Lower Bounds for Runtime Complexity of Term Rewriting

We present the first approach to deduce lower bounds for (worst-case) runtime complexity of term rewrite systems (TRSs) automatically. Inferring lower runtime bounds is useful to detect bugs and to complement existing methods that compute upper complexity bounds. Our approach is based on two techniques: the induction technique generates suitable families of rewrite sequences and uses induction proofs to find a relation between the length of a rewrite sequence and the size of the first term in the sequence. The loop detection technique searches for “decreasing loops”. Decreasing loops generalize the notion of loops for TRSs, and allow us to detect families of rewrite sequences with linear, exponential, or infinite length. We implemented our approach in the tool AProVE and evaluated it by extensive experiments.     

Automatically Proving Termination and Memory Safety for Programs with Pointer Arithmetic

While automated verification of imperative programs has been studied intensively, proving termination of programs with explicit pointer arithmetic fully automatically was still an open problem. To close this gap, we introduce a novel abstract domain that can track allocated memory in detail. We use it to automatically construct a symbolic execution graph that over-approximates all possible runs of a program and that can be used to prove memory safety. This graph is then transformed into an integer transition system, whose termination can be proved by standard techniques. We implemented this approach in the automated termination prover AProVE and demonstrate its capability of analyzing C programs with pointer arithmetic that existing tools cannot handle.     

Proving operational termination of membership equational programs

Reasoning about the termination of equational programs in sophisticated equational languages such as Elan, Maude, OBJ, CafeOBJ, Haskell, and so on, requires support for advanced features such as evaluation strategies, rewriting modulo, use of extra variables in conditions, partiality, and expressive type systems (possibly including polymorphism and higher-order). However, many of those features are, at best, only partially supported by current term rewriting termination tools (for instance mu-term, C i ME, AProVE, TTT, Termptation, etc.) while they may be essential to ensure termination. We present a sequence of theory transformations that can be used to bridge the gap between expressive membership equational programs and such termination tools, and prove the correctness of such transformations. We also discuss a prototype tool performing the transformations on Maude equational programs and sending the resulting transformed theories to some of the aforementioned standard termination tools.     

On selection of samples in algebraic attacks and a new technique to find hidden low degree equations

The best way of selecting samples in algebraic attacks against block ciphers is not well explored and understood. We introduce a simple strategy for selecting the plaintexts and demonstrate its strength by breaking reduced-round KATAN32, LBlock and SIMON. For each case, we present a practical attack on reduced-round version which outperforms previous attempts of algebraic cryptanalysis whose complexities were close to exhaustive search. The attack is based on the selection of samples using cube attack and ElimLin which was presented at FSE’12, and a new technique called Universal Proning. In the case of LBlock, we break 10 out of 32 rounds. In KATAN32, we break 78 out of 254 rounds. Unlike previous attempts which break smaller number of rounds, we do not guess any bit of the key and we only use structural properties of the cipher to be able to break a higher number of rounds with much lower complexity. We show that cube attacks owe their success to the same properties and therefore can be used as a heuristic for selecting the samples in an algebraic attack. The performance of ElimLin is further enhanced by the new Universal Proning technique, which allows to discover linear equations that are not found by ElimLin.     

Quantum commitments from complexity assumptions

Bit commitment schemes are at the basis of modern cryptography. Since information-theoretic security is impossible both in the classical and in the quantum regime, we examine computationally secure commitment schemes. In this paper we study worst-case complexity assumptions that imply quantum bit commitment schemes. First, we show that QSZK \({\not\subseteq}\) QMA implies a computationally hiding and statistically binding auxiliary-input quantum commitment scheme. We then extend our result to show that the much weaker assumption QIP \({\not\subseteq}\) QMA (which is weaker than PSPACE \({\not\subseteq}\) PP) implies the existence of auxiliary-input commitment schemes with quantum advice. Finally, to strengthen the plausibility of the separation QSZK \({\not\subseteq}\) QMA, we find a quantum oracle relative to which honest-verifier QSZK is not contained in QCMA, the class of languages that can be verified using a classical proof in quantum polynomial time.     

SAT Solving for Termination Proofs with Recursive Path Orders and Dependency Pairs

This paper introduces a propositional encoding for recursive path orders (RPO), in connection with dependency pairs. Hence, we capture in a uniform setting all common instances of RPO, i.e., lexicographic path orders (LPO), multiset path orders (MPO), and lexicographic path orders with status (LPOS). This facilitates the application of SAT solvers for termination analysis of term rewrite systems (TRSs). We address four main inter-related issues and show how to encode them as satisfiability problems of propositional formulas that can be efficiently handled by SAT solving: (A) the lexicographic comparison w.r.t. a permutation of the arguments; (B) the multiset extension of a base order; (C) the combined search for a path order together with an argument filter to orient a set of inequalities; and (D) how the choice of the argument filter influences the set of inequalities that have to be oriented (so-called usable rules). We have implemented our contributions in the termination prover AProVE. Extensive experiments show that by our encoding and the application of SAT solvers one obtains speedups in orders of magnitude as well as increased termination proving power.     

A quantitative approach to belief revision in structured probabilistic argumentation

Many real-world knowledge-based systems must deal with information coming from different sources that invariably leads to incompleteness, overspecification, or inherently uncertain content. The presence of these varying levels of uncertainty doesn’t mean that the information is worthless – rather, these are hurdles that the knowledge engineer must learn to work with. In this paper, we continue work on an argumentation-based framework that extends the well-known Defeasible Logic Programming (DeLP) language with probabilistic uncertainty, giving rise to the Defeasible Logic Programming with Presumptions and Probabilistic Environments (DeLP3E) model. Our prior work focused on the problem of belief revision in DeLP3E, where we proposed a non-prioritized class of revision operators called AFO (Annotation Function-based Operators) to solve this problem. In this paper, we further study this class and argue that in some cases it may be desirable to define revision operators that take quantitative aspects into account, such as how the probabilities of certain literals or formulas of interest change after the revision takes place. To the best of our knowledge, this problem has not been addressed in the argumentation literature to date. We propose the QAFO (Quantitative Annotation Function-based Operators) class of operators, a subclass of AFO, and then go on to study the complexity of several problems related to their specification and application in revising knowledge bases. Finally, we present an algorithm for computing the probability that a literal is warranted in a DeLP3E knowledge base, and discuss how it could be applied towards implementing QAFO-style operators that compute approximations rather than exact operations.     

Common2 extended to stacks and unbounded concurrency

This paper extends Common2, the family of objects that implement and are wait-free implementable from 2 consensus objects, in two ways: First, the stack object is shown to be in the family, refuting a conjecture to the contrary [6]. Second, Common2 is investigated in the unbounded concurrency model, whereas until now it was considered only in an n-process model. We show that the fetch-and-add, test-and-set , and stack objects are in Common2 even with respect to this stronger notion of wait-free implementation. Our constructions rely on a wait-free implementation of immediate snapshots in the unbounded concurrency model, which was previously not known to be possible. The introduction of unbounded concurrency to the study of Common2 opens several directions of research: are there objects that have n-process implementations but are not unbounded concurrency implementable? We conjecture that swap is such an object. Additionally, the hope is that a queue impossibility proof, which eludes us in the n-process model, will be easier to establish in the unbounded concurrency model.     

A<Emphasis Type="SmallCaps">rgonauts</Emphasis>: a working system for motivated cooperative agents

This paper presents the Argonauts multi-agent framework which was developed as part of a one year student project at Technische Universität Dortmund. The Argonauts framework builds on a BDI approach to model rational agents that act cooperatively in a dynamic and indeterministically changing environment. However, our agent model extends the traditional BDI approach in several aspects, most notably by incorporating motivation into the agent’s goal selection mechanism. The framework has been applied by the Argonauts team in the 2010 version of the annual multi-agent programming contest organized by Technische Universität Clausthal. In this paper, we present a high-level specification and analysis of the actual system used for solving the given scenario. We do this by applying the GAIA methodology, a high-level and iterative approach to model communication and roles in multi-agent scenarios. We further describe the technical details and insights gained during our participation in the multi-agent programming contest.     

Computing weight constraint reachability in large networks

Reachability is a fundamental problem on large-scale networks emerging nowadays in various application domains, such as social networks, communication networks, biological networks, road networks, etc. It has been studied extensively. However, little existing work has studied reachability with realistic constraints imposed on graphs with real-valued edge or node weights. In fact, such weights are very common in many real-world networks, for example, the bandwidth of a link in communication networks, the reliability of an interaction between two proteins in PPI networks, and the handling capacity of a warehouse/storage point in a distribution network. In this paper, we formalize a new yet important reachability query in weighted undirected graphs, called weight constraint reachability (WCR) query that asks: is there a path between nodes \(a\) and \(b\), on which each real-valued edge (or node) weight satisfies a range constraint. We discover an interesting property of WCR, based on which, we design a novel edge-based index structure to answer the WCR query in \(O(1)\) time. Furthermore, we consider the case when the index cannot entirely fit in the memory, which can be very common for emerging massive networks. An I/O-efficient index is proposed, which provides constant I/O (precisely four I/Os) query time with \(O(|V|\log |V|)\) disk-based index size. Extensive experimental studies on both real and synthetic datasets demonstrate the efficiency and scalability of our solutions in answering the WCR query.     

The Matrix Reproved (Verification Pearl)

In this paper we describe a complete solution for the first challenge of the VerifyThis 2016 competition held at the 18th ETAPS Forum. We present the proof of two variants for the multiplication of matrices: a naive version using three nested loops and Strassen’s algorithm. The proofs are conducted using the Why3 platform for deductive program verification and automated theorem provers to discharge proof obligations. In order to specify and prove the two multiplication algorithms, we develop a new Why3 theory of matrices. In order to prove the matrix identities on which Strassen’s algorithm is based, we apply the proof by reflection methodology, which we implement using ghost state.To our knowledge, this is the first time such a methodology is used under an auto-active setting.     

Inductive proof search modulo

We present an original narrowing-based proof search method for inductive theorems in equational rewrite theories given by a rewrite system $\mathcal{R}$ and a set E of equalities. It has the specificity to be grounded on deduction modulo and to rely on narrowing to provide both induction variables and instantiation schemas. Whenever the equational rewrite system $(\mathcal{R},E)$ has good properties of termination, sufficient completeness, and when E is constructor and variable preserving, narrowing at defined-innermost positions leads to consider only unifiers which are constructor substitutions. This is especially interesting for associative and associative-commutative theories for which the general proof search system is refined. The method is shown to be sound and refutationally correct and complete. A major feature of our approach is to provide a constructive proof in deduction modulo for each successful instance of the proof search procedure.     

Top-K representative documents query over geo-textual data stream

The increasing popularity of location-based social networks encourages more and more users to share their experiences. It deeply impacts the decision of customers when shopping, traveling, and so on. This paper studies the problem of top-K valuable documents query over geo-textual data stream. Many researchers have studied this problem. However, they do not consider the reliability of documents, where some unreliable documents may mislead customers to make improper decisions. In addition, they lack the ability to prune documents with low representativeness. In order to increase user satisfaction in recommendation systems, we propose a novel framework named PDS. It first employs an efficiently machine learning technique named ELM to prune unreliable documents, and then uses a novel index named \(\mathcal {GH}\) to maintain documents. For one thing, this index maintains a group of pruning values to filter low quality documents. For another, it utilizes the unique property of sliding window to further enhance the PDS performance. Theoretical analysis and extensive experimental results demonstrate the effectiveness of the proposed algorithms.     

High-Performance Computation of Bézier Surfaces on Parallel and Heterogeneous Platforms

Bézier surfaces are mathematical tools employed in a wide variety of applications. Some works in the literature propose parallelization strategies to improve performance for the computation of Bézier surfaces. These approaches, however, are mainly focused on graphics applications and often are not directly applicable to other domains. In this work, we propose a new method for the computation of Bézier surfaces, together with approaches to efficiently map the method onto different platforms (CPUs, discrete and integrated GPUs). Additionally, we explore CPU–GPU cooperation mechanisms for computing Bézier surfaces using two integrated heterogeneous systems with different characteristics. An exhaustive performance evaluation—including different data-types, rendering and several hardware platforms—is performed. The results show that our method achieves speedups as high as 3.12x (double-precision) and 2.47x (single-precision) on CPU, and 3.69x (double-precision) and 13.14x (single-precision) on GPU compared to other methods in the literature. In heterogeneous platforms, the CPU–GPU cooperation increases the performance up to 2.09x with respect to the GPU-only version. Our method and the associated parallelization approaches can be easily employed in domains other than computer-graphics (e.g., image registration, bio-mechanical modeling and flow simulation), and extended to other Bézier formulations and Bézier constructions of higher order than surfaces.     

Dataset Popularity Prediction for Caching of CMS Big Data

The Compact Muon Solenoid (CMS) experiment at the European Organization for Nuclear Research (CERN) deploys its data collections, simulation and analysis activities on a distributed computing infrastructure involving more than 70 sites worldwide. The historical usage data recorded by this large infrastructure is a rich source of information for system tuning and capacity planning. In this paper we investigate how to leverage machine learning on this huge amount of data in order to discover patterns and correlations useful to enhance the overall efficiency of the distributed infrastructure in terms of CPU utilization and task completion time. In particular we propose a scalable pipeline of components built on top of the Spark engine for large-scale data processing, whose goal is collecting from different sites the dataset access logs, organizing them into weekly snapshots, and training, on these snapshots, predictive models able to forecast which datasets will become popular over time. The high accuracy achieved indicates the ability of the learned model to correctly separate popular datasets from unpopular ones. Dataset popularity predictions are then exploited within a novel data caching policy, called PPC (Popularity Prediction Caching). We evaluate the performance of PPC against popular caching policy baselines like LRU (Least Recently Used). The experiments conducted on large traces of real dataset accesses show that PPC outperforms LRU reducing the number of cache misses up to 20% in some sites.     

MASA : a library for verification using manufactured and analytical solutions

In this paper we introduce the Manufactured Analytical Solution Abstraction ( MASA ) library for applying the method of manufactured solutions to the verification of software used for solving a large class of problems stemming from numerical methods in mathematical physics including nonlinear equations, systems of algebraic equations, and ordinary and partial differential equations. We discuss the process of scientific software verification, manufactured solution generation using symbolic manipulation with computer algebra systems such as Maple? or SymPy, and automatic differentiation for forcing function evaluation. We discuss a hierarchic methodology that can be used to alleviate the combinatorial complexity in generating symbolic manufactured solutions for systems of equations based on complex physics. Finally, we detail the essential features and examples of the Application Programming Interface behind MASA , an open source library designed to act as a central repository for manufactured and analytical solutions over a diverse range of problems.     

An executable formal semantics for UML-RT

We propose a formal semantics for UML-RT, a UML profile for real-time and embedded systems. The formal semantics is given by mapping UML-RT models into a language called kiltera, a real-time extension of the \(\pi \)-calculus. Previous attempts to formalize the semantics of UML-RT have fallen short by considering only a very small subset of the language and providing fundamentally incomplete semantics based on incorrect assumptions, such as a one-to-one correspondence between “capsules” and threads. Our semantics is novel in several ways: (1) it deals with both state machine diagrams and capsule diagrams; (2) it deals with aspects of UML-RT that have not been formalized before, such as thread allocation, service provision points, and service access points; (3) it supports an action language; and (4) the translation has been implemented in the form of a transformation from UML-RT models created with IBM’s RSA-RTE tool, into kiltera code. To our knowledge, this is the most comprehensive formal semantics for UML-RT to date.     

ATP and Presentation Service for Mizar Formalizations

This paper describes the Automated Reasoning for Mizar ( $\textsf{Miz}\mathbb{AR}$ ) service, which integrates several automated reasoning, artificial intelligence, and presentation tools with Mizar and its authoring environment. The service provides ATP assistance to Mizar authors in finding and explaining proofs, and offers generation of Mizar problems as challenges to ATP systems. The service is based on a sound translation from the Mizar language to that of first-order ATP systems, and relies on the recent progress in application of ATP systems in large theories containing tens of thousands of available facts. We present the main features of $\textsf{Miz}\mathbb{AR}$ services, followed by an account of initial experiments in finding proofs with the ATP assistance. Our initial experience indicates that the tool offers substantial help in exploring the Mizar library and in preparing new Mizar articles.     

Efficiently summarizing attributed diffusion networks

Given a large attributed social network, can we find a compact, diffusion-equivalent representation while keeping the attribute properties? Diffusion networks with user attributes such as friendship, email communication, and people contact networks are increasingly common-place in the real-world. However, analyzing them is challenging due to their large size. In this paper, we first formally formulate a novel problem of summarizing an attributed diffusion graph to preserve its attributes and influence-based properties. Next, we propose ANeTS, an effective sub-quadratic parallelizable algorithm to solve this problem: it finds the best set of candidate nodes and merges them to construct a smaller network of ‘super-nodes’ preserving the desired properties. Extensive experiments on diverse real-world datasets show that ANeTS outperforms all state-of-the-art baselines (some of which do not even finish in 14 days). Finally, we show how ANeTS helps in multiple applications such as Topic-Aware viral marketing and sense-making of diverse graphs from different domains.