Practical applications of probabilistic model checking to communication protocols

Probabilistic model checking is a formal verification technique for the analysis of systems that exhibit stochastic behaviour. It has been successfully employed in an extremely wide array of application domains including, for example, communication and multimedia protocols, security and power management. In this chapter we focus on the applicability of these techniques to the analysis of communication protocols. An analysis of the performance of such systems must successfully incorporate several crucial aspects, including concurrency between multiple components, real-time constraints and randomisation. Probabilistic model checking, in particular using probabilistic timed automata, is well suited to such an analysis. We provide an overview of this area, with emphasis on an industrially relevant case study: the IEEE 802.3 (CSMA/CD) protocol. We also discuss two contrasting approaches to the implementation of probabilistic model checking, namely those based on numerical computation and those based on discrete-event simulation. Using results from the two tools PRISM and APMC, we summarise the advantages, disadvantages and trade-offs associated with these techniques

An efficient multi-core implementation of a novel HSS-structured multifrontal solver using randomized sampling

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factorization leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK -- STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices

Doctor of Philosophy

dissertationFormal verification of hardware designs has become an essential component of the overall system design flow. The designs are generally modeled as finite state machines, on which property and equivalence checking problems are solved for verification. Reachability analysis forms the core of these techniques. However, increasing size and complexity of the circuits causes the state explosion problem. Abstraction is the key to tackling the scalability challenges. This dissertation presents new techniques for word-level abstraction with applications in sequential design verification. By bundling together k bit-level state-variables into one word-level constraint expression, the state-space is construed as solutions (variety) to a set of polynomial constraints (ideal), modeled over the finite (Galois) field of 2^k elements. Subsequently, techniques from algebraic geometry -- notably, Groebner basis theory and technology -- are researched to perform reachability analysis and verification of sequential circuits. This approach adds a "word-level dimension" to state-space abstraction and verification to make the process more efficient. While algebraic geometry provides powerful abstraction and reasoning capabilities, the algorithms exhibit high computational complexity. In the dissertation, we show that by analyzing the constraints, it is possible to obtain more insights about the polynomial ideals, which can be exploited to overcome the complexity. Using our algorithm design and implementations, we demonstrate how to perform reachability analysis of finite-state machines purely at the word level. Using this concept, we perform scalable verification of sequential arithmetic circuits. As contemporary approaches make use of resolution proofs and unsatisfiable cores for state-space abstraction, we introduce the algebraic geometry analog of unsatisfiable cores, and present algorithms to extract and refine unsatisfiable cores of polynomial ideals. Experiments are performed to demonstrate the efficacy of our approaches

Advancements in symbolic traversal techniques

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Taking advantage of hybrid systems for sparse direct solvers via task-based runtimes

The ongoing hardware evolution exhibits an escalation in the number, as well as in the heterogeneity, of computing resources. The pressure to maintain reasonable levels of performance and portability forces application developers to leave the traditional programming paradigms and explore alternative solutions. PaStiX is a parallel sparse direct solver, based on a dynamic scheduler for modern hierarchical manycore architectures. In this paper, we study the benefits and limits of replacing the highly specialized internal scheduler of the PaStiX solver with two generic runtime systems: PaRSEC and StarPU. The tasks graph of the factorization step is made available to the two runtimes, providing them the opportunity to process and optimize its traversal in order to maximize the algorithm efficiency for the targeted hardware platform. A comparative study of the performance of the PaStiX solver on top of its native internal scheduler, PaRSEC, and StarPU frameworks, on different execution environments, is performed. The analysis highlights that these generic task-based runtimes achieve comparable results to the application-optimized embedded scheduler on homogeneous platforms. Furthermore, they are able to significantly speed up the solver on heterogeneous environments by taking advantage of the accelerators while hiding the complexity of their efficient manipulation from the programmer.Comment: Heterogeneity in Computing Workshop (2014

Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation

A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Progamming (ILP) formulation Mixed Integer Programming (MIP) formulation is presented. An ILP stated as a system of linear constraints involving integer variables and an objective function, provides a powerful representation of decision problems through a tightly interrelated closed system of choices. It supports direct representation of logical (Boolean or prepositional calculus) expressions. Binary variables (hereafter called logical variables) are first introduced and methods of logically connecting these to other variables are then presented. Simple constraints can be combined to construct logical relationships and the methods of formulating these are discussed. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. These reformulation procedures are illustrated by two examples. A scheme of implementation.ithin an LP modelling system is outlined

Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial

Knowledge-Based Automatic Generation of Linear Algebra Algorithms and Code

This dissertation focuses on the design and the implementation of domain-specific compilers for linear algebra matrix equations. The development of efficient libraries for such equations, which lie at the heart of most software for scientific computing, is a complex process that requires expertise in a variety of areas, including the application domain, algorithms, numerical analysis and high-performance computing. Moreover, the process involves the collaboration of several people for a considerable amount of time. With our compilers, we aim to relieve the developers from both designing algorithms and writing code, and to generate routines that match or even surpass the performance of those written by human experts.Comment: Dissertatio