976 research outputs found
Formalization of Fixed-Point Arithmetic in HOL
This paper addresses the formalization in higher-order logic of fixed-point arithmetic. We encoded the fixed-point number system and specified the different quantization modes in fixed-point arithmetic such as the directed and even quantization modes. We also considered the formalization of exceptions detection and their handling like overflow and invalid operation. An error analysis is then performed to check the correctness of the quantized result after carrying out basic arithmetic operations, such as addition, subtraction, multiplication and division against their mathematical counterparts. Finally, we showed by an example how this formalization can be used to enable the verification of the transition from floating-point to fixed-point algorithmic level in the signal processing design flow
Modeling and verification of DSP designs in HOL
In this thesis we propose a framework for the incorporation of formal methods in the design flow of DSP (Digital Signal Processing) systems in a rigorous way. In the proposed approach we model and verify DSP descriptions at different abstraction levels using higher-order logic based on the HOL (Higher Order Logic) theorem prover. This framework enables the formal verification of DSP designs which in the past could only be done partially using conventional simulation techniques. To this end, we provide a shallow embedding of DSP descriptions in HOL at the floating-point, fixed-point, behavioral, RTL (Register Transfer Level), and netlist gate levels. We make use of existing formalization of floating-point theory in HOL and introduce a parallel one for fixed-point arithmetic. The high ability of abstraction in HOL allows a seamless hierarchical verification encompassing the whole DSP design path, starting from top level floating- and fixed-point algorithmic descriptions down to RTL, and gate level implementations. We illustrate the new verification framework using different case studies such as digital filters and FFT (Fast Fourier Transform) algorithms
Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)
Oxford, UK, 26 August 200
An approach for the formal verification of DSP designs using Theorem proving
This paper proposes a framework for the incorporation of formal methods in the design flow of digital signal processing (DSP) systems in a rigorous way. In the proposed approach, DSP descriptions were modeled and verified at different abstraction levels using higher order logic based on the higher order logic (HOL) theorem prover. This framework enables the formal verification of DSP designs that in the past could only be done partially using conventional simulation techniques. To this end, a shallow embedding of DSP descriptions in HOL at the floating-point (FP), fixed-point (FXP), behavioral, register transfer level (RTL), and netlist gate levels is provided. The paper made use of existing formalization of FP theory in HOL and a parallel one developed for FXP arithmetic. The high ability of abstraction in HOL allows a seamless hierarchical verification encompassing the whole DSP design path, starting from top-level FP and FXP algorithmic descriptions down to RTL, and gate level implementations. The paper illustrates the new verification framework on the fast Fourier transform (FFT) algorithm as a case study
A Verified Certificate Checker for Finite-Precision Error Bounds in Coq and HOL4
Being able to soundly estimate roundoff errors of finite-precision
computations is important for many applications in embedded systems and
scientific computing. Due to the discrepancy between continuous reals and
discrete finite-precision values, automated static analysis tools are highly
valuable to estimate roundoff errors. The results, however, are only as correct
as the implementations of the static analysis tools. This paper presents a
formally verified and modular tool which fully automatically checks the
correctness of finite-precision roundoff error bounds encoded in a certificate.
We present implementations of certificate generation and checking for both Coq
and HOL4 and evaluate it on a number of examples from the literature. The
experiments use both in-logic evaluation of Coq and HOL4, and execution of
extracted code outside of the logics: we benchmark Coq extracted unverified
OCaml code and a CakeML-generated verified binary
Formalization of Transform Methods using HOL Light
Transform methods, like Laplace and Fourier, are frequently used for
analyzing the dynamical behaviour of engineering and physical systems, based on
their transfer function, and frequency response or the solutions of their
corresponding differential equations. In this paper, we present an ongoing
project, which focuses on the higher-order logic formalization of transform
methods using HOL Light theorem prover. In particular, we present the
motivation of the formalization, which is followed by the related work. Next,
we present the task completed so far while highlighting some of the challenges
faced during the formalization. Finally, we present a roadmap to achieve our
objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201
Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations
We present a formal tool for verification of multivariate nonlinear
inequalities. Our verification method is based on interval arithmetic with
Taylor approximations. Our tool is implemented in the HOL Light proof assistant
and it is capable to verify multivariate nonlinear polynomial and
non-polynomial inequalities on rectangular domains. One of the main features of
our work is an efficient implementation of the verification procedure which can
prove non-trivial high-dimensional inequalities in several seconds. We
developed the verification tool as a part of the Flyspeck project (a formal
proof of the Kepler conjecture). The Flyspeck project includes about 1000
nonlinear inequalities. We successfully tested our method on more than 100
Flyspeck inequalities and estimated that the formal verification procedure is
about 3000 times slower than an informal verification method implemented in
C++. We also describe future work and prospective optimizations for our method.Comment: 15 page
Formal Probabilistic Analysis of a Wireless Sensor Network for Forest Fire Detection
Wireless Sensor Networks (WSNs) have been widely explored for forest fire
detection, which is considered a fatal threat throughout the world. Energy
conservation of sensor nodes is one of the biggest challenges in this context
and random scheduling is frequently applied to overcome that. The performance
analysis of these random scheduling approaches is traditionally done by
paper-and-pencil proof methods or simulation. These traditional techniques
cannot ascertain 100% accuracy, and thus are not suitable for analyzing a
safety-critical application like forest fire detection using WSNs. In this
paper, we propose to overcome this limitation by applying formal probabilistic
analysis using theorem proving to verify scheduling performance of a real-world
WSN for forest fire detection using a k-set randomized algorithm as an energy
saving mechanism. In particular, we formally verify the expected values of
coverage intensity, the upper bound on the total number of disjoint subsets,
for a given coverage intensity, and the lower bound on the total number of
nodes.Comment: In Proceedings SCSS 2012, arXiv:1307.802
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