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      1 Brief explanation of the hyphenation algorithm herein.[1]
      2 
      3 Raph Levien <raph (a] acm.org>
      4 4 Aug 1998
      5 
      6    The hyphenation algorithm is basically the same as Knuth's TeX
      7 algorithm. However, the implementation is quite a bit faster.
      8 
      9    The hyphenation files from TeX can almost be used directly. There
     10 is a preprocessing step, however. If you don't do the preprocessing
     11 step, you'll get bad hyphenations (i.e. a silent failure).
     12 
     13    Start with a file such as hyphen.us. This is the TeX ushyph1.tex
     14 file, with the exception dictionary encoded using the same rules as
     15 the main portion of the file. Any line beginning with % is a comment.
     16 Each other line should contain exactly one rule.
     17 
     18    Then, do the preprocessing - "perl substrings.pl hyphen.us". The
     19 resulting file is hyphen.mashed. It's in Perl, and it's fairly slow
     20 (it uses brute force algorithms; about 17 seconds on a P100), but it
     21 could probably be redone in C with clever algorithms. This would be
     22 valuable, for example, if it was handle user-supplied exception
     23 dictionaries by integrating them into the rule table.[2]
     24 
     25    Once the rules are preprocessed, loading them is quite quick -
     26 about 200ms on a P100. It then hyphenates at about 40,000 words per
     27 second on a P100. I haven't benchmarked it against other
     28 implementations (both TeX and groff contain essentially the same
     29 algorithm), but expect that it runs quite a bit faster than any of
     30 them.
     31 
     32 Knuth's algorithm
     33 
     34    This section contains a brief explanation of Knuth's algorithm, in
     35 case you missed it from the TeX books. We'll use the semi-word
     36 "example" as our running example.
     37 
     38    Since the beginning and end of a word are special, the algorithm is
     39 actually run over the prepared word (prep_word in the source)
     40 ".example.". Knuths algorithm basically just does pattern matches from
     41 the rule set, then applies the matches. The patterns in this case that
     42 match are "xa", "xam", "mp", and "pl". These are actually stored as
     43 "x1a", "xam3", "4m1p", and "1p2l2". Whenever numbers appear between
     44 the letters, they are added in. If two (or more) patterns have numbers
     45 in the same place, the highest number wins. Here's the example:
     46 
     47  . e x a m p l e .
     48      x1a
     49      x a m3
     50         4m1p
     51           1p2l2
     52  -----------------
     53  . e x1a4m3p2l2e .
     54 
     55    Finally, hyphens are placed wherever odd numbers appear. They are,
     56 however, suppressed after the first letter and before the last letter
     57 of the word (TeX actually suppresses them before the next-to-last, as
     58 well). So, it's "ex-am-ple", which is correct.
     59 
     60    Knuth uses a trie to implement this. I.e. he stores each rule in a
     61 trie structure. For each position in the word, he searches the trie,
     62 searching for a match. Most patterns are short, so efficiency should
     63 be quite good.
     64 
     65 Theory of the algorithm
     66 
     67    The algorithm works as a slightly modified finite state machine.
     68 There are two kinds of transitions: those that consume one letter of
     69 input (which work just like your regular finite state machine), and
     70 "fallback" transitions, which don't consume any input. If no
     71 transition matching the next letter is found, the fallback is used.
     72 One way of looking at this is a form of compression of the transition
     73 tables - i.e. it behaves the same as a completely vanilla state
     74 machine in which the actual transition table of a node is made up of
     75 the union of transition tables of the node itself, plus its fallbacks.
     76 
     77    Each state is represented by a string. Thus, if the current state
     78 is "am" and the next letter is "p", then the next state is "amp".
     79 Fallback transitions go to states which chop off one or (sometimes)
     80 more letters from the beginning. For example, if none of the
     81 transitions from "amp" match the next letter, then it will fall back
     82 to "mp". Similarly, if none of the transitions from "mp" match the
     83 next letter, it will fall back to "m".
     84 
     85    Each state is also associated with a (possibly null) "match"
     86 string. This represents the union of all patterns which are
     87 right-justified substrings of the match string. I.e. the pattern "mp"
     88 is a right-justified substring of the state "amp", so it's numbers get
     89 added in. The actual calculation of this union is done by the
     90 Perl preprocessing script, but could probably be done in C just about
     91 as easily.
     92 
     93    Because each state transition either consumes one input character
     94 or shortens the state string by one character, the total number of
     95 state transitions is linear in the length of the word.
     96 
     97 [1] Documentations:
     98 
     99 Franklin M. Liang: Word Hy-phen-a-tion by Com-put-er.
    100 Stanford University, 1983. http://www.tug.org/docs/liang.
    101 
    102 Lszl Nmeth: Automatic non-standard hyphenation in OpenOffice.org,
    103 TUGboat (27), 2006. No. 2., http://hunspell.sourceforge.net/tb87nemeth.pdf
    104 
    105 [2] There is the C version of pattern converter "substrings.c"
    106 in the distribution written by Nanning Buitenhuis. Unfortunatelly,
    107 this version hasn't handled the non standard extension of the
    108 algorithm, yet.
    109