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May 2, 2020 at 12:53 history edited YCor
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Feb 17, 2020 at 22:26 history edited YCor
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Feb 23, 2019 at 17:49 comment added Eran David Clark used ''genetic programming'' to find a discriminator term. I'm not sure if genetic programming and evolutionary algorithms are synonyms but they seem similar at least. Here's a link to his paper: link
Feb 11, 2019 at 23:04 comment added Joseph Van Name So the problem of obtaining a compatible partial ordering on the classical Laver tables is an instance of Horn-satisfiability which is solvable in polynomial time. On the other hand, I have not been able to axiomatize the notion of a compatible linear ordering using Horn formulas. Perhaps, one can use the polynomial time Horn-satisfiability algorithm to help make an algorithm for the linear ordering case?
Feb 10, 2019 at 16:11 comment added Joseph Van Name So I have used this SAT solver (for SAT in CNF form) jgalenson.github.io/research.js/demos/minisat.html to produce linear orderings on $A_{5}$ with $32$ elements in 0.357 seconds.
Feb 10, 2019 at 14:03 comment added Joseph Van Name @Bullet51 I have never considered using SAT solvers. That may be an interesting idea especially for the linear orderings on Laver tables.
Feb 10, 2019 at 8:39 comment added LeechLattice Why not use SAT solvers?
Feb 10, 2019 at 7:56 comment added Joseph Van Name @Bullet51 The associative operations were successful for $n<30$ (I have not tried to maximize the cardinality of the semigroups), but for the Laver table linear ordering example, the algorithm was successful for $A_{8}$ (I think) which has 256 elements. Of course, it is probably much easier to produce linear orderings using evolutionary algorithms than associative operations since there are fewer linear orders on a finite set than there are associative operations. I have not made any attempts to optimize the Laver table linear ordering search algorithm (there may be better algorithms).
Feb 10, 2019 at 7:31 comment added LeechLattice How large are those algebraic structures? It seems that evolutionary algorithms can hardly succeed when $n>30$.
Feb 10, 2019 at 5:27 history asked Joseph Van Name CC BY-SA 4.0