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-rw-r--r--tex/thesis/contribution/contribution.tex17
1 files changed, 8 insertions, 9 deletions
diff --git a/tex/thesis/contribution/contribution.tex b/tex/thesis/contribution/contribution.tex
index 5b3acb9..1709d40 100644
--- a/tex/thesis/contribution/contribution.tex
+++ b/tex/thesis/contribution/contribution.tex
@@ -49,9 +49,9 @@
In this chapter the main theoretical contribution of this thesis is
presented: an extension on a $\max$-strategy iteration algorithm for
solving fixpoint equations over the integers with monotonic
-operators\cite{Gawlitza:2007:PFC:1762174.1762203} (see Section
-\ref{sec:gawlitza-algorithm}). We devise an algorithm which performs
-considerably better for practical equation systems.
+operators~\cite{Gawlitza:2007:PFC:1762174.1762203}. We devise an
+algorithm which performs considerably better for practical equation
+systems.
In this chapter we will begin by presenting the Work-list Depth First
Search (W-DFS) fixpoint algorithm developed by Seidl et
@@ -61,12 +61,11 @@ chapter will conclude with our Demand-driven Strategy
Improvement (DSI) algorithm to perform efficient strategy iteration
and fixpoint iteration. % TODO: fix me, or something
-The existing algorithm as presented in Section
-\ref{section:basic-algorithm} consists of two iterative operations:
-fixpoint iteration and max-strategy iteration. Each of these
-operations consists of naively ``evaluating'' the system repeatedly
-until a further evaluation results in no change. Gawlitza et
-al.~proved that these iterations converge in a finite number of
+The existing algorithm consists of two iterative operations: fixpoint
+iteration and max-strategy iteration. Each of these operations
+consists of naively ``evaluating'' the system repeatedly until a
+further evaluation results in no change. Gawlitza et al.~proved that
+these iterations converge in a finite number of
steps\cite{Gawlitza:2007:PFC:1762174.1762203} , but in practice this
naive approach performs a large number of re-calculations of results
which are already known.