Aleksandar S. Dimovski

Aleksandar S. Dimovski, Sven Apel, Axel Legay

Lifted (family-based) static analysis by abstract interpretation is capable of analyzing all variants of a program family simultaneously, in a single run without generating any of the variants explicitly. The elements of the underlying lifted analysis domain are tuples, which maintain one property per variant. Still, explicit property enumeration in tuples, one by one for all variants, immediately yields combinatorial explosion. This is particularly apparent in the case of program families that, apart from Boolean features, contain also numerical features with big domains, thus admitting astronomic configuration spaces. The key for an efficient lifted analysis is proper handling of variability-specific constructs of the language (e.g., feature-based runtime tests and #if directives). In this work, we introduce a new symbolic representation of the lifted abstract domain that can efficiently analyze program families with numerical features. This makes sharing between property elements corresponding to different variants explicitly possible. The elements of the new lifted domain are constraint-based decision trees, where decision nodes are labeled with linear constraints defined over numerical features and the leaf nodes belong to an existing single-program analysis domain. To illustrate the potential of this representation, we have implemented an experimental lifted static analyzer, called SPLNUM^2Analyzer, for inferring invariants of C programs. It uses existing numerical domains (e.g., intervals, octagons, polyhedra) from the APRON library as parameters. An empirical evaluation on benchmarks from SV-COMP and BusyBox yields promising preliminary results indicating that our decision trees-based approach is effective and outperforms the tuple-based approach, which is used as a baseline lifted analysis based on abstract interpretation.

Nino Arsov, Goran Velinov, Aleksandar S. Dimovski et al.

The excessively increased volume of data in modern data management systems demands an improved system performance, frequently provided by data distribution, system scalability and performance optimization techniques. Optimized horizontal data partitioning has a significant influence of distributed data management systems. An optimally partitioned schema found in the early phase of logical database design without loading of real data in the system and its adaptation to changes of business environment are very important for a successful implementation, system scalability and performance improvement. In this paper we present a novel approach for finding an optimal horizontally partitioned schema that manifests a minimal total execution cost of a given database workload. Our approach is based on a formal model that enables abstraction of the predicates in the workload queries, and are subsequently used to define all relational fragments. This approach has predictive features acquired by simulation of horizontal partitioning, without loading any data into the partitions, but instead, altering the statistics in the database catalogs. We define an optimization problem and employ a genetic algorithm (GA) to find an approximately optimal horizontally partitioned schema. The solutions to the optimization problem are evaluated using PostgreSQL's query optimizer. The initial experimental evaluation of our approach confirms its efficiency and correctness, and the numbers imply that the approach is effective in reducing the workload execution cost.

Aleksandar S. Dimovski, Axel Legay, Andrzej Wasowski

Variability models allow effective building of many custom model variants for various configurations. Lifted model checking for a variability model is capable of verifying all its variants simultaneously in a single run by exploiting the similarities between the variants. The computational cost of lifted model checking still greatly depends on the number of variants (the size of configuration space), which is often huge. One of the most promising approaches to fighting the configuration space explosion problem in lifted model checking are variability abstractions. In this work, we define a novel game-based approach for variability-specific abstraction and refinement for lifted model checking of the full CTL, interpreted over 3-valued semantics. We propose a direct algorithm for solving a 3-valued (abstract) lifted model checking game. In case the result of model checking an abstract variability model is indefinite, we suggest a new notion of refinement, which eliminates indefinite results. This provides an iterative incremental variability-specific abstraction and refinement framework, where refinement is applied only where indefinite results exist and definite results from previous iterations are reused.

Aleksandar S. Dimovski

Variational systems allow effective building of many custom variants by using features (configuration options) to mark the variable functionality. In many of the applications, their quality assurance and formal verification are of paramount importance. Family-based model checking allows simultaneous verification of all variants of a variational system in a single run by exploiting the commonalities between the variants. Yet, its computational cost still greatly depends on the number of variants (often huge). In this work, we show how to achieve efficient family-based model checking of CTL* temporal properties using variability abstractions and off-the-shelf (single-system) tools. We use variability abstractions for deriving abstract family-based model checking, where the variability model of a variational system is replaced with an abstract (smaller) version of it, called modal featured transition system, which preserves the satisfaction of both universal and existential temporal properties, as expressible in CTL*. Modal featured transition systems contain two kinds of transitions, termed may and must transitions, which are defined by the conservative (over-approximating) abstractions and their dual (under-approximating) abstractions, respectively. The variability abstractions can be combined with different partitionings of the set of variants to infer suitable divide-and-conquer verification plans for the variational system. We illustrate the practicality of this approach for several variational systems.

Aleksandar S. Dimovski

In this paper we describe a method for verifying secure information flow of programs, where apart from direct and indirect flows a secret information can be leaked through covert timing channels. That is, no two computations of a program that differ only on high-security inputs can be distinguished by low-security outputs and timing differences. We attack this problem by using slot-game semantics for a quantitative analysis of programs. We show how slot-games model can be used for performing a precise security analysis of programs, that takes into account both extensional and intensional properties of programs. The practicality of this approach for automated verification is also shown.