Graph models for reachability analysis of concurrent programs

Reachability analysis is an attractive technique for analysis of concurrent programs because it is simple and relatively straightforward to automate, and can be used in conjunction with model-checking procedures to check for application-specific as well as general properties. Several techniques have been proposed differing mainly on the model used; some of these propose the use of flowgraph based models, some others of Petri nets.This paper addresses the question: What essential difference does it make, if any, what sort of finite-state model we extract from program texts for purposes of reachability analysis? How do they differ in expressive power, decision power, or accuracy? Since each is intended to model synchronization structure while abstracting away other features, one would expect them to be roughly equivalent.We confirm that there is no essential semantic difference between the most well known models proposed in the literature by providing algorithms for translation among these models. This implies that the choice of model rests on other factors, including convenience and efficiency.Since combinatorial explosion is the primary impediment to application of reachability analysis, a particular concern in choosing a model is facilitating divide-and-conquer analysis of large programs. Recently, much interest in finite-state verification systems has centered on algebraic theories of concurrency. Yeh and Young have exploited algebraic structure to decompose reachability analysis based on a flowgraph model. The semantic equivalence of graph and Petri net based models suggests that one ought to be able to apply a similar strategy for decomposing Petri nets. We show this is indeed possible through application of category theory

Generating and Searching Families of FFT Algorithms

A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm held the record by requiring just 4n log n - 6n + 8 arithmetic operations on real numbers for a size-n DFT, and was widely believed to be the best possible. Recent work by Van Buskirk et al. demonstrated improvements to the split-radix operation count by using multiplier coefficients or "twiddle factors" that are not n-th roots of unity for a size-n DFT. This paper presents a Boolean Satisfiability-based proof of the lowest operation count for certain classes of DFT algorithms. First, we present a novel way to choose new yet valid twiddle factors for the nodes in flowgraphs generated by common power-of-two fast Fourier transform algorithms, FFTs. With this new technique, we can generate a large family of FFTs realizable by a fixed flowgraph. This solution space of FFTs is cast as a Boolean Satisfiability problem, and a modern Satisfiability Modulo Theory solver is applied to search for FFTs requiring the fewest arithmetic operations. Surprisingly, we find that there are FFTs requiring fewer operations than the split-radix even when all twiddle factors are n-th roots of unity.Comment: Preprint submitted on March 28, 2011, to the Journal on Satisfiability, Boolean Modeling and Computatio

Axiomatic Testing of Structure Metrics

Axiomatic testing of software metrics is described, based on axioms from representational measurement theory. In a case study, the axioms are given for the formal relational structure and the empirical relational structure. Two approaches to axiomatic testing are elaborated: deterministic testing and probabilistic testin

Symbolical Analysis of RF-Network Problems using Mason’s Rule

We briefly review Mason’s rule for the computation of RF-network problems and show its implementation into the software package freeMASON. This tool solves symbolically Mason’s rule for any wave quantity and allows to derive analytical expressions as well as their functional evaluation. We demonstrate our approach studying the effect of an unbalanced magictee on the RF power distribution to two accelerating cavities

A methodology for component-based system integration

Component-based software based on software architectures is emerging to be the next generation software development paradigm. The paradigm shifts the development focus from lines-of-codes to coarser-grained components and the interconnections among them. It consists of system architecture design, architecture description, component search and system integration from components to generate a software system. However, one of the bottlenecks in this paradigm is the integration of the individual components into the overall system. In this dissertation a methodology for component-based system integration is proposed. It is based on an architectural aggregation view, a component model, flowgraphs and cyclomatic complexity. We introduce this view, model, and new ways to compute cyclomatic complexity based on flowgraphs. The methodology makes use of Jackson diagram to represent the detailed design of a system and decomposes the system into components and aggregations. An aggregation is a set of components glued together by one connector, and is represented as a flowgraph. Then an aggregation flowgraph is decomposed into prime flowgraphs called prime connections. An Implementation Description Language (IDL) is introduced to represent the aggregations and components. Finally a system synthesis mechanism is proposed that is responsible for translating prime connections, embedding functional units into them, and composing aggregations and the integrated system from them

Nonparametric estimation of first passage time distributions in flowgraph models

Statistical flowgraphs represent multistate semi-Markov processes using integral transforms of transition time distributions between adjacent states; these are combined algebraically and inverted to derive parametric estimates for first passage time distributions between nonadjacent states. This dissertation extends previous work in the field by developing estimation methods for flowgraphs using empirical transforms based on sample data, with no assumption of specific parametric probability models for transition times. We prove strong convergence of empirical flowgraph results to the exact parametric results; develop alternatives for numerical inversion of empirical transforms and compare them in terms of computational complexity, accuracy, and ability to determine error bounds; discuss (with examples) the difficulties of determining confidence bands for distribution estimates obtained in this way; develop confidence intervals for moment-based quantities such as the mean; and show how methods based on empirical transforms can be modified to accommodate censored data. Several applications of the nonparametric method, based on reliability and survival data, are presented in detail

Transmittance matrices and flowgraph reduction

AbstractThe subject of this paper is the computer representation and reduction of a particular graph known as a flowgraph. Basic terminology is developed in Section 1. Properties that are most pertinent to the reduction of flowgraphs are stated in Section 2. Examples of applications are given in Section 3. The structure of the reduction procedure is presented in Section 4

Explicit Preemption Placement For Real-Time Conditional Code Via Graph Grammars And Dynamic Programming

Traditional worst-case execution time (WCET) analysis must make very pessimistic assumptions regarding the cost of preemptions for a real-time job. For every potential preemption point, the analysis must add to the WCET of a job the cache-related preemption delay (CRPD) incurred due to the contention for memory resources with other jobs in the system. However, recent work has shown that CRPD can vary at each preemption point (due to the cache lines that must be reloaded for subsequent code after the preemption). Using this observation and information obtained from schedulability analysis on the maximum length of the non-preemptive region of a job, we seek to find the optimal set of explicit preemption-points (EPPs) that minimize the WCET and ensure system schedulability. Utilizing graph grammars and dynamic programming, we develop a pseudo-polynomial-time algorithm that is capable of analyzing jobs that can be represented by control flowgraphs with arbitrarily-nested conditional structures. This algorithm extends previous work that could only handle sequential flowgraphs. Exhaustive experiments are included to show that the proposed approach is able to significantly improve the bounds on the worst-case execution times of limited preemptive tasks

Robotic workcell analysis and object level programming

For many years robots have been programmed at manipulator or joint level without any real thought to the implementation of sensing until errors occur during program execution. For the control of complex, or multiple robot workcells, programming must be carried out at a higher level, taking into account the possibility of error occurrence. This requires the integration of decision information based on sensory data.Aspects of robotic workcell control are explored during this work with the object of integrating the results of sensor outputs to facilitate error recovery for the purposes of achieving completely autonomous operation.Network theory is used for the development of analysis techniques based on stochastic data. Object level programming is implemented using Markov chain theory to provide fully sensor integrated robot workcell control