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Martin Jonáš
DTEDI
Commits
a2b78be4
Commit
a2b78be4
authored
Sep 02, 2016
by
Martin Jonas
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First draft of Objectives
parent
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Chapters/Chapter04.tex
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a2b78be4
...
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@@ 4,10 +4,56 @@
\section
{
Objectives and Expected Results
}
\subsection
{
Unconstrained variable propagation for quantified bitvectors
}
\subsection
{
Unconstrained variable propagation for quantified
bitvectors
}
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 proofofconcept
simplification procedure using unconstrained variables for the
quantified bitvector formulas. Although the initial experimental
results, conducted on the formula from the semisymbolic 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 bitwidth
$
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 bitvectors
}
\subsection
{
Symbolic solver for quantified bitvectors
}
We also plan to further develop the implemented symbolic
\smt
solver
for quantified bitvecors 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 bitvectors
}
Although our results with the symbolic
\smt
solver for quantified
bitvectors 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 bitvector 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 modelbased 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
overapproximations by bitpatterns 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.
\newpage
\section
{
Progression Schedule
}
...
...
@@ 16,6 +62,8 @@ The plan of my future study and research activities is following:
\begin{description}
[style=nextline,leftmargin=0.8cm]
\item
[now  January 2017] Extending unconstrained variable
propagation to quantified formulas and to nonlinear 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 bitvector formulas without uninterpreted functions
...
...
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