Minor changes

Obhajoba/slides.tex

@@ -119,9 +119,14 @@
 \newcommand{\QFBV}{\ensuremath{\mathcal{QFBV}}}
 
 
+\let\otp\titlepage
+\renewcommand{\titlepage}{\otp\addtocounter{framenumber}{-1}}
+
 \begin{document}
 
-\frame{\titlepage}
+\begin{frame}[plain]
+ \titlepage
+\end{frame}
 
 \section{Propositional Satisfiability}
 \begin{frame}
@@ -188,17 +193,19 @@
 
   \bigskip
 
-  Traditionally solved by the \alert{CDCL modulo theories} -- combination of
+  Traditionally solved by \alert{CDCL modulo theories} -- combination of
   CDCL and a specialized theory solver.
 
+  \pause
+
   \begin{example}
     Let $\varphi = (x + y = 3) \wedge (x > 1) \wedge (y = 2 \vee y = 1)$.
 
     \begin{enumerate}[<+->]
-    \item Propositional model $\{ x + y = 3,~x > 1,~y = 2 \} $.
+    \item Propositional model $\{ x + y = 3,~x > 1,~y = 2,~\neg(y = 1) \} $.
     \item This model \textbf{is not} consistent with the theory of integers.
-    \item Conjoin $\neg (x + y = 3) \vee \neg (x > 1) \vee \neg (y = 2)$ to $\varphi$.
-    \item Propositional model $\{ x + y = 3,~x > 1,~y = 1 \} $.
+    \item Conjoin $\neg (x + y = 3) \vee \neg (x > 1) \vee \neg (y = 2) \vee (y = 1)$ to $\varphi$.
+    \item Propositional model $\{ x + y = 3,~x > 1,~\neg(y=2),~y = 1\} $.
     \item This model \textbf{is} consistent with the theory of integers.
     \item $\varphi$ is satisfiable.
     \end{enumerate}
@@ -260,15 +267,18 @@
 
   Quantifier bit-vector formulas traditionally solved by
   \alert{quantifier instantiation}.
+
+  \pause
+
   \begin{example}
-    Let $\varphi = 3 < a ~\wedge~ \forall x\,(a \not = 2 \times x)$
+    Let $\varphi = a > 3 ~\wedge~ \forall x\,(a \not = 2 \cdot x)$
     \pause
     \begin{itemize}[<+->]
-    \item $3 < a$ is satisfiable with model $a = 4$.
-    \item $a = 4$ not a model of $\forall x \,(a \not = 2 \times x)$ (corresponding counter-example is $x = 2$).
+    \item $a > 3$ is satisfiable with model $a = 4$.
+    \item $a = 4$ not a model of $\forall x \,(a \not = 2 \cdot x)$ -- consider $x = 2$.
     \item Add instance of the quantifier for $x = 2$.
-    \item $3 < a ~\wedge~ (a \not = 2 \times 2)$ is satisfiable with model $a = 5$.
-    \item $a = 5$ is a model of $\forall x \,(a \not = 2 \times x)$.
+    \item $a > 3 ~\wedge~ (a \not = 2 \cdot 2)$ is satisfiable with model $a = 5$.
+    \item $a = 5$ is a model of $\forall x \,(a \not = 2 \cdot x)$.
     \item $\varphi$ is satisfiable
     \end{itemize}
   \end{example}
@@ -319,13 +329,18 @@
   Efficient algorithm are known for operations with BDDs (conjunction,
   disjunction, quantifiers).
 
-  \smallskip
+  \bigskip
 
   Quantification usually reduces the size of the BDD -- useful for
   quantified bit-vectors.
 
   \bigskip
 
+  Representation by (reduced and ordered) BDDs is canonical -- formula
+  is unsatisfiable iff the BDD has root false.
+\end{frame}
+
+\begin{frame}
   We have implemented the solver Q3B, which
   \begin{itemize}
   \item simplifies the formula,
@@ -334,7 +349,10 @@
     too expensive.
   \end{itemize}
 
-  Results show that Q3B is \alert{more efficient} than standard SMT solvers.
+  \bigskip
+
+  Our results and results of SMT-COMP 2016 show that Q3B is
+  \alert{more efficient} than standard SMT solvers.
 \end{frame}
 
 \section{Aims of the Work}