Mechanical Analysis of Finite Idempotent Relations

Abstract

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A Verified Algorithm Enumerating Event Structures

“…It should also be noticed that, with the definition above, the definition of countEs needed to be different, since we do not want to count duplicates, and therefore was based on a card o set operation, rather than on a combination of listsum and of size, as in Listing 1.1. The problem coming from duplicates is typical of formal enumerations and counting algorithms [12]. Therefore, a second attempt was tried: whereby a remdups operation was simply added at the end of each recursion to remove duplicate entries.…”

“…We therefore submitted it to the OEIS; it passed the review process and is now published at http://oeis.org/A284276. Although there is existing work on the verified enumeration and counting of mathematical objects [11,7,12], this is the first mechanically certified addition to the OEIS we are aware of. Another immediate consequence upon looking at the obtained sequence is that even the counting problem is likely to be as hard as that of counting posets, given the fact that no advanced result permitting to detach the numbering of event structures from that of posets is known, and given the fast growth of the sequence, testified by the last column of table 5.…”