Automated compositional proofs for real-time systems

Abstract

We present a framework for formally proving that the composition of the behaviors of the different parts of a complex, realtime system ensures a desired global specification of the overall system. The framework is based on a simple compositional rely/guarantee circular inference rule, plus a methodology concerning the integration of the different parts into a whole system. The reference specification language is the TRIO metric linear temporal logic.The novelty of our approach with respect to existing compositional frameworks -most of which do not deal explicitly with real-time requirements -consists mainly in its generality and abstraction from any assumptions about the underlying computational model and from any semantic characterizations of the temporal logic language used in the specification. Moreover, the framework deals equally well with continuous and discrete time. It is supported by a tool, implemented on top of the proof-checker PVS, to perform deduction-based verification through theorem-proving of modular real-time axiom systems.As an example of application, we show the verification of a real-time version of the old-fashioned but still relevant "benchmark" of the dining philosophers problem.

Bounded satisfiability checking of metric temporal logic specifications

“…The works of McMillan (McMillan [2000] and Jhala and McMillan [2001]) present some similarities both with that of Furia et al [2007] and with ours, though they are focused on verification of hardware architectures and they use somewhat domainspecific proof techniques. An abstract model of the architecture is used as a specification, against which a more detailed one, considered as an implementation, is verified.…”

“…The contribution [Furia et al 2007] introduces an automated compositional proof system for modular specifications expressed in the TRIO metric linear temporal logic, adopts a simple compositional rely/guarantee circular inference rule plus a methodology for the integration of different parts into a whole system. The main difference with respect to our approach in the present work derives from the provided tool support, implemented on top of the proof-checker PVS, allowing for deduction-based verification through theorem proving of modular real-time axiom systems.…”

Towards repairing critical embedded software on-the-fly

“…E.g., Sherif [8] presents a specification and validation framework based on Circus, a language that combines CSP (Communicating Sequential Processes), Z, and refinement calculus constructs. In [9] Furia gives a formal composition framework based on the TROL, a metric temporal logic language for modeling and analysis of time-critical systems. On the whole, rigorous derivation history provides good traceability, which makes the repair of critical software much more convenient, effective, and comprehensible, as opposed to intricate, time-consuming and expensive reverse engineering.…”