Abstract:
An improved pattern recognition system, using an improved method for merging low-level recognition information with auxiliary contextual information such as a Deterministic Finite Automaton (DFA). The system comprises a low-level shape recognizer for handwriting input, an English Language dictionary organized as a Trie (a special type of DFA), and software to merge the results of the two. An input of digitized handwriting strokes is translated into characters using the shape recognizer and the Trie in tandem, allowing the system to reject nonsense translations at the earliest possible stage of the process and without the overhead traversing the trie from the top with each translation.

Description:
BACKGROUND OF THE INVENTION 
     The area of this patent is mechanical pattern recognition. This would include but not be limited to hardware and software for performing computer speech recognition, optical character recognition, and computer handwriting recognition. 
     STATEMENT OF RELATED ART 
     A large class of pattern recognition algorithms can be described as &#34;tree traversals.&#34; By way of example, consider a printed-handwriting recognition system that tries to convert a series of digitized points into letters and words. It divides the points into strokes and attempts to assign a letter to each stroke (or sequence of strokes). It then attempts to assemble these letters into words. 
     The strokes-to-letters problem is greatly complicated by the fact that letters vary greatly in size, the smallest being single strokes (such as the letter `o`) and the largest being as many as five or six strokes (such as capital `E`). So the system starts with the first stroke and hypothesizes several choices for it, including some that require more than one stroke. These choices will affect future choices later in the translation process. For this reason, the system cannot discard any of the initial hypotheses until it has analyzed more of the strokes beyond them. 
     For example, consider an input of &#34;Hippopotamus&#34; where the bar on the `H` doesn&#39;t quite reach the right vertical (so that it looks like a `tl`, the first `o` is open at the top (so it looks like an `u`), the second `o` spirals in (so it looks like a capital `G`), the `t` is tilted (so it looks like an `x`) the `a` is open to the right (so it looks like a `c`), the `m` has a strong downstroke and a weak tail, so it looks like a `w`, and the downstroke on the `u` is widely separated from the body of the letter (so it looks like an `n`). Since there are two choices for each of seven letters, there are 128 different possible translations, from a letter basis alone, only one of which actually forms a real word. 
     Systems in the prior art, such as (&#34;A Verifier of Lexical Hypotheses in a Speech Recognition System&#34;; Silvano Rivoira and Piero Torasso; Proceedings of the International Conference on Cybernetics and Society; Oct. 8-10, 1979; IEEE Systems, Man, and Cybernetics Society) and (&#34;A multi-level perception approach to Reading Cursive Script&#34;; Sargur N. Srihari and Radmilo M. Bozinovic; Artificial Intelligence 33; 1987; Elsevier Science Publishers B. V.; North Holland) work by assigning a measure of likelihood to each character hypothesis and first taking the most likely hypothesis, but storing the others on a stack, then repeating the analysis on the remainder of the strokes and keeping a cumulative probability until that probability gets too low or until the end of the data is reached. (The above references are incorporated herein by reference.) At that point, it then backs up and tries the other possibilities until it has tried everything. It then picks the combination that had the best score. This is called a search tree because of all the branches at the decision points. 
     For our &#34;Hippopotamus&#34; example, the search tree might look like the following example. First, it scans straight to the end, looking at the possibilities at each position and keeping them in order from most to least likely. (In this example, we never had more than two possibilities for any one position): 
     
         ______________________________________tl   i     p     p    u    p    o    x    c    w   n   sH                     o         G    t    a    m   u______________________________________ 
    
     Having reached the end of the input, it could simply put out the &#34;most probable&#34; entry, &#34;tlippupoxcwns&#34;, but that&#39;s obviously not adequate. Prior art often uses Deterministic Finite Automata (DFA&#39;s) (Compiler Design, Aho and Ullman, Addison Wesley) or Trie-structured dictionaries (The Art of Computer Programming, Vol 3; Knuth; Addison Wesley) to represent specific allowed (or expected) input. These references are incorporated herein by reference. A prior art system might use a dictionary of English to validate results (or at least, to choose among them), and since &#34;tlippupoxcwns&#34; isn&#39;t in the dictionary, the system would know to keep looking. In this case, however, the system will try 110 nonsense words before it gets to &#34;Hippopotamus.&#34; (The first few will look like this: 
     
         ______________________________________tlippupoxcwnstlippupoxcwustlippupoxcmnstlippupoxcmustlippupoxawns          etc.)______________________________________ 
    
     Prior art uses other heuristics to reduce the search, such as noting that combinations such as &#34;tl&#34; and &#34;cw&#34; are unusual and not considering them. This makes the problem manageable, but leads to other problems (such as an inability to recognize words like &#34;bottle.&#34;) 
     Another approach would be to use the dictionary from the beginning and reject (or at least defer) any alternative which would make the prefix (the word so far) deviate from the dictionary. For example, no words begin with &#34;tl&#34;, so it&#39;s safe to select `H` over `tl` in the first position. Unfortunately, this requires accessing the dictionary at each decision point, and the time involved is proportional to the length of the word up to that point, so the total time required is proportional to the square of the length of the word. In the case of Hippopotamus, the savings are worth the cost, but in general, the cost is so heavy that prior art never uses this technique. 
     In the situation where the input may consist of multiple words, this problem is greatly aggravated because at many points the possibility that any given letter may be followed by a space must also be included. 
     It will be apparent to one skilled in the art that this represents a very large class of difficult problems and is not strictly limited to Handwriting Recognition. Examples include Optical Character Recognition, Speech Recognition, Radar or Sonar Analysis, and any other system that requires a mostly-linear, not-100%-reproducible data stream be matched against a set of expected patterns. 
     For Handwriting Recognition, we would like to use a trie-structured dictionary (possibly more than one) and/or a DFA to restrict the possible input. (For example, number format with commas, decimal points etc. is best expressed by a DFA). But as described above, prior art must either use these as a post-processing step, after the recognition algorithm has already narrowed the possibilities down to a relative handful of choices (running the risk of missing the correct word), or it must devote tremendous computational resources to checking the dictionary at every decision point. 
     SUMMARY OF THE INVENTION 
     In the present invention, a trie or DFA is organized in such a way that each node or state can be entered independently. That is, all that is required to represent a state or node is a pointer to it (i.e. a machine address). Further, for the trie, each of the characters that defines an arc to an adjacent node is immediately available, and for the DFA, each allowed transition character must be easily available from the pointer to the state. 
     In other words, we can jump into the middle of a trie or DFA; we don&#39;t have to start from the top and work our way down. FIG. 1 illustrates a traditional trie; and FIG. 2 illustrates a trie organized by state. 
     We then evaluate hypotheses according to the prior art, except that at each decision point (even if there is only one choice from the recognition system), we generate a separate set of choices from the trie-based dictionary which we use to augment the list from the rest of the system. Each of those choices comes with a pointer back into the trie, so that when and if any of them is explored, we can jump directly into the trie and proceed from where we left off. 
     For example, in the &#34;Hippopotamus&#34; example, the first choices from the stroke information were `t` and `H`, while the first set of choices from the trie will be every letter from `a` to `z` (upper and lower case), representing the fact that there are words that begin with all letters. We only keep the `t` and the `H` entries, since those are the only ones that came back from the hypothesis generator. The next generated letter is `l` (following the `t`). Exploring possibilities from t` gives us `aehioruy` as second letters, which does not include `l`, so we back up to `H`. The next letter after `H` is `i`, and `H` may be followed by `aeiouy&#34;, so `i` is accepted and we proceed to the end of the word. At every step from this point, we select the correct entry at each decision point, since Hippu-, HippopG-, Hippopox-, Hippopotc-, Hippopotaw-, and Hippopotamn- are all invalid word prefixes (i.e. no English words begin like that). Because we only go back to the dictionary for one character at a time, our total character lookup is only slightly greater than it would have been to look up a single word one time. 
     We also store the relative probabilities of each letter in the trie (where such are available) and combine that with the probabilities generated in the recognition engine. For example, a word is far more likely to begin with `s` or `c` than `x` or `j`. 
     This does not require that the concatenation of hypotheses so far be saved or referenced. In fact, the computation required is equal to checking a single character of a string, rather than processing the entire thing. We use more memory by storing a pointer with each stack element, but we tremendously reduce the computation time. Thus we have the speed advantage of a postprocessing implementation with the same accuracy of a full lookup implementation. 
     A computer in conjunction with which the method of the present application may be used is described in detail in another United States patent application, namely Agulnick et al., &#34;Control of a Computer Through a Position-Sensed Stylus,&#34; Ser. No. 07/610,231, filed Oct. 31, 1990. That application, including its appendices, are incorporated herein by reference. The appendices are all from GO Corporation of Foster City, Calif., and are entitled: 
     I. Architecture--Parts 0 to 5 
     II. Architecture--Parts 6 to End 
     III. Application Developer&#39;s Guide 
     IV. API Reference. 
     Another patent application which includes disclosure which may be used in conjunction with the present invention is the United States patent application of Carr et al., entitled &#34;Computer Documents as Compound Documents in a Notebook Metaphor, &#34; Ser. No. 07,607,139, filed Oct. 31, 1990. That application is also incorporated herein by reference. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 illustrates a traditional trie. 
     FIG. 2 illustrates a trie organized by state according to the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The invention is intended to be used as a piece of a larger pattern recognition &#34;engine.&#34; To better understand the invention, one must understand a piece of the larger application. 
     All the examples here and below are rendered in the C programming language (see The C Programming Language; Kernighan and Ritchie; Prentice Hall, Inc.), but it will be apparent to one skilled in the art that this process is applicable to other languages and even to mechanical implementations. Within the program listing the descriptive comments are begun with &#34;/*&#34; and ended with &#34;*/&#34;. These two symbols are the standard delimiters for comments in the C programming language. 
     
         ______________________________________* THIS IS THE START OF THE PROGRAM LISTING */______________________________________* A prior art piece of computer software, the shapematcher, accepts as input a set of digitized strokes andproduces as output a list of characters recognized, thenumber of strokes used by each such character, and somemeasure of likelihood of each character.______________________________________ 
    
     The returned data structure might look like this: */ 
     
         ______________________________________The returned data structure might look likethis: */typedef struct SHAPE.sub.-- PROPOSAL/* Character proposed */unsigned char character;/* number of strokes in character */int strokes;/* measure of confidence in character */double probability;} SHAPE.sub.-- PROPOSAL;/* And the subroutine might be declared like this: *//* This subroutine returns the number of proposals */int ShapeMatch(/* pointer to digitized handwriting */void *pStrokes,/* Out: list of proposals */SHAPE.sub.-- PROPOSAL *pProposals);/* For example, if pStrokes pointed to three digitizedstrokes (in some representation) which looked like acapital `H` whose crossbar didn&#39;t quite meet the rightvertical bar, ShapeMatch might return 2 (meaning thatthere are two ways to interpret the strokes) andpProposals might point to something like this:`H`, 3, 0.4`t`, 2, 0.6signifying that it might be a capital `H` (which wouldexplain the first three strokes) or it might be alower-case `t` , which would explain the first twostrokes. ShapeMatch always returns its proposals inalphabetical order. ShapeMatch always returns at leastone character as long as pStrokes is not equal to NULL.We define ` 0×01` as an &#34;unknown&#34; character having onestroke and a probability of 0.01 to guarantee that we canalways return something. ShapeMatch may return space asthe character with zero strokes.______________________________________ 
    
     There would also be a routine called StrokeIndex which allows the system to advance the stroke list pointer. This might be declared like this: */ 
     
         ______________________________________/* This subroutine returns a pointer to new stroke listvoid * StrokeIndex(/* specify a name for the value of a null pointer */#define NULL 0/* pointer to stroke list */void *pStrokes,/* number of strokes to skip over */int i);/* StrokeIndex(pStrokes,0) is always just pStrokes. Inour example above, StrokeIndex(pStrokes,1) would point tothe cross-bar on the `H` , and StrokeIndex(pStrokes,2)would point to the right hand vertical bar. This allowsthe recognition engine to advance through the list ofstrokes using the number-of-strokes information returnedfrom ShapeMatch. StrokeIndex returns NULL if asked toindex beyond the end of the stroke list. For example, if`H` were the only strokes in the list,StrokeIndex(pStrokes,3) would return NULL.______________________________________ 
    
     The internal structure of ShapeMatch and StrokeIndex is not critical in the present invention. 
     We also define a Determinate Finite Automaton (DFA) from the following structures: */ 
     
         ______________________________________typedef struct DFA.sub.-- ELEMENT {/* a character proposal */unsigned char character;/* likelihood of this character */double probability;/* The state this character takes us to */struct DFA.sub.-- STATE/* number of elements in this state */int count;/* pointer to elements in this state */struct DFA.sub.-- ELEMENT *pDFAElement;} *pDFANextState;} DFA.sub.-- ELEMENT;typedef struct DFA.sub.-- STATE DFA.sub.-- STATE;/* Base of a pre-defined DFA */extern DFA.sub.-- STATE DFA[];/* For this illustration, the DFA is considered torepresent a dictionary of the English language, but itshould be obvious that this representation can describeany regular expression. Aho and Ullman and Knuth givegood algorithms for constructing DFA&#39;s from regularexpressions.______________________________________ 
    
     The DFA is an array of DFA --  STATE structures. Each such structure contains a pointer to an array of DFA --  ELEMENTS and a count of how many elements are in that array. Each element contains a character (which is a character that is allowed at this point in the translation), a probability (the likelihood that that character will in fact occur at this point in the translation), and a pointer back into the state array (which is the state the system is in if that character is in fact accepted). 
     FIG. 2 illustrates how a very simple DFA (i.e. a trie) might be built from the seven strings: 
     
         ______________________________________      a      able      do      doable      Hi      Hip      Hippopotamus______________________________________ 
    
     In the illustration, the first state contains `a`, `d`, and `H`, indicating that words in our little dictionary may only begin with those three letters. If we already know that a word begins with `a`, looking at the next state down shows us that the next letter must either be `b` or `O` (an ASCII null, binary zero, the end-of-string character in the C programming language). Note that in this representation of the trie, a single pointer suffices to represent all the possible words containing a particular prefix. 
     Of course, to properly allow parsing multi-word entries, the DFA needs to allow space as a character, and transition back to the top state if space is received. 
     An additional subroutine, DFAGetProposals, takes a pointer to a state and returns a list of proposals and states: */ 
     
         ______________________________________typedef struct DFA.sub.-- PROPOSAL/* character suggested */unsigned char character;/* state that character goes to */DFA.sub.-- STATE *pDFAState;/* likelihood of that character */double probability;} DFA.sub.-- PROPOSAL;/* This subroutine returns the number of proposals */int DFAGetProposals(/* Pointer to a DFA state */DFA.sub.-- STATE *pDFAState,/* Out: proposals from that state*/DFA.sub.-- PROPOSAL *pDFAProposals);/* From the state-organized trie in FIG. 2, where theboxed characters represent proposed letters, the arrowsrepresent pointers, and the alphanumerics to the left ofeach set of boxes represent addresses, we can see that:______________________________________ 
    
     
         DFAGetProposals(DFA,pDFAProposals) 
    
     will return 3, and pDFAProposals will point to this: 
     
         ______________________________________        a, S1        d, S5        H, S8______________________________________ 
    
     and if we then set pDFAState=S1 
     
         DFAGetProposals(pDFAState,pDFAProposals) 
    
     will return 2, and pDFAProposals will point to this: 
     
         ______________________________________   ` 0`,        NULL   `b`,         S2______________________________________ 
    
     DFAGetProposals always returns its choices in alphabetical order. 
     If DFAGetProposals is passed a NULL for pDFAState, it will return 0. This is desirable behavior because users may write words that are not in the dictionary (i.e. not described by the DFA) so it is necessary to have a state that represents &#34;out of bounds.&#34; 
     To merge the Shape proposals and the DFA proposals together into a single list of hypotheses, we define the following structure and subroutine: */ 
     
         ______________________________________typedef struct HYPOTHESIS {/* Character considered at this point*/unsigned char character;/* Pointer to first stroke from leftNOT used up to this point*/void *pStrokes;/* next state from this point */DFA.sub.-- STATE *pDFAState;/* product of probabilities thus far */double probability;} HYPOTHESIS;/* Routine to compare two hypotheses by probability forqsort in reverse order (most probable first) */int HypCmp(HYPOTHESIS *pHyp1, HYPOTHESIS *pHyp2) {if (pHyp1-&gt;probability &gt; pHyp2-&gt;probability) {return (-1);if (pHyp1-&gt;probability &lt; pHyp2-&gt;probability) {return (1);}return (0);}/* This subroutine returns the number of entries in theoutput list */int MakeHypotheses/* Current stroke list */void * pStrokes,/* list of shape proposals */SHAPE.sub.-- PROPOSAL *pShapeProposals,/* number of shape proposals */int shapeCount,/* list of DFA proposals */DFA.sub.-- PROPOSAL *pDFAProposals,/* number of DFA proposals */int dfaCount,/* best so far */double bestProbability,/* probability of prefix string up to here */double oldProbability,/* Out: hypothesis list */HYPOTHESIS *pHypotheses) {/* This routine is called after a shape proposal list anda DFA proposal list have been generated to merge theminto a hypothesis structure. Because both the shape listand the DFA list are in alphabetical order, the routineis straightforward: */int count;/* saved pointer to beginning of hypothesis list*/HYPOTHESIS *pHypotheses0;count = 0;pHypotheses0 = pHypotheses;while (shapeCount &gt; 0 &amp;&amp; dfaCount &gt; 0) {/* If a character matches from the two lists, we put thatcharacter into the hypothesis list, advance the strokelist pointer, advance the DFA, set the new probability,consume one shape proposal and one DFA proposal, andactually add this to the hypothesis list if it isn&#39;tpointless. */if (pShapeProposals-&gt;character ==pDFAProposals-&gt;character)pHypotheses-&gt;character =pShapeProposals-&gt;character;pHypotheses-&gt;pStrokes =StrokeIndex(pStrokes,pShapeProposals-&gt;strokes);pHypotheses-&gt;pDFAState =pDFAProposals-&gt;pDFAState;pHypotheses-&gt;probability =pShapeProposals-&gt;probability *pDFAProposals-&gt;probability * oldProbability;--shapeCount;++pShapeProposals;--dfaCount;++pDFAProposals;/* If there has already been a full translation that hada higher probability than this fragment, there is nopoint in putting it into the list, since adding morecharacters can only make the probability lower. */if (pHypotheses-probability &gt;= bestProbability) {++count;++pHypotheses;}}/* if we have a shape proposal with no matching DFAproposal, we still accept it, but we drop its probabilityby a factor of 10. Any expansion of this will have anempty DFA proposal list. */else if (pShapeProposals-&gt;character &lt;pDFAProposals-&gt;character) {pHypotheses-&gt;character =pShapeProposals-&gt;character;pHypotheses-&gt;pStrokes =StrokeIndex(pStrokes,pShapeProposals-&gt;strokes);pHypotheses-&gt;pDFAState = NULL;pHypotheses-&gt;probability =pShapeProposals-&gt;probability * 0.1 *oldProbability;--shapeCount;++pShapeProposals;if (pHypotheses-&gt;probability &gt;= bestProbability) {++count;++pHypotheses;}}/* We simply skip DFA proposals that have no matchingshape proposals. Just because, any word CAN begin withany letter of the alphabet doesn&#39;t mean we have toconsider all of them seriously */else {--dfaCount;++pDFAProposals;}}/* It is possible that we will run out of DFA proposalsbefore we run out of shape proposals. For example, theremay not have been any DFA proposals at all. This code isequivalent to the code above for shape proposals withoutmatching DFA proposals. */while (shapeCount &gt; 0) {pHypotheses-&gt;character =pShapeProposals-&gt;character;pHypotheses-&gt;pStrokes =StrokeIndex(pStrokes,pShapeProposals-&gt;strokes);pHypotheses-&gt;pDFAState = NULL;pHypotheses-&gt;probability =pShapeProposals-&gt;probability * 0.1 *oldProbability;--shapeCount;++pShapeProposals;if (pHypotheses-&gt;probability &gt;= bestProbability) {++count;++pHypotheses;}}/* Sort by probability, highest first */qsort(pHypotheses0, count, sizeof(HYPOTHESIS),HypCmp);return (count);}/* Note that this implementation of MakeHypothesesrequires that no letter appears twice in either list. Bydefinition, this cannot happen with the DFA, but thereare a very few characters for which ShapeMatch couldreturn the same letter with different stroke counts.This can be got around by defining different bytes torepresent (for example) an `i` with a dot and an `i`without one.______________________________________ 
    
     Finally, we need a routine that scans a hypothesis list updating bestString and bestProbability when it finds hypotheses that use up all the strokes, and returning the number of left-over hypotheses whenever it finds a hypothesis with strokes still to be analyzed. It also updates the currentHypothesis number on the stack (explained below). */ 
     
         ______________________________________typedef struct STACK.sub.-- ELEM {/* Number of hypotheses */int count;/* list of hypotheses */HYPOTHESIS *pHypotheses;/* hypothesis to consider next */int currentHypothesis;} STACK.sub.-- ELEM;int HypothesisProcess(STACK.sub.-- ELEM *pStackElem,int stackIndex,double *pBestProbability,char *pBestString,char *pCurrString) {HYPOTHESIS *pHypothesis;int count;/* Get a pointer into the current hypothesis list to thenext hypothesis we need to deal with and compute a countof the number remaining to deal with */pStackElem += stackIndex;pHypothesis = pStackElem-&gt;pHypotheses +pStackElem-&gt;currentHypothesis;count = pStackElem-&gt;count -pStackElem-&gt;currentHypothesis;while (count &gt; 0) {/* Update the current string */pCurrString[stackIndex] = pHypothesis-&gt;character;/* If one of these hypotheses actually has strokes leftin it, return now so that can be dealt with */if (pHypothesis-&gt;pStrokes) {++pStackElem-&gt;currentHypothesis;return (count);/* Otherwise, we&#39;re pointing to a fully-analyzedhypothesis; see if it beats the best score so far, and ifso, keep track of it */*pBestHypothesis = pHypothesis-&gt;probability;if (pHypothesis-&gt;probability &gt; *pBestProbability) {strcpy(pBestString,pCurrString);} -count;}/* If we got here, that means we exhausted thishypothesis list, which means the next routine up shouldpop the stack */return (0);}/* All of these routines are called from within asubroutine called TranslateHandwriting, which is definedas follows: *//* This subroutine returns the probability of thereturned string*/double TranslateHandwriting(/* pointer to a list of strokes to translate */void *pStrokes,/* Out: ASCII translation */char *pString) {/* As its name implies, this routine takes a pointer to aseries of digitized strokes and returns an ASCII stringthat represents what was written. In the case of ourfirst example, it should return &#34;Hippopotamus&#34;.______________________________________ 
    
     As described in the literature (see &#34;A Verifier of Lexical Hypotheses in a Speech Recognition System&#34; by Rivoira and Torasso, cited above), this routine works by traversing the tree of possible translations, eliminating branches of low probability. However, we also traverse the DFA in tandem, greatly enhancing our ability to avoid unlikely translations and thus increasing the speed and accuracy of the translation. 
     Since there will be one stack element for every translated character, we&#39;ll arbitrarily assume that no one can fit more than 132 characters on a single line. TranslateHandwriting looks like this: */ 
     
         ______________________________________/* Hypothesis Stack */STACK.sub.-- ELEM stack[132];/* Current Hypothesis */int stackIndex = 0;/* probability of best full translation so far */double bestProbability = 0.0;double currProbability;/* best matching string */unsigned char bestString[132];/* current partial string */unsigned char currString[132];/* temp storage for DFA proposals */DFA.sub.-- PROPOSAL dfaProposals[256];/* DFA State being evaluated */DFA.sub.-- STATE *;DFAState;/* temp storage for shape proposals */SHAPE.sub.-- PROPOSAL shapeProposals[256];/* temp storage for hypotheses */HYPOTHESIS hypotheses[256];/* pointer to current hypothesis */HYPOTHESIS *pHypothesis;int shapeCount, dfaCount, hypCount;/* Start at the top of the DFA and the beginning of thestack. The stroke pointer was passed in and alreadypoints to the left-most stroke */pDFAState = DFA;stackIndex = 0;currProbability = 1.0;while (1) {/* Create a new stack entry; merge a new set of shape andDFA proposals into a new hypothesis list, and put all therelevant information into the new stack element */ shapeCount = ShapeMatch(pStrokes,shapeProposals);dfaCount = DFAGetProposals(pDFAState,dfaProposals);hypCount =MakeHypotheses(pStrokes,shapeProposals,shapeCount,dfaProposals,dfaCount,bestProbability,currProbability,hypotheses);stack[stackIndex].count = hypCount;stack[stackIndex].pHypotheses =(HYPOTHESIS *)malloc(hypCount*sizeof(HYPOTHESIS));memcpy(stack[stackIndex].pHypotheses,hypotheses);stack[stackIndex].currentHypothesis = 0;Hypothesis process goes down the hypothesis listupdating bestString and bestProbability when it findshypotheses that use up all the strokes, and returning thenumber of left-over hypotheses whenever it finds ahypothesis with strokes still to be analyzed. It alsoupdates the currentHypothesis (which may be referred toas the &#34;current active hypothesis&#34;) number on thestack. When it returns to zero, that means this hypothesislist is exhausted and we should pop the stack. When we can&#39;tpop the stack any further, we&#39;ve completed the analysis */while (HypothesisProcess(stack,stackIndex,&amp;bestProbability, bestString, currString) == 0) {if (stackIndex == 0) {strcpy(pString,bestString);return (bestProbability);free(stack[stackIndex].pHypotheses);--stackIndex;}/* At this point, the current hypothesis still hasstrokes to be analyzed, so we need to set up to pushanother element on the stack */pHypothesis = stack[stackIndex].pHypotheses +stack[stackIndex].currentHypothesis;pStrokes = pHypothesis-&gt;pStrokes;pDFAState = pHypothesis-&gt;pDFAState;currProbability = pHypothesis-&gt;probability;++stackIndex;} /* end of while (true) loop */} /* end of TranslateHandwriting *//* THIS IS THE END OF THE PROGRAM LISTING */______________________________________ 
    
     The embodiment so far described contains two &#34;experts&#34;: ShapeMatch and DFAGetProposals. ShapeMatch has the power to propose new characters and to veto other proposals. DFAGetProposals can affect the probability of other proposals, but cannot propose on it sown, nor can it veto proposals. In an alternative embodiment including multiple experts representing different types of information, such as vertical position, gross character shape, punctuation, case, numeric information, etc. and in which several of the experts are allowed to propose, it becomes easier to use a single proposal table of 256 entries (one per character) that all the experts update, rather than having each expert produce a separate list of proposals that another routine merges into a composite hypothesis list. Each element of this table would look like this: 
     
         ______________________________________typedef int EXPERT1.sub.-- STATE;typedef struct PROPOSAL.sub.-- TABLE {/* cumulative probability */double probability;/* number of experts proposing this */int proposed;/* number of experts vetoing it */int vetoed;struct expert1 {  EXPERT1.sub.-- STATE *pExpertState;} expert1;struct expert2 {EXPERT2.sub.-- STATE *pExpert2State;} expert2;..};______________________________________ 
    
     The probability must be initialized to 1.0, and the proposed and vetoed counts must be initialized to 0. Each expert must increment the proposed count on each character it proposes for this position, increment the vetoed count on each character it vetoes for this position, multiply the probability by the probability it assigns to each character, and update its state pointer in each character to reflect the state that expert transitions to should that character be expanded later. 
     To be hypothesized, a character must be proposed at least once and must not be vetoed at all.