### 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 bit-vectors} 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. \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 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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