[PPL-devel] [GIT] ppl/ppl(master): Fixed KapurZHZLN13.

[Roberto Bagnara]

Module: ppl/ppl
Branch: master
Commit: fdcab35567fd8b9031b4dff2e968476485f74ebd
URL:    http://www.cs.unipr.it/git/gitweb.cgi?p=ppl/ppl.git;a=commit;h=fdcab35567fd8b9031b4dff2e968476485f74ebd

Author: Roberto Bagnara <roberto.bagnara at bugseng.com>
Date:   Sun Dec 29 10:12:27 2013 +0100

Fixed KapurZHZLN13.

---

 doc/ppl_citations.bib |   25 ++++++++++++++-----------
 1 files changed, 14 insertions(+), 11 deletions(-)

diff --git a/doc/ppl_citations.bib b/doc/ppl_citations.bib
index 1df5397..1c0c7fa 100644
--- a/doc/ppl_citations.bib
+++ b/doc/ppl_citations.bib
@@ -3183,8 +3183,10 @@ Summarizing:
 }
 
 @InCollection{KapurZHZLN13,
-  Author = "D. Kapur and Z. Zhang and M. Horbach and H. Zhao and Q. Lu and T. Nguyen",
-  Title = "Geometric Quantifier Elimination Heuristics for Automatically Generating Octagonal and Max-plus Invariants",
+  Author = "D. Kapur and Z. Zhang and M. Horbach and H. Zhao and Q. Lu
+            and T. Nguyen",
+  Title = "Geometric Quantifier Elimination Heuristics
+           for Automatically Generating Octagonal and Max-plus Invariants",
   Booktitle = "Automated Reasoning and Mathematics:
                Essays in Memory of William W. McCune",
   Editor = "M. P. Bonacina and M. E. Stickel",
@@ -3197,26 +3199,27 @@ Summarizing:
   Abstract = "Geometric heuristics for the quantifier elimination
               approach presented by Kapur (2004) are investigated to
               automatically derive loop invariants expressing weakly
-              relational numerical properties (such as l =< x =< h or
-              l =< +/- x +/- y =< h) for imperative programs. Such properties
+              relational numerical properties (such as $l \leq x \leq h$ or
+              $l \leq  \pm x \pm y \leq h)$ for imperative programs.
+              Such properties
               have been successfully used to analyze commercial
               software consisting of hundreds of thousands of lines of
               code (using for example, the Astr\'ee tool based on
               abstract interpretation framework proposed by Cousot and
               his group). The main attraction of the proposed approach
               is its much lower complexity in contrast to the abstract
-              interpretation approach (O(n^2) in contrast to O(n^4),
-              where n is the number of variables) with the ability to
+              interpretation approach ($O(n^2)$ in contrast to $O(n^4)$,
+              where $n$ is the number of variables) with the ability to
               still generate invariants of comparable strength. This
               approach has been generalized to consider disjunctive
               invariants of the similar form, expressed using maximum
-              function (such as max (x + a,y + b,z + c,d) ≤ max
-              (x + e,y + f,z + g,h)), thus enabling automatic
-              generation of a subclass of disjunctive invariants for
-              imperative programs as well."
+              function (such as
+              $\max(x + a, y + b, z + c, d) \leq \max (x + e, y + f, z + g, h)$),
+              thus enabling automatic generation of a subclass of
+              disjunctive invariants for imperative programs as well."
 }
 
- at Incollection {KhalilGP09,
+ at Incollection{KhalilGP09,
   Author = "G. Khalil and E. Goubault and S. Putot",
   Title = "The Zonotope Abstract Domain {Taylor1+}",
   Booktitle = "Computer Aided Verification: