diff 991b4a6..d14ce2b generalized_star_height_four_v2.txt
diff --git a/generalized_star_height_four_v2.txt b/generalized_star_height_four_v2.txt index 1698e89..0246d67 100644 --- a/generalized_star_height_four_v2.txt +++ b/generalized_star_height_four_v2.txt @@ -51,13 +51,9 @@ Straubing, and Therien extended the conclusion to finite nilpotent groups of class two and established closure properties for the star-height strata. Straubing formulated the absolute boundedness question and the sharper question whether height one always suffices. -Earlier reports include studies of the height-three case and of -uniform computations for finite monoids. ./pst-1992.pdf ./straubing2002.pdf -./height3.pdf -./uniform13.pdf Reduction. A regular language L is recognized by a finite monoid M through a morphism T: Sigma* -> M. The syntactic monoid of L is @@ -214,7 +210,7 @@ most The symmetric Lovasz local lemma (Erdos and Lovasz, 1975) is applied next. -./erdos-lovasz-1975.pdf +./sources/erdos-lovasz-1975.pdf Suppose a finite family of events has a dependency graph of maximum degree D and each @@ -1052,6 +1048,4 @@ produces such an expression, and it has star height at most 4. This completes the proof. A complementary question, whether star height 1 always suffices, -remains open. The proofs in the papers cited above for nilpotent -class-two groups, and the analogues of the height-four construction -for a uniform bound, leave the sharp threshold at 4 unresolved. +remains open.