# HG changeset patch # User Chengsong # Date 1656934983 -3600 # Node ID 9d18f3eac484edf033a34e004eecfa4478eed22b # Parent 671a83abccf39f7149a26b3ebebade27cff24387 data diff -r 671a83abccf3 -r 9d18f3eac484 ChengsongTanPhdThesis/Chapters/Finite.tex --- a/ChengsongTanPhdThesis/Chapters/Finite.tex Mon Jul 04 12:27:13 2022 +0100 +++ b/ChengsongTanPhdThesis/Chapters/Finite.tex Mon Jul 04 12:43:03 2022 +0100 @@ -1046,7 +1046,7 @@ \end{proof} \noindent This closed form has a variant which can be more convenient in later proofs: -\begin{corollary} +\begin{corollary}{altsClosedForm1} If $s \neq []$ then $\rderssimp \; (\sum \; rs) \; s = \rsimp{(\sum \; (\map \; \rderssimp{\_}{s} \; rs))}$. @@ -1498,8 +1498,7 @@ \end{proof} \noindent -where in (1) the $\textit{Suffix}( r_1, s)$ are the all the suffixes of $s$ where $\rderssimp{ r_1}{s'}$ is nullable ($s'$ being a suffix of $s$). -The reason why we could write the derivatives of a sequence this way is described in section 2. +(1) is by the corollary \ref{seqEstimate1} The term (2) is used to control (1). That is because one can obtain an overall smaller regex list diff -r 671a83abccf3 -r 9d18f3eac484 ChengsongTanPhdThesis/a_aa_star_bsimp.data --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/ChengsongTanPhdThesis/a_aa_star_bsimp.data Mon Jul 04 12:43:03 2022 +0100 @@ -0,0 +1,21 @@ +0 6 +1 10 +2 17 +3 17 +4 17 +5 17 +6 17 +7 17 +8 17 +9 17 +10 17 +11 17 +12 17 +13 17 +14 17 +15 17 +16 17 +17 17 +18 17 +19 17 +20 17 \ No newline at end of file