Generating Non-Linear Interpolants by Semidefinite Programming

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure

Synthesis for Polynomial Lasso Programs

We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities). Central to this approach is the discovery of non-linear (algebraic) loop invariants. We extend Sankaranarayanan, Sipma, and Manna's template-based approach and prove a completeness criterion. We perform program synthesis by generating a constraint whose solution is a synthesized program together with a loop invariant that proves the program's correctness. This constraint is non-linear and is passed to an SMT solver. Moreover, we can enforce the termination of the synthesized program with the support of test cases.Comment: Paper at VMCAI'14, including appendi

An Artificial Immune System Approach to Automated Program Verification: Towards a Theory of Undecidability in Biological Computing

We propose an immune system inspired Artificial Immune System (AIS) algorithm for the purposes of automated program verification. It is proposed to use this AIS algorithm for a specific automated program verification task: that of predicting shape of program invariants. It is shown that the algorithm correctly predicts program invariant shape for a variety of benchmarked programs. Program invariants encapsulate the computability of a particular program, e.g. whether it performs a particular function correctly and whether it terminates or not. This work also lays the foundation for applying concepts of theoretical incomputability and undecidability to biological systems like the immune system that perform robust computation to eliminate pathogens

Выбор оптимальных стратегий перевозчика на рынке транспортно-экспедиционных услуг

The method of choice of an optimal strategy by the carrier at a freight forwarding market with regard to a fleet structure has been proposed.Предложена методика выбора перевозчиком оптимальных стратегий на рынке транспортно-экспедиционных услуг относительно парка подвижного состава.Запропонована методика вибору перевізником оптимальних стратегій на ринку транспортно-експедиційних послуг відносно парку рухомого складу

Методы генерации учебных примеров программ с нетривиальными полиномиальными инвариантами

The problem of generation of program examples with nontrivial polynomial invariants is considered. These examples are used in mathematical system of educational purpose “Static Analysis Systems”. The two methods are proposed: the method of algebraic dependencies and the method of L-invariants.Рассматривается задача построения примеров программ, обладающих нетривиальными полиномиальными инвариантами. Эти примеры используются в математической системе учебного назначения «Статический анализ программ». Предложены два метода: метод алгебраической зависимости и метод L-инвариантов.Розглянуто задачу побудови прикладів програм, що мають нетривіальні поліноміальні інваріанти. Ці приклади використовуються в математичній системі навчального призначення «Статичний аналіз програм». Запропоновані два методи: метод алгебраїчної залежності й метод L-інваріантів