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A Hierarchy of Tractable Subclasses for SAT and Counting SAT Problems

A Hierarchy of Tractable Subclasses for SAT and Counting SAT...

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international symposium on symbolic and numeric algorithms for scientific computing (SYNASC)

作者： Stefan Andrei Gheorghe Grigoras Martin Rinard Roland Hock Chuan Yap Department of Computer Science Lamar University Beaumont USA Department of Computer Science Cuza University of Iaşi Romania Massachusetts Institute of Technology Cambridge USA National University of Singapore Singapore

Finding subclasses of formulae for which the SAT problem can be solved in polynomial time has been an important problem in computer science. We present a new hierarchy of propositional formulæ subclasses for which the SAT and counting SAT problems can be solved in polynomial time. Our tractable subclasses are those propositional formulae in conjunctive normal form where any set of k + 1 clauses are related, i.e., there exists at least one literal in one clause that appears negated in another clause of the considered set of k + 1 clauses. We say this subclass of formulæ is of rank k and it is different from previously known subclasses that are solvable in polynomial time. this is an improvement over the SAT Dichotomy theorem and the counting SAT Dichotomy theorem, since our subclass can be moved out from the ¿P-complete class to the P class. the membership problem for this new subclass can be solved in O(n·l k+1 ), where n, l and k are the number of variables, clauses and the rank (1 ¿ k ¿ l - 1), respectively. We give an efficient algorithm to approximate the number of assignments for any arbitrary conjunctive normal form propositional formula by an upper bound.

关键词： Polynomials Computer science NP-complete problem scientific computing Upper bound Application software Real time systems Embedded system Artificial intelligence Complexity theory

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Simple Relation between the Lowest-Order Element of Ideal 〈G,H〉 and the Last Element of Polynomial Remainder Sequence

Simple Relation between the Lowest-Order Element of Ideal 〈...

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international symposium on symbolic and numeric algorithms for scientific computing (SYNASC)

作者： Tateaki Sasaki Daiju Inaba Professor emeritus University of Tsukuba Ibaraki Japan The Mathematics Certification Institute of Japan Tokyo Japan

ISBN: (纸本)9781538626276

Let G and H be relatively prime polynomials in K[x,u], where K is a number field and (u) = (u 1 , . . . , u ℓ ), with ℓ ≥ 2. Let GB(G,H) be the reduced Gröbner basis of ideal hG,Hi, w.r.t. the elimination order for x. Let r̂ be the lowest-order element of GB(G,H), and Ã, B ∈ K[x,u] be the cofactors of r̂: ÃG+ e BH = r̂. Let PRS(G,H) be the polynomial remainder sequence w.r.t. x, with initial polynomials G and H. Let Pk ∈ K[u] be the last element of PRS(G,H), and A k , B k ∈ K[x,u] be cofactors of P k : A k G + B k H = P k . Ak and B k satisfy degree conditions: deg x (Ak) x(H) and deg x (B k ) x(G), while e Ã and B in general do not. computing Â and B by reducing the degrees w.r.t. x, of Ã and B, respectively, and by normalizing Pk suitably, we show that (P k ,A k ,B k ) = c ( r̂, Â, B), where (P,A,B) denotes a tuple and c ∈ K. We then present a new method for solving the multivariate Diophantine equation φ G + ψH = F for given F ∈ K[x,u] and unknowns φ , ψ ∈ K(u)[x]. Furthermore, we show a new method for solving the ideal-membership problem for 〈G,H〉, without computing any Gröbner basis.

关键词： scientific computing Algebra Mathematical model Complexity theory Computational modeling Analytical models

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Finding Loop Invariants for Programs over Arrays Using a theorem Prover

Finding Loop Invariants for Programs over Arrays Using a The...

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international symposium on symbolic and numeric algorithms for scientific computing (SYNASC)

作者： Laura Kovacs Andrei Voronkov ETH Zürich Switzerland University of Manchester Institute of Science and Technology UK

Invariants with quantifiers are important for verification and static analysis of programs over arrays due to the unbounded nature of arrays. Such invariants can express relationships among array elements and properties involving array and scalar variables of the loop. this talk presents how quantified loop invariants of programs over arrays can be automatically inferred using a first order theorem prover, reducing the burden of annotating loops with complete invariants. Unlike all previously known methods, our method is able to generate loop invariants containing quantifier alternations. the method is based on the following steps. (1) Given a loop over array and scalar variables, we first try to extract from it various information that can be expressed by first-order formulas. For example, these formulas can express the values of loop variables in terms of the loop counter, monotonicity properties of these variables considered as functions of the loop counter and polynomial relations among these variables. For extracting this information we deploy techniques from symbolic computation, such as recurrence solving and quantifier elimination, as presented in, to perform inductive reasoning over scalar variables. (2) Using the derived loop properties, we then automatically discover first-order properties of the so-called update predicates for array variables used in the loop and monotonicity properties for scalar variables. the update predicates describe the positions at which arrays are updated, iterations at which the updates occur and the update values. the first-order information extracted from the loop description can use auxiliary symbols, such as symbols denoting update predicates or loop counters. By relying on the update predicates of arrays and the monotonicity properties of scalars, we avoid inductive reasoning over arrays. (3) After having collected the first-order information, we run a saturation theorem prover to eliminate the auxiliary symbols and obtain

关键词： Data mining Counting circuits Packaging scientific computing Algorithm design and analysis Polynomials Reduced instruction set computing Contracts Arithmetic Artificial intelligence

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A Comparison of Open-Source Static Analysis Tools for Vulnerability Detection in C/C++ Code

A Comparison of Open-Source Static Analysis Tools for Vulner...

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international symposium on symbolic and numeric algorithms for scientific computing (SYNASC)

作者： Andrei Arusoaie Stefan Ciobâca Vlad Craciun Dragos Gavrilut Dorel Lucanu Faculty of Computer Science Alexandru Ioan Cuza University Iaşi Bitdefender Iaşi

ISBN: (纸本)9781538626276

We describe work that is part of a research project on static code analysis between the Alexandru Ioan Cuza University and Bitdefender. the goal of the project is to develop customized static analysis tools for detecting potential vulnerabilities in C/C++ code. We present the results of benchmarking several existing open source static analysis tools for C/C++ against the Toyota ITC test suite [1] in order to determine which tools are best suited to our purpose. the Toyota ITC test suite is a synthetic benchmark for C/C++ consisting of around 650 test cases organized by defect type and defect subtype and is well-suited to our purpose, since it contains various bugs such as buffer overflows that are common in C/C++ code. We analyze the open-source static analysis tools according to the existing quality indicators such as detection rate and false positive rate proposed in [1], but we also introduce a new quality metric that we call robust detection which also allows us to measure unique detections by tool and by (sub)defect type. We also find several mistakes in the Toyota ITC testsuite that we fix. We publish the harness used to benchmark the static analyzers in order for anyone to be able to reproduce our results.

关键词： Tools Static analysis Memory management Computer bugs Resource management Concurrent computing Benchmark testing

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Expressive Data Storage Policies for Multi-cloud Storage Configurations

Expressive Data Storage Policies for Multi-cloud Storage Con...

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international symposium on symbolic and numeric algorithms for scientific computing (SYNASC)

作者： Ansar Rafique Dimitri Van Landuyt Wouter Joosen Iminds-DistriNet KU Leuven Leuven Belgium iMinds-DistriNet Katholieke Universiteit Leuven Leuven Flanders BE

Software-as-a-Service (SaaS) providers increasingly rely on multi-cloud setups to leverage the combined benefits of different enabling technologies and third-party providers. Especially, in the context of NoSQL storage systems, which are characterized by heterogeneity and quick technological evolution, adopting the multi-cloud paradigm is a promising way to deal with different data storage requirements. Existing data access middleware platforms that support this type of setup (polyglot persistence) commonly rely on (i) configuration models that describe the multi-cloud setup, and (ii) the hard-coded logic in the application source code or the data storage policies that define how the middleware platforms should store data across different storage systems. In practice, however, both models are tightly coupled, i.e. the hard-coded logic in the application source code and data storage policies refer to specific configuration model elements, leads to fragility issues (ripple effects) and hinders reusability. More specifically, in multi-cloud configurations that change often (e.g., in dynamic cloud federations), this is a key problem. In this paper, we present a more expressive way to specify storage policies, that involves (i) enriching the configuration models with metadata about the technical capabilities of the storage systems, (ii) referring to the desired capabilities of the storage system in the storage policies, and (iii) leaving actual resolution to the policy engine. Our validation in the context of a realistic SaaS application shows how the policies accommodate such changes for a number of realistic policy change scenarios. In addition, we evaluate the performance overhead, showing that policy evaluation is on average less than 2% of the total execution time.

关键词： Memory Data models Cloud computing Context Engines scientific computing

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A Serious Game to Learn Greek Doric Architecture

A Serious Game to Learn Greek Doric Architecture

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international symposium on symbolic and numeric algorithms for scientific computing (SYNASC)

作者： Giulio Cellura Department of Physics and Chemistry University of Palermo Palermo Italy Technologies and methods for university education Palermo Italy

ISBN: (数字)9798331532833

ISBN: (纸本)9798331532840

the present contribution aims to describe the development of a serious game designed to disseminate knowledge in the field of architecture and archeology. In recent decades, educational video games, or serious games, have emerged as a significant means of engaging students across various educational disciplines. Notably, some of these games have shown considerable potential in conveying both the tangible and intangible aspects of cultural heritage, particularly within the teaching of historical subjects. the case study under consideration involves the initial phase of a game focused on the reconstruction of one corner of the Temple of Olympian Zeus in the Archeological Park of Agrigento. Following an evaluative test will be conducted with high school and first year university students, in order to gather data generated by its use.

关键词： Video games Archeology scientific computing Education Prototypes Games Computer architecture Serious games Cultural differences

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Assessing Features Importance in the 15-Class Galaxy Classification Problem

Assessing Features Importance in the 15-Class Galaxy Classif...

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international symposium on symbolic and numeric algorithms for scientific computing (SYNASC)

作者： Marc Frincu Raul Urechiatu Department of Computer Science Faculty of Mathematics and Computer Science West University of Timisoara Timisoara Romania

ISBN: (数字)9798331532833

ISBN: (纸本)9798331532840

this study explores feature selection for classifying galaxy morphology using the extensive Galaxy Zoo 2 dataset. We investigate supervised and unsupervised learning methods to group galaxies based on key features, aiming to replicate supervised learning results. We evaluate various feature selection methods and compare them to an existing classification approach. Our results demonstrate that a reduced set of features based on adjusted vote fractions improves classification accuracy and potentially reduces computational complexity. While unsuper-vised clustering partially groups galaxies by morphology, further optimization is required. this work suggests that feature selection and unsupervised learning are promising techniques for the efficient classification of large galaxy datasets in upcoming astronomical surveys.

关键词： Surveys Accuracy scientific computing Scalability Supervised learning Morphology Feature extraction Computational complexity Unsupervised learning Optimization

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On the Variants of Subset Sum: Projected and Unbounded

On the Variants of Subset Sum: Projected and Unbounded

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international symposium on symbolic and numeric algorithms for scientific computing (SYNASC)

作者： Pranjal Dutta Mahesh Sreekumar Rajasree School of Computing National University of Singapore (NUS) Singapore Department of Computer Science and Engineering Indian Institute of Technology Delhi Delhi India

In this work, we focus on variants of Subset Sum. We first define a new variant called the Unique Projection Subset Sum (u – PSSUM) problem: Given $\left(a_th, \ldots, a_{n}\right) \in \mathbb{Z}_{\geq 0}^{n}$, such that for every $t, \sum_{i \in[n]} c_{i} a_{i}=t$, for $c_{i} \in\{0,1\}$ has unique solution if exists, u-PSSUM asks for a vector $\vec{x}=\left(x_th, \ldots, x_{n}\right)$, such that there exists an $S \subseteq[n]$, where $\sum_{i \in S} x_{i}=t$, and $\|\vec{a}-\vec{x}\|_{p}$ is minimized, where $\|\cdot\|_{p}$ denotes the $\ell_{p}$ norm. We present a deterministic $O(n t)$-time algorithm and a randomized $\widetilde{O}(n+t)$-time algorithm for u-PSSUM, in $\ell_th$-norm. the second one is already a known variant called Un-bounded Subset Sum (UBSSUM) problem, which takes a tuple of non-negative integers $\left(a_th, \ldots, a_{n}, t\right)$, as an input, and asks whether there exists non-negative integers $\beta_th, \ldots, \beta_{n}$, such that $\sum_{i=1}^{n} \beta_{i} a_{i}=t$. We present the first polynomial time reductions from UBSSUM to Closest Vector Problem (CVP) in $\ell_th$ and $\ell_{\infty}$ norms. We also give new algorithms for two variants of UBSSUM problem.

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A Software Engineering Approach into Analyzing Microsoft Office-Based Email Attacks

A Software Engineering Approach into Analyzing Microsoft Off...

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international symposium on symbolic and numeric algorithms for scientific computing (SYNASC)

作者： Cosmin Turtureanu Gheorghiţă Mutu Dragoş-Teodor Gavriluţ Al. I. Cuza University Bitdefender Iaşi România

ISBN: (数字)9798331532833

ISBN: (纸本)9798331532840

Phishing emails are among today's most common attack vectors since most enterprises and consumer users still rely on email for day-to-day operations. At the same time, some functionalities (such as MACRO support and Visual Basic Programming) available in Microsoft Office Suite make it easier for an attacker to inject malicious code into a document that can be sent via email. From a research perspective, analyzing such an attack implies understanding not only the artifacts that compose the kill chain steps but also being able to extract, from a document, the embedded macros and the scripts. this paper focuses on building such a system using the forensics platform GView by adding various plugins and functionalities designed to augment the existing support and allow a security researcher to analyze the content of an email and attached documents quickly.

关键词： Visual BASIC scientific computing Phishing Software algorithms Programming Vectors Malware Electronic mail Security Software engineering

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An Analysis of Multitask Deep Learning Models for Histopathology

An Analysis of Multitask Deep Learning Models for Histopatho...

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international symposium on symbolic and numeric algorithms for scientific computing (SYNASC)

作者： Alexandru Manole Faculty of Mathematics and Computer Science Babeş-Bolyai University Cluj-Napoca Romania

ISBN: (数字)9798331532833

ISBN: (纸本)9798331532840

Artificial Intelligence has the potential to streamline and facilitate numerous processes in the medical field, increasing the quality of life for millions and potentially saving lives. One area which requires a lot of effort when it comes to diagnosing severe diseases is Histopathology. Recently, a modern learning strategy, Multitask learning, was applied in Digital Histopathology in order to obtain relevant medical information from histological images. this paradigm is able to increase performance by learning multiple objectives simultaneously resulting in more general features. the resulting methods reduce overfitting and computational complexity while increasing data efficiency making it a suitable choice for the high-dimensionality, low sample size sets from the medical field. the aim of this work is to present novel multitask approaches with applications in Histopathology, analyse them, showcase their advantages and drawbacks and identify possible future research directions.

关键词： Training Deep learning Analytical models Histopathology scientific computing Computational complexity Artificial intelligence Medical diagnostic imaging Overfitting Diseases

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