Hugh Anderson

Affine-Based Size-Change Termination

The size-change principle devised by Lee, Jones and Ben-Amram, provides an effective method of determining program termination for recursive functions over well-founded types. Termination analysis using the principle involves the classification of functions either into size-change terminating ones, or ones which are not size-change terminating. Size-change graphs are constructed to represent the functions, and decreasing parameter sizes in those graphs that are idempotent are identified. In this paper, we propose a translation of the size-change graphs to affine-based graphs, in which affine relations among parameters are expressed by Presburger formulae. We show the correctness of our translation by defining the size-change graph composition in terms of affine relation manipulation, and identifying the idempotent size-change graphs with transitive closures in affine relations. We then propose an affine-based termination analysis, in which more refined termination size-change information is admissible by affine relations. Specifically, our affine-related analysis improves the effectiveness of the termination analysis by capturing constant changes in parameter sizes, affine relationships of the sizes of the source parameters, and contextual information pertaining to function calls. We state and reason about the corresponding soundness and termination of this affine-related analysis. Our approach widens the set of size-change terminating functions.

Calculating Polynomial Runtime Properties

Affine size-change analysis has been used for termination analysis of eager functional programming languages. The same style of analysis is also capable of compactly recording and calculating other properties of programs, including their runtime, maximum stack depth, and (relative) path time costs. In this paper we show how precise (not just big- \(\mathcal{O}\)) polynomial bounds on such costs may be calculated on programs, by a characterization as a problem in quantifier elimination. The technique is decidable, and complete for a class of size-change terminating programs with limited-degree polynomial costs. An extension to the technique allows the calculation of some classes of exponential-cost programs. We demonstrate the new technique by recording the calculation in numbers-of-function (or procedure) calls for a simple functional definition language, but it can also be applied to imperative languages. The technique is automated within the reduce computer algebra system.

A real-time on-chip algorithm for IMU-Based gait measurement

This paper presents a real-time and on-chip gait measurement algorithm used in our Gait Measurement System (GMS). Our GMS is a small foot-mounted device based on an Inertial Measurement Unit (IMU), which contains an accelerometer and a gyroscope. The GMS can compute spatio-temporal gait parameters in real-time and transmit them to a remote receiver. Measured gait parameters include cadence, velocity, stride length, swing/stance ratio and so on. The algorithm is optimized to run in a ATmega328 microprocessor with only 2kB data memory. During a walking session, each stride is recognized instantaneously, and the stride length and other parameters are computed at the same time. Although inexpensive components are utilized, the algorithm achieves high accuracy, with an average stride length error smaller than 3%, and error in total walking distance less than 2%.

Reducing the power consumption of an IMU-Based gait measurement system

This paper presents our approach to reducing the power consumption in our Gait Measurement System (GMS), which is the foundation for various monitoring and assistive systems. Our GMS is a small foot-mounted device based on an Inertial Measurement Unit (IMU), containing an accelerometer and a gyroscope. It can compute gait parameters in real-time, including cadence, velocity and stride length, before transmitting them to a nearby receiver via a radio frequency (RF) module. Our power saving strategy exploits the cooperation between both hardware and software. By realizing on-chip computing, reducing RF usage and enabling sleep mode, the GMSs current consumption was dramatically reduced. In active mode, the GMS consumes about 2.1mA, while in standby mode, the current is only 20μA. Powered by a small rechargeable 110mAh battery, we expect the GMS to last for months of normal usage without recharging; a duration necessary for our intended applications in e-health.

MANA: Designing and Validating a User-Centered Mobility Analysis System

In this paper, we demonstrate a new IMU-based wearable system (dubbed MANA or Mobility ANAlytics) for measuring gait in a clinical setting. The design process and choices that were made to ensure that the technology was invisible and accessible are described. We collect a rich and diverse dataset of walking data from sixty participants, including forty people with Parkinsons Disease (PD). The system is then validated in a clinical setting with this dataset. We present novel and innovative algorithms to measure common gait parameters. The system is able to estimate these gait parameters with high accuracy, with a mean absolute error of 4.0 cm for stride length and 2.6 cm for step length, outperforming all state-of-the-art methods that included data from people with PD.

A Tool for Calculating Exponential Run-Time Properties

Affine size-change analysis has been used for calculating precise polynomial bounds on the run times, and stack depths of affine size-change terminating programs. Such polynomial costs may be discovered by a characterization as a problem in quantifier elimination. In this paper we extend this work to cover a class of exponential cost programs. The tool described allows the calculation of run-time and stack-depth costs for some classes of exponential-cost programs, again by using quantifier elimination. The technique is automated, and uses the reduce computer algebra system.

Abstract Interpretation with a Theorem Prover

This paper presents an approach to the implementation of the abstract interpretation style of program analysis by first constructing a logic for representing the process of abstract analysis, and then embedding this logic in the theorem prover HOL. Programs to be analysed undergo a two-phase process, first being mechanically transformed to an analysis model, and then this being used to test or verify program properties. A specific advantage of this approach is that it allows abstract interpretation to be used in a consistent framework with other analysis methods, such as Hoare Logic or exhaustive state space analysis.

Data acquisition and analysis in a vehicle with a Commodore PET

A fast data acquisition system has been developed to extract cycle-by-cycle information on car engine performance and fuel consumption on the road. The information is stored on cassette for later analysis and digital plotting. A Commodore PET is used for both stages of the process. The paper describes the interface system and both acquisition and analysis methodologies. These are readily adaptable to other applications.