Commit a2b78be4 authored by Martin Jonas's avatar Martin Jonas
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First draft of Objectives

parent 23460bbd
......@@ -4,10 +4,56 @@
\section{Objectives and Expected Results}
\subsection{Unconstrained variable propagation for quantified bit-vectors}
\subsection{Unconstrained variable propagation for quantified
Simplifications using unconstrained variables can be extended to
quantified formulas. However, in the quantified setting, constraints
can be induced also by the order of the quantified variables. We have
hypothesis of the necessary condition for the quantified variable to
be unconstrained and we have implemented an proof-of-concept
simplification procedure using unconstrained variables for the
quantified bit-vector formulas. Although the initial experimental
results, conducted on the formula from the semi-symbolic model checker
\SymDivine look promissing, the formal proof of the correctnes is not
yet complete.
Furthermore, we suggest simplifications even for term in the form
$k \times x$ with odd values of $x$. If $x$ has bit-width $n$, $i$ is
the largest number such that $2^i$ which divides the constant $k$ and
the value $x$ is unconstrained, the term $k \times x$ can be rewritten
to $extract_0^{n-i}(x) \cdot 0^i$. This approach can possibly be extended
to the multiplication of two variables from one is unconstrained and
further generalized. We plan to prove the correctness of these rules
and develop a formal framework to classify such rewrite rules.
\subsection{Complexity of BV2}
\subsection{Hybrid approach to quantified bit-vectors}
\subsection{Symbolic solver for quantified bit-vectors}
We also plan to further develop the implemented symbolic \smt solver
for quantified bit-vecors Q3B. Besides implementing the proposed
simplifiactions using unconstrained variables, we plan to add support
of uninterpreted functions and theory of arrays to the Q3B. Also used
approximations are right now very simple and could benefit from better
refinement of the approximation in the case that the current
approximation is too coarse.
\subsection{Hybrid approach to quantified bit-vectors}
Although our results with the symbolic \smt solver for quantified
bit-vectors look promissing, standard \smt solvers still perform
better on simple queries and on queries containing
multiplication. Therefore, I want to develop a hybrid approach to \smt
solving of quantified bit-vector formulas, which combines strengths of
both of these approaches. For example, a part of the quantified
formula without multiplication can be converted to the \bdd, which can
be used to guide the model search in the model-based quantifier
instantiation. One possible way of achieving this is adding \bdd based
representation of sets of assignments to the \mcbv solver developed by
Zeljić et al. The \bdd representation can be added to current
over-approximations by bit-patterns and arithmetic intervals.
As the part of my PhD study, also an implementation of a proposed
hybrid approach and its evaluation on the representative set of
benchmark is expected.
\section{Progression Schedule}
......@@ -16,6 +62,8 @@ The plan of my future study and research activities is following:
\item [now -- January 2017] Extending unconstrained variable
propagation to quantified formulas and to non-linear multiplication.
\item [now -- January 2019] Improvements and mantaining of the
developed symbolic \smt solver Q3B.
\item [January 2017] Doctoral exam and defence of this thesis proposal.
\item [January 2017 -- May 2017] Proving a precise complexity class of
the quantfied bit-vector formulas without uninterpreted functions
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