Профиль российской бедности: факторы и риски для работающего населения

Выявлены факторы и соответствующие им риски возникновения бедности среди работающего населения России. Доказывается, что причины возникновения бедности лежат в плоскости экономического развития страны: особенностей прохождения экономических циклов на волне спада и кризиса, качества экономического роста на волне подъема. Выработаны направления стратегии качественного экономического роста страны для преодоления бедности работающего населения

A Lazy SMT-Solver for a Non-Linear Subset of Real Algebra

There are several methods for the synthesis and analysis of hybrid systems that require efficient algorithms and tools for satisfiability checking. For analysis, e.g., bounded model checking describes counterexamples of a fixed length by logical formulas, whose satisfiability corresponds to the existence of such a counterexample. As an example for parameter synthesis, we can state the correctness of a parameterized system by a logical formula; the solution set of the formula gives us possible safe instances of the parameters. For discrete systems, which can be described by propositional logic formulas, SAT-solvers can be used for the satisfiability checks. For hybrid systems, having mixed discrete-continuous behavior, SMT-solvers are needed. SMT-solving extends SAT with theories, and has its main focus on linear arithmetic, which is sufficient to handle, e.g., linear hybrid systems. However, there are only few solvers for more expressive but still decidable logics like the first-order theory of the reals with addition and multiplication -- real algebra. Since the synthesis and analysis of non-linear hybrid systems requires such a powerful logic, we need efficient SMT-solvers for real algebra. Our goal is to develop such an SMT-solver for the real algebra, which is both complete and efficient

Accelerating Parametric Probabilistic Verification

We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key ingredients: a graph decomposition into strongly connected subgraphs combined with a novel factorization strategy for polynomials. Experimental evaluations show that these approaches can lead to a speed-up of up to several orders of magnitude in comparison to existing approache

Integrating virtual substitution into strategic SMT solving

This thesis addresses the integration of real algebraic procedures as theory solvers into satisfiability modulo theories (SMT) solvers, in order to check non-linear real- and integer-arithmetic formulas for satisfiability. There are plenty of procedures to choose from and we aim for a general framework that allows us to select and combine them. The main part of this thesis concerns one specific example of the aforementioned integration: the virtual substitution method. Here we also optimize this method with respect to satisfiability checking and extend it such that it can be used for integer arithmetic