol that can be read at the state 0 of T3 is &#34;a&#34;. Thus there will be only one output transition at the state 72. This only transition will be labeled with the input symbol &#34;a&#34;. To determinize the output symbol, one looks at all the output symbols in T3, to obtain &#34;b&#34; and &#34;c&#34; which means that one cannot yet determine for sure what has to be emitted. Therefore nothing (i.e.ε) is emitted and the postponed emissions are stored in the arrival state 74. In this state (74), (1,b) means that one could be in state 1 of T3 (i.e. ε) with &#34;b&#34; as postponed emission and (2,c) means that one could be in state 2 of T3 (70) with &#34;c&#34; as postponed emission. From this last state 74, since it corresponds to either 68 or 70, two input symbols are possible, namely &#34;d&#34; for 68 and &#34;e&#34; for 70. For the symbol &#34;d&#34;, the corresponding state is 1 of T3 (68) which means, according to the pair (1,b) stored in 74, that the postponed symbol was &#34;b&#34;. The output symbol for &#34;d&#34; between 68 and 76 is &#34;d&#34;. Thus, putting together the postponed symbol with the newly emitted symbol, it will be appreciated that the emission of 78 should be &#34;bd&#34;. Moreover, there is no reason to postpone any emission. Therefore the arrival state of 78 should be 80 labeled with state 2 of T3 and the empty string as a postponed symbol. In similar way, the emission for the symbol &#34;e&#34; from the state 74 should be &#34;ce&#34;. In this case too, no postponed symbol is required. Thus the arrival state should also be labeled by (2, ε), thus the arrival state of the transition 82 is 80 as well. This completes the construction of the deterministic finite-state transducer T4. This transducer is equivalent to T3 in the sense that they perform the same transformation on their input (for instance &#34;ad&#34; is transformed into &#34;bd&#34; both by T3 and T4). However, because it is deterministic, applying T4 can be done much faster than applying T3. The program for performing the tagging described above is now presented. ##SPC1##Having above indicated several embodiments of the Subject Invention, it will occur to those skilled in the art that modifications and alternatives can be practiced within the spirit of the invention, It is accordingly intended to define the scope of the invention only as indicated in the following claims.