diff c617890..763cb89 generalized_star_height_four_v2.txt
diff --git a/generalized_star_height_four_v2.txt b/generalized_star_height_four_v2.txt index 138e936..b8c281a 100644 --- a/generalized_star_height_four_v2.txt +++ b/generalized_star_height_four_v2.txt @@ -36,14 +36,14 @@ first few levels using transition graphs of deterministic automata. Dejean and Schutzenberger proved unbounded ordinary star height over a binary alphabet. -./eggan-1963.pdf -./dejean-schutzenberger-1966.pdf +./pdf/eggan-1963.pdf +./pdf/dejean-schutzenberger-1966.pdf Schutzenberger characterized the languages of ordinary star height zero, equivalently the languages of generalized star height zero, as those recognized by finite aperiodic monoids. -./schutzenberger-1965.pdf +./pdf/schutzenberger-1965.pdf Henneman proved that every language recognized by a finite commutative group has generalized star height at most one. Pin, @@ -52,8 +52,8 @@ 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. -./pst-1992.pdf -./straubing2002.pdf +./pdf/pst-1992.pdf +./pdf/straubing2002.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 @@ -210,7 +210,7 @@ most The symmetric Lovasz local lemma (Erdos and Lovasz, 1975) is applied next. -./sources/erdos-lovasz-1975.pdf +./pdf/sources/erdos-lovasz-1975.pdf Suppose a finite family of events has a dependency graph of maximum degree D and each @@ -427,14 +427,14 @@ roster serves whenever many residues are required. Only the elementary root bound over the prime field is used; the coding theory that follows from the Reed-Solomon construction plays no role. -./reed-solomon-1960.pdf +./pdf/reed-solomon-1960.pdf Local markers. The marker-versus-local-periodicity principle appears in Krieger's analysis of subsystems of topological Markov chains, with a finite clopen merging formulation in Meyerovitch. -./krieger1982.pdf -./meyerovitch-2025.pdf +./pdf/krieger1982.pdf +./pdf/meyerovitch-2025.pdf Lemma (local markers). Let d >= 2 and K > 3 d^2 be integers. There is a translation-equivariant rule that marks integer positions of any