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

Sharper and Simpler Nonlinear Interpolants for Program Verification

Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the current paper contributes its enhancement that yields sharper and simpler interpolants. The enhancement is made possible by: theoretical observations in real algebraic geometry; and our continued fraction-based algorithm that rounds off (potentially erroneous) numerical solutions of SDP solvers. Experiment results support our tool's effectiveness; we also demonstrate the benefit of sharp and simple interpolants in program verification examples

Subsumer-First: Steering Symbolic Reachability Analysis

Abstract. Symbolic reachability analysis provides a basis for the veri-fication of software systems by offering algorithmic support for the ex-ploration of the program state space when searching for proofs or coun-terexamples. The choice of exploration strategy employed by the anal-ysis has direct impact on its success, whereas the ability to find short counterexamples quickly and—as a complementary task—to efficiently perform the exhaustive state space traversal are of utmost importance for the majority of verification efforts. Existing exploration strategies can optimize only one of these objectives which leads to a sub-optimal reach-ability analysis, e.g., breadth-first search may sacrifice the exploration ef-ficiency and chaotic iteration can miss minimal counterexamples. In this paper we present subsumer-first, a new approach for steering symbolic reachability analysis that targets both minimal counterexample discovery and efficiency of exhaustive exploration. Our approach leverages the re-sult of fixpoint checks performed during symbolic reachability analysis to bias the exploration strategy towards its objectives, and does not require any additional computation. We demonstrate how the subsumer-first ap-proach can be applied to improve efficiency of software verification tools based on predicate abstraction. Our experimental evaluation indicates the practical usefulness of the approach: we observe significant efficiency improvements (median value 40%) on difficult verification benchmarks from the transportation domain.

The Reed-Stanton press rig for the generation of reproducible fingermarks : towards a standardised methodology for fingermark research

In the search for better or new methods/techniques to visualise fingermarks or to analyse them exploiting their chemical content, fingermarks inter-variability may hinder the assessment of the method effectiveness. Variability is due to changes in the chemical composition of the fingermarks between different donors and within the same donor, as well as to differential contact time, pressure and angle. When validating a method or comparing it with existing ones, it is not always possible to account for this type of variability. One way to compensate for these issues is to employ, in the early stages of the method development, a device generating reproducible fingermarks. Here the authors present their take on such device, as well as quantitatively describing its performance and benefits against the manual production of marks. Finally a short application is illustrated for the use of this device, at the method developmental stages, in an emerging area of fingerprinting research concerning the retrieval of chemical intelligence from fingermarks

Material Symmetry to Partition Endgame Tables

Many games display some kind of material symmetry . That is, some sets of game elements can be exchanged for another set of game elements, so that the resulting position will be equivalent to the original one, no matter how the elements were arranged on the board. Material symmetry is routinely used in card game engines when they normalize their internal representation of the cards. Other games such as chinese dark chess also feature some form of material symmetry, but it is much less clear what the normal form of a position should be. We propose a principled approach to detect material symmetry. Our approach is generic and is based on solving multiple rel- atively small sub-graph isomorphism problems. We show how it can be applied to chinese dark chess , dominoes , and skat . In the latter case, the mappings we obtain are equivalent to the ones resulting from the standard normalization process. In the two former cases, we show that the material symmetry allows for impressive savings in memory requirements when building endgame tables. We also show that those savings are relatively independent of the representation of the tables

Eomes is sufficient to regulate IL-10 expression and cytotoxic effector molecules in murine CD4+ T cells

The T-box transcription factors T-bet and Eomesodermin regulate type 1 immune responses in innate and adaptive lymphocytes. T-bet is widely expressed in the immune system but was initially identified as the lineage-specifying transcription factor of Th1 CD4+ T cells, where it governs expression of the signature cytokine IFN- γ and represses alternative cell fates like Th2 and Th17. T-bet’s paralog Eomes is less abundantly expressed and Eomes+ CD4+ T cells are mostly found in the context of persistent antigen exposure, like bone marrow transplantation, chronic infection or inflammation as well as malignant disorders. However, it has remained unresolved whether Eomes executes similar transcriptional activities as T-bet in CD4+ T cells. Here we use a novel genetic approach to show that Eomes expression in CD4+ T cells drives a distinct transcriptional program that shows only partial overlap with T-bet. We found that Eomes is sufficient to induce the expression of the immunoregulatory cytokine IL-10 and, together with T-bet, promotes a cytotoxic effector profile, including Prf1, Gzmb, Gzmk, Nkg7 and Ccl5, while repressing alternative cell fates. Our results demonstrate that Eomes+ CD4+ T cells, which are often found in the context of chronic antigen stimulation, are likely to be a unique CD4+ T cell subset that limits inflammation and immunopathology as well as eliminates antigen-presenting and malignant cells