A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Formally Verified Approximations of Definite Integrals

2018
*
Journal of automated reasoning
*

This paper presents an efficient method for automatically computing and proving bounds on some

doi:10.1007/s10817-018-9463-7
fatcat:g3jumo65prehlovv7mwnoqjsse
*definite**integrals*inside the Coq*formal*system. ... Some*of*the numerical*integration*methods can even be made rigorous: not only do they compute an*approximation**of*the*integral*value but they also bound its inaccuracy. ...*Formally**Verified**Approximations**of**Definite**Integrals*...##
###
Formally Verified Approximations of Definite Integrals
[chapter]

2016
*
Lecture Notes in Computer Science
*

Some

doi:10.1007/978-3-319-43144-4_17
fatcat:gbqhtd2kvvbxzlbd6i7g7wqoqa
*of*the numerical*integration*methods can even be made rigorous: not only do they compute an*approximation**of*the*integral*value but they also bound its inaccuracy. ... This paper presents an efficient method for automatically computing and proving bounds on some*definite**integrals*inside the Coq*formal*system. ... Conclusion We have presented a method for computing and*formally**verifying*numerical enclosures*of*univariate*definite**integrals*using the Coq proof assistant. ...##
###
On the formal analysis of Gaussian optical systems in HOL

2016
*
Formal Aspects of Computing
*

To demonstrate the usefulness

doi:10.1007/s00165-016-0367-1
fatcat:env7aa6ivzbojly4pr4rwcgj2e
*of*the reported*formalization*, we utilize it to*formally*analyze some fractional order systems, namely, a fractional electrical component Resistoductance, a fractional*integrator*... Fractional order systems, which involve*integration*and differentiation*of*non integer order, are increasingly being used in the fields*of*control systems, robotics, signal processing and circuit theory ... We*verified*the continuity by differentiability using the classical*definition**of*derivative*formalized*in HOL [15] . ...##
###
Formalization of Transform Methods Using HOL Light
[chapter]

2017
*
Lecture Notes in Computer Science
*

In particular, we present the motivation

doi:10.1007/978-3-319-62075-6_22
fatcat:nh6h44hfkbc5dh6kk7aaz4cf4y
*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*. ... Acknowledgements This work was supported by the National Research Program for Universities grant (number 1543)*of*Higher Education Commission (HEC), Pakistan. ...##
###
Formalization of Transform Methods using HOL Light
[article]

2017
*
arXiv
*
pre-print

In particular, we present the motivation

arXiv:1705.10050v1
fatcat:wpigu4et6bgp5m3m7xmtqicuxm
*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*. ... Acknowledgements This work was supported by the National Research Program for Universities grant (number 1543)*of*Higher Education Commission (HEC), Pakistan. ...##
###
On the Formalization of Gamma Function in HOL

2014
*
Journal of automated reasoning
*

Firstly, we extend the existing

doi:10.1007/s10817-014-9311-3
fatcat:utrfokmtdzgwhk3fg7x5jnmzka
*integration*theory*of*HOL4 by*formalizing*a variant*of*improper*integrals*using sequential limits. ... In order to illustrate the practical effectiveness and utilization*of*our work, we*formally**verify*some properties*of*Euler's generalized power rule*of*differentiation, Mittag-Leffler functions and the ... The*formalization*, presented in this section, took around 5500 lines*of*HOL code and*approximately*300 man-hours. ...##
###
Formal verification of the heavy hitter problem

2012
*
2012 25th IEEE Canadian Conference on Electrical and Computer Engineering (CCECE)
*

This model is then utilized to

doi:10.1109/ccece.2012.6335035
dblp:conf/ccece/HelaliTH12
fatcat:cl4fa2ay3fculaupr7m4pjwrou
*formally**verify*some interesting probabilistic and statistical properties associated with the heavy hitter problem in HOL. ... The heavy hitter problem is used to assess the frequency*of*occurrence*of*an element in a given data stream. ... However, Coble's*formalization**of*Lebesgue*integral*can only consider finite-valued measures, functions and*integrals*. ...##
###
Towards the Formalization of Fractional Calculus in Higher-Order Logic
[article]

2015
*
arXiv
*
pre-print

Fractional calculus is a generalization

arXiv:1505.02140v1
fatcat:hvyf3xhf2nbh7bj4gijiav7rai
*of*classical theories*of**integration*and differentiation to arbitrary order (i.e., real or complex numbers). ... Mainly, we present the motivation and application*of*such*formalization*efforts, a roadmap to achieve our goals, current status*of*the project and future milestones. ... But now the current*formalization*seems quite stable as most*of*the classical properties have been*formally**verified*for our*definitions*. ...##
###
Formal Reasoning about Expectation Properties for Continuous Random Variables
[chapter]

2009
*
Lecture Notes in Computer Science
*

Starting from the relatively complex higher-order-logic

doi:10.1007/978-3-642-05089-3_28
fatcat:4ppnedhwjbf3pp3b7jsc6moski
*definition**of*expectation, based on Lebesgue*integration*, we*formally**verify*key expectation properties that allow us to reason about expectation ... This paper presents an infrastructure that can be used to*formally*reason about expectation properties*of*most*of*the continuous random variables in a theorem prover. ... Besides the*formalization**of*the above*definitions*, many useful properties regarding the Lebesgue*integral*have also been*verified*in [4] as higher-orderlogic theorems. ...##
###
Towards the Formalization of Fractional Calculus in Higher-Order Logic
[chapter]

2015
*
Lecture Notes in Computer Science
*

Fractional calculus is a generalization

doi:10.1007/978-3-319-20615-8_21
fatcat:lgx5adcufvfenedqbkpuuo4wnu
*of*classical theories*of**integration*and differentiation to arbitrary order (i.e., real or complex numbers). ... Mainly, we present the motivation and application*of*such*formalization*efforts, a roadmap to achieve our goals, current status*of*the project and future milestones. ... But now the current*formalization*seems quite stable as most*of*the classical properties have been*formally**verified*for our*definitions*. ...##
###
A Certificate-Based Approach to Formally Verified Approximations

2019
*
International Conference on Interactive Theorem Proving
*

Finally, we provide an implementation

doi:10.4230/lipics.itp.2019.8
dblp:conf/itp/BrehardMP19
fatcat:b2twcbftqrdihpid6s3fxlw4ha
*of**verified*Chebyshev*approximations*, and we discuss a few examples*of*computations. ... We present a library to*verify*rigorous*approximations**of*univariate functions on real numbers, with the Coq proof assistant. ... I T P 2 0 1 9 8:16 A Certificate-Based Approach to*Formally**Verified**Approximations*Error bounding. ...##
###
Formalization of Lerch's Theorem using HOL Light
[article]

2018
*
arXiv
*
pre-print

In this paper, we extend our higher-order logic

arXiv:1806.03049v1
fatcat:dxqnz5t2pvhvzaueddrd2hxq7a
*formalization**of*the Laplace transform, which includes the*formal**definition**of*the Laplace transform and verification*of*its various classical properties ... For illustration, we present the*formal*analysis*of*a 4-π soft error crosstalk model, which is widely used in nanometer technologies, such as,*Integrated*Circuits (ICs). ... We*formally**verified*these using our new*definition**of*the Laplace transform [27] . ...##
###
Formalization of Laplace Transform Using the Multivariable Calculus Theory of HOL-Light
[chapter]

2013
*
Lecture Notes in Computer Science
*

In order to demonstrate the practical effectiveness

doi:10.1007/978-3-642-45221-5_50
fatcat:fks2jihksrfalktlbopv5weapy
*of*this*formalization*, we use it to*formally**verify*the transfer function*of*Linear Transfer Converter (LTC) circuit, which is a commonly used electrical ... To facilitate*formal*analysis*of*these systems, we present the*formalization**of*Laplace transform using the multivariable calculus theories*of*HOL-Light. ... This work was supported by the National Research Program for Universities grant (number 1543)*of*Higher Education Commission (HEC), Pakistan. ...##
###
One-parameter extension of the Doi-Peliti formalism and its relation with orthogonal polynomials

2012
*
Physical Review E
*

An extension

doi:10.1103/physreve.86.042102
pmid:23214630
fatcat:4d5ytjszkjhe3dvkzij7bsuewq
*of*the Doi-Peliti*formalism*for stochastic chemical kinetics is proposed. Using the extension, path-*integral*expressions consistent with previous studies are obtained. ... In addition, the extended*formalism*is naturally connected to orthogonal polynomials. ... Here, we briefly explain some basic*definitions*for a coherent-state path-*integral*expression, which are especially useful in the Doi-Peliti*formalism*. ...##
###
Formal Probabilistic Analysis: A Higher-Order Logic Based Approach
[chapter]

2010
*
Lecture Notes in Computer Science
*

Some major contributions include the

doi:10.1007/978-3-642-11811-1_2
fatcat:hhk4xlpnevflrf2w3ijc3hweni
*formalization**of*both discrete and continuous random variables and the verification*of*some*of*their corresponding probabilistic and statistical properties. ... Recently, a significant amount*of**formalization*has been done in higherorder logic that allows us to conduct precise probabilistic analysis using theorem proving and thus overcome the limitations*of*the ... In order to*verify*the correctness*of*the above*definitions**of*expectation, they are utilized in [20, 21] to*formally**verify*the following classical expectation properties. ...
« Previous

*Showing results 1 — 15 out of 292,822 results*