Applying Reversibility Theory for the Performance Evaluation of Reversible Computations

Reversible computations have been widely studied from the functional point of view and energy consumption. In the literature, several authors have proposed various formalisms (mainly based on process algebras) for assessing the correctness or the equivalence among reversible computations. In this paper we propose the adoption of Markovian stochastic models to assess the quantitative properties of reversible computations. Under some conditions, we show that the notion of time-reversibility for Markov chains can be used to efficiently derive some performance measures of reversible computations. The importance of time-reversibly relies on the fact that, in general, the process’s stationary distribution can be derived efficiently by using numerically stable algorithms. This paper reviews the main results about time-reversible Markov processes and discusses how to apply them to tackle the problem of the quantitative evaluation of reversible computationsReversible computations have been widely studied from the functional point of view and energy consumption. In the literature, several authors have proposed various formalisms (mainly based on process algebras) for assessing the correctness or the equivalence among reversible computations. In this paper we propose the adoption of Markovian stochastic models to assess the quantitative properties of reversible computations. Under some conditions, we show that the notion of time-reversibility for Markov chains can be used to efficiently derive some performance measures of reversible computations. The importance of time-reversibly relies on the fact that, in general, the process's stationary distribution can be derived efficiently by using numerically stable algorithms. This paper reviews the main results about time-reversible Markov processes and discusses how to apply them to tackle the problem of the quantitative evaluation of reversible computations

On approximating the stochastic behaviour of Markovian process algebra models

Markov chains offer a rigorous mathematical framework to describe systems that exhibit stochastic behaviour, as they are supported by a plethora of methodologies to analyse their properties. Stochastic process algebras are high-level formalisms, where systems are represented as collections of interacting components. This compositional approach to modelling allows us to describe complex Markov chains using a compact high-level specification. There is an increasing need to investigate the properties of complex systems, not only in the field of computer science, but also in computational biology. To explore the stochastic properties of large Markov chains is a demanding task in terms of computational resources. Approximating the stochastic properties can be an effective way to deal with the complexity of large models. In this thesis, we investigate methodologies to approximate the stochastic behaviour of Markovian process algebra models. The discussion revolves around two main topics: approximate state-space aggregation and stochastic simulation. Although these topics are different in nature, they are both motivated by the need to efficiently handle complex systems. Approximate Markov chain aggregation constitutes the formulation of a smaller Markov chain that approximates the behaviour of the original model. The principal hypothesis is that states that can be characterised as equivalent can be adequately represented as a single state. We discuss different notions of approximate state equivalence, and how each of these can be used as a criterion to partition the state-space accordingly. Nevertheless, approximate aggregation methods typically require an explicit representation of the transition matrix, a fact that renders them impractical for large models. We propose a compositional approach to aggregation, as a means to efficiently approximate complex Markov models that are defined in a process algebra specification, PEPA in particular. Regarding our contributions to Markov chain simulation, we propose an accelerated method that can be characterised as almost exact, in the sense that it can be arbitrarily precise. We discuss how it is possible to sample from the trajectory space rather than the transition space. This approach requires fewer random samples than a typical simulation algorithm. Most importantly, our approach does not rely on particular assumptions with respect to the model properties, in contrast to otherwise more efficient approaches

Algorithms for Performance, Dependability, and Performability Evaluation using Stochastic Activity Networks

Modeling tools and technologies are important for aerospace development. At the University of Illinois, we have worked on advancing the state of the art in modeling by Markov reward models in two important areas: reducing the memory necessary to numerically solve systems represented as stochastic activity networks and other stochastic Petri net extensions while still obtaining solutions in a reasonable amount of time, and finding numerically stable and memory-efficient methods to solve for the reward accumulated during a finite mission time. A long standing problem when modeling with high level formalisms such as stochastic activity networks is the so-called state space explosion, where the number of states increases exponentially with size of the high level model. Thus, the corresponding Markov model becomes prohibitively large and solution is constrained by the the size of primary memory. To reduce the memory necessary to numerically solve complex systems, we propose new methods that can tolerate such large state spaces that do not require any special structure in the model (as many other techniques do). First, we develop methods that generate row and columns of the state transition-rate-matrix on-the-fly, eliminating the need to explicitly store the matrix at all. Next, we introduce a new iterative solution method, called modified adaptive Gauss-Seidel, that exhibits locality in its use of data from the state transition-rate-matrix, permitting us to cache portions of the matrix and hence reduce the solution time. Finally, we develop a new memory and computationally efficient technique for Gauss-Seidel based solvers that avoids the need for generating rows of A in order to solve Ax = b. This is a significant performance improvement for on-the-fly methods as well as other recent solution techniques based on Kronecker operators. Taken together, these new results show that one can solve very large models without any special structure

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

Measurements, Models, Systems and Design

531 s.

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

Proceedings of the USDA-ARS workshop "Real world" infiltration

Compiled and edited by L.R. Ahuja and Amy Garrison.Includes bibliographical references.Proceedings of the 1996 workshop held on July 22-25, 1996 in Pingree Park, Colorado

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications