From: Martin Mares <mj@ucw.cz>
Date: Sat, 3 May 2008 19:02:09 +0000 (+0200)
Subject: Unified typesetting of complexity classes.
X-Git-Tag: printed~17
X-Git-Url: http://mj.ucw.cz/gitweb/?a=commitdiff_plain;h=8fd2be655a14c00bd6a4339b1cfce027122196ea;p=saga.git

Unified typesetting of complexity classes.
---

diff --git a/PLAN b/PLAN
index b429fd9..900e7bd 100644
--- a/PLAN
+++ b/PLAN
@@ -65,8 +65,6 @@ Ranking:
 Typography:
 
 * formatting of multi-line \algin, \algout
-- unify names of complexity classes
-- automatic \raggedbottom?
 
 Global:
 
diff --git a/rank.tex b/rank.tex
index 91121ab..b2c9421 100644
--- a/rank.tex
+++ b/rank.tex
@@ -442,19 +442,19 @@ and Schrijver \cite{schrijver} for more references on flows and matchings.)
 \qed
 
 \para
-The bad news is that computing the permanent is known to be~$\#P$-complete even
+The bad news is that computing the permanent is known to be~$\#\rm P$-complete even
 for zero-one matrices (as proven by Valiant \cite{valiant:permanent}).
 As a~ranking function for a~set of~matchings can be used to count all such
 matchings, we obtain the following theorem:
 
 \thm\id{pcomplete}%
 If there is a~polynomial-time algorithm for lexicographic ranking of permutations with
-a~set of restrictions which is a~part of the input, then $P=\#P$.
+a~set of restrictions which is a~part of the input, then $\rm P=\#P$.
 
 \proof
 We will show that a~polynomial-time ranking algorithm would imply a~po\-ly\-nom\-ial-time
 algorithm for computing the permanent of an~arbitrary zero-one matrix, which
-is a~$\#P$-complete problem.
+is a~$\#\rm P$-complete problem.
 
 We know from Lemma \ref{permchar} that non-zero
 summands in the permanent of a~zero-one matrix~$M$ correspond to permutations restricted