4,557 research outputs found
Fourth NASA Langley Formal Methods Workshop
This publication consists of papers presented at NASA Langley Research Center's fourth workshop on the application of formal methods to the design and verification of life-critical systems. Topic considered include: Proving properties of accident; modeling and validating SAFER in VDM-SL; requirement analysis of real-time control systems using PVS; a tabular language for system design; automated deductive verification of parallel systems. Also included is a fundamental hardware design in PVS
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
A library of Taylor models for PVS automatic proof checker
We present in this paper a library to compute with Taylor models, a technique
extending interval arithmetic to reduce decorrelation and to solve differential
equations. Numerical software usually produces only numerical results. Our
library can be used to produce both results and proofs. As seen during the
development of Fermat's last theorem reported by Aczel 1996, providing a proof
is not sufficient. Our library provides a proof that has been thoroughly
scrutinized by a trustworthy and tireless assistant. PVS is an automatic proof
assistant that has been fairly developed and used and that has no internal
connection with interval arithmetic or Taylor models. We built our library so
that PVS validates each result as it is produced. As producing and validating a
proof, is and will certainly remain a bigger task than just producing a
numerical result our library will never be a replacement to imperative
implementations of Taylor models such as Cosy Infinity. Our library should
mainly be used to validate small to medium size results that are involved in
safety or life critical applications
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
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