Marc Csernel

Usual operations with symbolic data under normal symbolic form

Rather than representing data as points within the description space, symbolic objects represent them as hyper-rectangles, in order to take into account some variability within the description. They also make it possible to add some domain knowledge represented by rules which reduce the description space. Unfortunately, this supplementary knowledge usually induces a combinatorial growing of the possible calculus time. In a previous paper we presented a method leading to a decomposition of symbolic objects into a normal symbolic form (NSF) which allows an easier calculation, however great the number of rules may be. In this paper, after recalling what symbolic objects and the NSF are, we focus on the different kinds of operation that can be used when dealing with symbolic objects. We show that the different operations are stable or quasi-stable regarding the NSF. We then see that by applying NSF to distance computation we obtained, in our first trial, a reduction of over 90 per cent in our computational time. Copyright

Towards A Normal Symbolic Form

Boolean Symbolic Objects were introduced by Diday (1988) and since that time a large number of applications have been defined, using these objects, but relatively few of them take constraints on the variables into account. Even in this case, when the graph of dependencies becomes too large, the computational time becomes huge because dependencies are treated in a combinatorial way. We present a method inspired by the technique used in relational data bases (Codd 1972) leading to a decomposition of symbolic objects into a Normal Symbolic Form which allows an easier calculation, however huge the graph of dependencies rules may be. We will apply our method to distance computation following a method due to De Carvalho and inspired by Ichino (1994) but the normal form we present in this paper could be used for other purposes. In our first trials we obtained a 90% reduction of the computational time. In the present text we will only deal with nominal boolean Symbolic Objects, but the method could be used with other kinds of symbolic objects.

Comparing Sanskrit Texts for Critical Editions: The Sequences Move Problem

A critical edition takes into account various versions of the same text in order to show the differences between two distinct versions, in terms of words that have been missing, changed, omitted or displaced. Traditionally, Sanskrit is written without spaces between words, and the word order can be changed without altering the meaning of a sentence. This paper describes the characteristics which make Sanskrit text comparisons a specific matter. It presents two different methods for comparing Sanskrit texts, which can be used to develop a computer assisted critical edition. The first one method uses the L.C.S., while the second one uses the global alignment algorithm. Comparing them, we see that the second method provides better results, but that neither of these methods can detect when a word or a sentence fragment has been moved. We then present a method based on N-gram that can detect such a movement when it is not too far from its original location. We show how the method behaves on several examples. Index Terms—Sanskrit, text alignment.