ionisorus · carlberton · Sep 9, 2025
diff --git a/instances/matrix_multiplication/README b/instances/matrix_multiplication/README
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+Nous nous sommes intéressés à un solveur de recherche locale nommé xnfSAT (https://www.cs.cmu.edu/~mheule/publications/xnfSAT.pdf), qui réalise ses expérimentations sur des instances issues du MM-Challenge-1 (https://github.com/marijnheule/matrix-challenges). Ces instances correspondent à des formules de multiplication matricielle avec 23 multiplications, basées sur les équations de Brent  (https://doi.org/10.1016/j.jsc.2020.10.003).
+
+Dans ce cadre, j’ai modélisé ces instances au format ANF à l’aide de schémas de multiplication connus (Laderman et Courtois), en fixant un certain nombre de variables (1/2, 1/3, 1/4, 2/3 et 4/5 du total des 621 variables).
+
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_1.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_1.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_10.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_10.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_11.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_11.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_12.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_12.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_13.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_13.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_14.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_14.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_15.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_15.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_16.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_16.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_17.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_17.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_18.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_18.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_19.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_19.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_2.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_2.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_20.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_20.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_3.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_3.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_4.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_4.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_5.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_5.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_6.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_6.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_7.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_7.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_8.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_8.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_9.anf b/instances/matrix_multiplication/courtois_scheme/var_1of2/anf/brent_equations_9.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_1.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_1.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_10.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_10.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_11.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_11.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_12.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_12.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_13.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_13.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_14.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_14.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_15.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_15.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_16.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_16.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_17.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_17.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_18.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_18.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_19.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_19.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_2.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_2.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_20.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_20.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_3.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_3.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_4.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_4.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_5.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_5.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_6.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_6.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_7.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_7.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_8.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_8.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_9.anf b/instances/matrix_multiplication/courtois_scheme/var_1of3/anf/brent_equations_9.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_1.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_1.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_10.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_10.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_11.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_11.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_12.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_12.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_13.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_13.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_14.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_14.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_15.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_15.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_16.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_16.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_17.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_17.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_18.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_18.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_19.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_19.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_2.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_2.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_20.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_20.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_3.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_3.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_4.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_4.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_5.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_5.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_6.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_6.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_7.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_7.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_8.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_8.anf
diff --git a/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_9.anf b/instances/matrix_multiplication/courtois_scheme/var_1of4/anf/brent_equations_9.anf
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		Nous nous sommes intéressés à un solveur de recherche locale nommé xnfSAT (https://www.cs.cmu.edu/~mheule/publications/xnfSAT.pdf), qui réalise ses expérimentations sur des instances issues du MM-Challenge-1 (https://github.com/marijnheule/matrix-challenges). Ces instances correspondent à des formules de multiplication matricielle avec 23 multiplications, basées sur les équations de Brent (https://doi.org/10.1016/j.jsc.2020.10.003).

		Dans ce cadre, j’ai modélisé ces instances au format ANF à l’aide de schémas de multiplication connus (Laderman et Courtois), en fixant un certain nombre de variables (1/2, 1/3, 1/4, 2/3 et 4/5 du total des 621 variables).