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Motivace různých charakterizací ekvivalentních persegramů
 Kratochvíl, Václav
In this paper we give the motivation and introduction for indirect characterization of equivalence. We have found three operations on persegram remaining induced independence model. By combining them together, one can generate a class of equivalent models. We are not sure whether one can generate the whole class. This problem is closely connected with the above mentioned problem of invariant properties.
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Problém ekvivalentu v kompozitních modelech
 Kratochvíl, Václav
Structure of each Compositional model can be visualized by a tool called persegram. Every persegram over a finite non-empty set of variables N induces an independence model over N, which is a list of conditional independence statements over N. The Equivalence problem is how to characterize (in graphical terms) whether all independence statements in the model induced by persegram P are in the model induced by a second persegram P' and vice versa. Three different operations preserving independence model were introduced in previous papers. If combined, one is able to generate the (whole) class of equivalent persegrams. This characterization is indirect: Two persegrams P,P' are equivalent if there exists a sequence of persegrams from P,P' such that only so called IE-operations are performed to get next persegram in the sequence. In this paper we give the motivation and introduction for direct characterization of equivalence.
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