Contains a report on a research project.National Science Foundatio

Cooper, W. S.

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XVII. MECHANICAL TRANSLATIONV. H. Yngve U. C. Dickman K. C. KnowltonJ. R. Applegate D. A. Dinneen G. H. MatthewsA. N. Chomsky (Absent) E. S. Klima R. A. RothsteinW. S. Cooper J. ViertelA. COMPACT ENCODING OF REFERENCE DATAIn some computer applications it is essential that the program have quick access tolarge quantities of reference data. The data might be a list of employees' names andtheir payroll numbers, or possibly a catalog of manufactured items with their prices.The mechanical translation of languages is such an application, for a large dictionaryof some sort must be stored in a rapid-access memory medium, no matter how sophis-ticated the translation program is. In these situations it is desirable to store the datain as compact a form as possible - to compress it, without losing any useful information.Various compression schemes have been devised; most of them are applicable only tothe argument part of an item of data, and not to the function-value part. These methodsusually introduce a risk of look-up error, which increases as higher rates of compres-sion are demanded. In this report we summarize a system that is confined to the argu-ment part of each item of data and introduces no risk of look-up error, even though itprovides a high degree of compression. The system requires only that the item thatis to be looked up shall be accounted for by the data, and that the arguments shall bearranged in numerical order.For simplicity, let us consider a list of binary arguments listed in ascending numer-ical order (see List 1). In every row of such a list except the first, we single out theleftmost bit that differs from the neighbor immediately above it. All such bits are, perforce, 1-bits. In List 1 these 1-bits have been underlined. The compression systemexploits the fact that knowledge of these bits alone is sufficient to deduce the position ofany item to be looked up in the list. That is, for look-up purposes we could reduceList 1 to a second list (List 2).This meager list (List 2) contains by implication a surprising amount of informa-tion about List 1. To show that it contains enough information for look-up purposes,we reconstruct as much as possible of List 1, using only the information shown inList 2 and utilizing the properties of the underlined 1-bits. As an example, considerthe neighbor immediately below an underlined 1-bit. This must itself be a 1-bit, pro-vided that it lies to the left of the underlined 1-bit in its own row. For the latter under-lined 1-bit, by definition, indicates that all bits to its left in its row are identical withtheir upstairs neighbors. Continuing by induction, we can reason that an underlined1-bit is the topmost bit of a column of 1-bits which extends downward through all succes-sive rows whose own underlined bits lie farther to the right than the column. When theThis work was supported in part by National Science Foundation.1759LIS T'Isjm[ I ----------0-------------I----------10T 0 ---- T-o--0 "00 "S- 00 - 0 -0 -0 - - o o - T o - o -0 0 - 0 -0 0 - 0 -TI-00'Z -sir-II~"I------mII--1-----I -II------1 ;sY100t1010001110011000110101001101T 0 0T T 0 TOt000010100001001100000OIO001001000010001001001100111O11000000ttoooTo 0To1 0 01 0 0o f I0 0 10 0 10 1 1T 1 01 T 00 0 01 0 01 0 000100011~001001011000100TOO010000111 01010110001100o0 0I I o I 0 0O0111000000000110000000100110000000010010000000010011000000001 0011000000000100000000000001000000000000ottooootttoto 0 0tot0 1toootttooo0 01t0t 1oo0ot0tt0oo0o0 t 0 0 0 0o0oooooo 00 O0 00 0 0O0 0 0000(XVII. MECHANICAL TRANSLATION)column arrives at a row whose underlined 1-bit lies to the left of the column bits, it isuncertain whether the column of 1-bits continues down into this row or not. So if weconfine ourselves to what can be deduced with certainty, the column of 1-bits terminatesjust above this uncooperative row. Such columns display all the 1-bits that are containedin or implied by List 2. Next, notice that the definition of an underlined 1-bit impliesthat the neighbor immediately above any underlined 1-bit must be a 0-bit. Reasoning asbefore, we see that such a 0-bit must be the bottom bit of a column of 0-bits whichextends upward past all underlined 1-bits that lie to its right, and that the column, infact, extends into the first row it encounters whose underlined 1-bit lies leftward of thecolumn. Such columns display all of the 0-bits that are implied by List 2.We have been able, a priori, to augment the second list sufficiently to form List 3.This list has the surprising property that any row differs from any other row in at leastone place; that is, for two arbitrary rows, some 0-bit in the upper row will lie directlyabove a 1-bit in the lower row. To see this, consider the rows between the two rows inquestion, and also the lower row itself. One of these rows must contain an underlined1-bit that lies farther toward the left than the underlined 1-bits of the other rows; this1-bit must be at the top of a column of 1-bits which extends down into the lower row inquestion, and this 1-bit must also lie under a column of 0-bits which extends into theupper row in question. Thus any row of List 3 is distinguishable from any other row,in spite of the large proportion of unknown bits. This proves that any item that couldbe looked up in List 1 could also be looked up in List 3, for it would be distinguishablefrom all but one member of the third list.The look-up routines need not be as forbiddingly involved as List 3 might suggest,for this list actually contains some superfluous information. The item to be looked upcorresponds, in reality, to some particular row of List 3 - viz., the row that lies inthe same position in List 3 as does the row in List 1 which matches the item beinglooked up. We regard this row in List 3 as the "correct" row, and we require a look-up program to point out its position. The item does not correspond to any row abovethe correct row, and a distinction will always be apparent between the item and sucha (higher) row, for the row must contain a 0-bit in at least one place where the itemcontains a 1-bit. Similarly, the item can be differentiated from any row lying below thecorrect row, for a lower row must contain at least one 1-bit where the item contains a0-bit. Observe now that the 0-bits shown in the third list are not needed, for it issufficient that the item be distinguishable from all rows lying below the correct row.Therefore, for the purposes of a look-up program, the correct row may be defined asthat row for which all succeeding rows contain at least one 1-bit in the same place thatthe item contains a 0-bit. With this definition, the look-up routine need reconstruct onlycolumns of 1-bits, and this is a one-way procedure whereby successive rows are gener-ated as the routine works downward through the list. A still simpler algorithm avoids the177(XVII. MECHANICAL TRANSLATION)formation of parts of some columns of 1-bits; only one column is essential in any givenrow, provided only one item is being looked up. These look-up procedures and theirvariations are more fully described in Mechanical Translation (1).The second list, which displays only the underlined 1-bits, comprises all of theinformation that needs to be stored. A simple way to code this information would be tonumber the columns of the list, and then store for each row the column number of itsunderlined 1-bit. With this system, N-bit arguments could be compressed to a lengthof [log 2 N] bits, where the square brackets indicate that the quantity within must beincreased until it is an integer. Should the computer happen to operate with a baseb 0 2, then the compression system can be modified in a straightforward manner, so thatan N character argument compresses to [1 + logb N] characters. These compressionrates could be improved a little by utilizing certain weak interdependencies among theunderlined digits themselves, but the improvement would be slight and would entail amore complex look-up procedure.Here is an illustration of the capabilities of this sort of compression system: Thename-and-address part of every listing in a city telephone directory could be replacedby a two-letter code in such a way that a user could still look up the phone number ofany friend whose name and address he knew exactlyW. S. CooperReferences1. W. S. Cooper, The storage problem, MT, Vol. II, No. 5 (in press).178

Mechanical Translation

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Mechanical Translation

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