Theorem-Proving Analysis of Digital Control Logic Interacting with Continuous Dynamics

AbstractThis work outlines an equation-based formulation of a digital control program and transducer interacting with a continuous physical process, and an approach using the Coq theorem prover for verifying the performance of the combined hybrid system. Considering thermal dynamics with linear dissipation for simplicity, we focus on a generalizable, physically consistent description of the interaction of the real-valued temperature and the digital program acting as a thermostat. Of interest in this work is the discovery and formal proof of bounds on the temperature, the degree of variation, and other performance characteristics. Our approach explicitly addresses the need to mathematically represent the decision problem inherent in an analog-to-digital converter, which for rare values can take an arbitrarily long time to produce a digital answer (the so-called Buridan's Principle); this constraint ineluctably manifests itself in the verification of thermostat performance. Furthermore, the temporal causality constraints in the thermal physics must be made explicit to obtain a consistent model for analysis. We discuss the significance of these findings toward the verification of digital control for more complex physical variables and fields

COMPOSE-HPC: A Transformational Approach to Exascale

The goal of the COMPOSE-HPC project is to 'democratize' tools for automatic transformation of program source code so that it becomes tractable for the developers of scientific applications to create and use their own transformations reliably and safely. This paper describes our approach to this challenge, the creation of the KNOT tool chain, which includes tools for the creation of annotation languages to control the transformations (PAUL), to perform the transformations (ROTE), and optimization and code generation (BRAID), which can be used individually and in combination. We also provide examples of current and future uses of the KNOT tools, which include transforming code to use different programming models and environments, providing tests that can be used to detect errors in software or its execution, as well as composition of software written in different programming languages, or with different threading patterns

COMPOSE-HPC: A Transformational Approach to Exascale

The goal of the COMPOSE-HPC project is to 'democratize' tools for automatic transformation of program source code so that it becomes tractable for the developers of scientific applications to create and use their own transformations reliably and safely. This paper describes our approach to this challenge, the creation of the KNOT tool chain, which includes tools for the creation of annotation languages to control the transformations (PAUL), to perform the transformations (ROTE), and optimization and code generation (BRAID), which can be used individually and in combination. We also provide examples of current and future uses of the KNOT tools, which include transforming code to use different programming models and environments, providing tests that can be used to detect errors in software or its execution, as well as composition of software written in different programming languages, or with different threading patterns