Formal Verification of Real-Time Function Blocks Using PVS

A critical step towards certifying safety-critical systems is to check their conformance to hard real-time requirements. A promising way to achieve this is by building the systems from pre-verified components and verifying their correctness in a compositional manner. We previously reported a formal approach to verifying function blocks (FBs) using tabular expressions and the PVS proof assistant. By applying our approach to the IEC 61131-3 standard of Programmable Logic Controllers (PLCs), we constructed a repository of precise specification and reusable (proven) theorems of feasibility and correctness for FBs. However, we previously did not apply our approach to verify FBs against timing requirements, since IEC 61131-3 does not define composite FBs built from timers. In this paper, based on our experience in the nuclear domain, we conduct two realistic case studies, consisting of the software requirements and the proposed FB implementations for two subsystems of an industrial control system. The implementations are built from IEC 61131-3 FBs, including the on-delay timer. We find issues during the verification process and suggest solutions.Comment: In Proceedings ESSS 2015, arXiv:1506.0325

Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)

Oxford, UK, 26 August 200

An Exercise in Invariant-based Programming with Interactive and Automatic Theorem Prover Support

Invariant-Based Programming (IBP) is a diagram-based correct-by-construction programming methodology in which the program is structured around the invariants, which are additionally formulated before the actual code. Socos is a program construction and verification environment built specifically to support IBP. The front-end to Socos is a graphical diagram editor, allowing the programmer to construct invariant-based programs and check their correctness. The back-end component of Socos, the program checker, computes the verification conditions of the program and tries to prove them automatically. It uses the theorem prover PVS and the SMT solver Yices to discharge as many of the verification conditions as possible without user interaction. In this paper, we first describe the Socos environment from a user and systems level perspective; we then exemplify the IBP workflow by building a verified implementation of heapsort in Socos. The case study highlights the role of both automatic and interactive theorem proving in three sequential stages of the IBP workflow: developing the background theory, formulating the program specification and invariants, and proving the correctness of the final implementation.Comment: In Proceedings THedu'11, arXiv:1202.453

A formal framework for modeling and validating Simulink diagrams

10.1007/s00165-009-0108-9Formal Aspects of Computing215451-483FACM

A PVS-Simulink Integrated Environment for Model-Based Analysis of Cyber-Physical Systems

This paper presents a methodology, with supporting tool, for formal modeling and analysis of software components in cyber-physical systems. Using our approach, developers can integrate a simulation of logic-based specifications of software components and Simulink models of continuous processes. The integrated simulation is useful to validate the characteristics of discrete system components early in the development process. The same logic-based specifications can also be formally verified using the Prototype Verification System (PVS), to gain additional confidence that the software design complies with specific safety requirements. Modeling patterns are defined for generating the logic-based specifications from the more familiar automata-based formalism. The ultimate aim of this work is to facilitate the introduction of formal verification technologies in the software development process of cyber-physical systems, which typically requires the integrated use of different formalisms and tools. A case study from the medical domain is used to illustrate the approach. A PVS model of a pacemaker is interfaced with a Simulink model of the human heart. The overall cyber-physical system is co-simulated to validate design requirements through exploration of relevant test scenarios. Formal verification with the PVS theorem prover is demonstrated for the pacemaker model for specific safety aspects of the pacemaker design

SPEEDY: An Eclipse-based IDE for invariant inference

SPEEDY is an Eclipse-based IDE for exploring techniques that assist users in generating correct specifications, particularly including invariant inference algorithms and tools. It integrates with several back-end tools that propose invariants and will incorporate published algorithms for inferring object and loop invariants. Though the architecture is language-neutral, current SPEEDY targets C programs. Building and using SPEEDY has confirmed earlier experience demonstrating the importance of showing and editing specifications in the IDEs that developers customarily use, automating as much of the production and checking of specifications as possible, and showing counterexample information directly in the source code editing environment. As in previous work, automation of specification checking is provided by back-end SMT solvers. However, reducing the effort demanded of software developers using formal methods also requires a GUI design that guides users in writing, reviewing, and correcting specifications and automates specification inference.Comment: In Proceedings F-IDE 2014, arXiv:1404.578

A Static Analyzer for Large Safety-Critical Software

We show that abstract interpretation-based static program analysis can be made efficient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement of a general purpose static analyzer and later adaptation to particular programs of the family by the end-user through parametrization. This is applied to the proof of soundness of data manipulation operations at the machine level for periodic synchronous safety critical embedded software. The main novelties are the design principle of static analyzers by refinement and adaptation through parametrization, the symbolic manipulation of expressions to improve the precision of abstract transfer functions, the octagon, ellipsoid, and decision tree abstract domains, all with sound handling of rounding errors in floating point computations, widening strategies (with thresholds, delayed) and the automatic determination of the parameters (parametrized packing)