A Study of Dietary Pattern and Costumes of Selected Castes of the Kachchh District of Gujarat State

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Interpolation Properties and SAT-based Model Checking

Craig interpolation is a widespread method in verification, with important applications such as Predicate Abstraction, CounterExample Guided Abstraction Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model checking techniques based on interpolation require collections of interpolants to satisfy particular properties, to which we refer as "collectives"; they do not hold in general for all interpolation systems and have to be established for each particular system and verification environment. Nevertheless, no systematic approach exists that correlates the individual interpolation systems and compares the necessary collectives. This paper proposes a uniform framework, which encompasses (and generalizes) the most common collectives exploited in verification. We use it for a systematic study of the collectives and of the constraints they pose on propositional interpolation systems used in SAT-based model checking

Refinement Type Inference via Horn Constraint Optimization

We propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a user-specified preference order. The flexible optimization of refinement types enabled by the proposed method paves the way for interesting applications, such as inferring most-general characterization of inputs for which a given program satisfies (or violates) a given safety (or termination) property. Our method reduces such a type optimization problem to a Horn constraint optimization problem by using a new refinement type system that can flexibly reason about non-determinism in programs. Our method then solves the constraint optimization problem by repeatedly improving a current solution until convergence via template-based invariant generation. We have implemented a prototype inference system based on our method, and obtained promising results in preliminary experiments.Comment: 19 page

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

Automatic Verification of Erlang-Style Concurrency

This paper presents an approach to verify safety properties of Erlang-style, higher-order concurrent programs automatically. Inspired by Core Erlang, we introduce Lambda-Actor, a prototypical functional language with pattern-matching algebraic data types, augmented with process creation and asynchronous message-passing primitives. We formalise an abstract model of Lambda-Actor programs called Actor Communicating System (ACS) which has a natural interpretation as a vector addition system, for which some verification problems are decidable. We give a parametric abstract interpretation framework for Lambda-Actor and use it to build a polytime computable, flow-based, abstract semantics of Lambda-Actor programs, which we then use to bootstrap the ACS construction, thus deriving a more accurate abstract model of the input program. We have constructed Soter, a tool implementation of the verification method, thereby obtaining the first fully-automatic, infinite-state model checker for a core fragment of Erlang. We find that in practice our abstraction technique is accurate enough to verify an interesting range of safety properties. Though the ACS coverability problem is Expspace-complete, Soter can analyse these verification problems surprisingly efficiently.Comment: 12 pages plus appendix, 4 figures, 1 table. The tool is available at http://mjolnir.cs.ox.ac.uk/soter

Splitting Proofs for Interpolation

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refuta- tion into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201

Flow- and context-sensitive points-to analysis using generalized points-to graphs

© Springer-Verlag GmbH Germany 2016. Bottom-up interprocedural methods of program analysis construct summary flow functions for procedures to capture the effect of their calls and have been used effectively for many analyses. However, these methods seem computationally expensive for flow- and context- sensitive points-to analysis (FCPA) which requires modelling unknown locations accessed indirectly through pointers. Such accesses are com- monly handled by using placeholders to explicate unknown locations or by using multiple call-specific summary flow functions. We generalize the concept of points-to relations by using the counts of indirection levels leaving the unknown locations implicit. This allows us to create sum- mary flow functions in the form of generalized points-to graphs (GPGs) without the need of placeholders. By design, GPGs represent both mem- ory (in terms of classical points-to facts) and memory transformers (in terms of generalized points-to facts). We perform FCPA by progressively reducing generalized points-to facts to classical points-to facts. GPGs distinguish between may and must pointer updates thereby facilitating strong updates within calling contexts. The size of GPGs is linearly bounded by the number of variables and is independent of the number of statements. Empirical measurements on SPEC benchmarks show that GPGs are indeed compact in spite of large procedure sizes. This allows us to scale FCPA to 158 kLoC using GPGs (compared to 35 kLoC reported by liveness-based FCPA). Thus GPGs hold a promise of efficiency and scalability for FCPA without compro- mising precision

Population structure and phenotypic variation of \u3ci\u3eSclerotinia sclerotiorum\u3c/i\u3e from dry bean (\u3ci\u3ePhaseolus vulgaris\u3c/i\u3e) in the United States

The ascomycete pathogen Sclerotinia sclerotiorum is a necrotrophic pathogen on over 400 known host plants, and is the causal agent of white mold on dry bean. Currently, there are no known cultivars of dry bean with complete resistance to white mold. For more than 20 years, bean breeders have been using white mold screening nurseries (wmn) with natural populations of S. sclerotiorum to screen new cultivars for resistance. It is thus important to know if the genetic diversity in populations of S. sclerotiorum within these nurseries (a) reflect the genetic diversity of the populations in the surrounding region and (b) are stable over time. Furthermore, previous studies have investigated the correlation between mycelial compatibility groups (MCG) and multilocus haplotypes (MLH), but none have formally tested these patterns.We genotyped 366 isolates of S. sclerotiorum from producer fields and wmn surveyed over 10 years in 2003–2012 representing 11 states in the United States of America, Australia, France, and Mexico at 11 microsatellite loci resulting in 165 MLHs. Populations were loosely structured over space and time based on analysis of molecular variance and discriminant analysis of principal components, but not by cultivar, aggressiveness, or field source. Of all the regions tested, only Mexico (n = 18) shared no MLHs with any other region. Using a bipartite network-based approach, we found no evidence that the MCGs accurately represent MLHs. Our study suggests that breeders should continue to test dry bean lines in several wmn across the United States to account for both the phenotypic and genotypic variation that exists across regions