formal proofs
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Author(s):  
Federico Reghenzani

AbstractThe difficulties in estimating the Worst-Case Execution Time (WCET) of applications make the use of modern computing architectures limited in real-time systems. Critical embedded systems require the tasks of hard real-time applications to meet their deadlines, and formal proofs on the validity of this condition are usually required by certification authorities. In the last decade, researchers proposed the use of probabilistic measurement-based methods to estimate the WCET instead of traditional static methods. In this chapter, we summarize recent theoretical and quantitative results on the use of probabilistic approaches to estimate the WCET presented in the PhD thesis of the author, including possible exploitation scenarios, open challenges, and future directions.


2021 ◽  
Vol 28 (4) ◽  
pp. 326-336
Author(s):  
Thomas Baar ◽  
Horst Schulte

KeYmaeraX is a Hoare-style theorem prover for hybrid systems. A hybrid system can be seen as an aggregation of both discrete and continuous variables, whose values can change abruptly or continuously, respectively. KeYmaeraX supports only variables having the primitive type bool or real. Due to the mixture of discrete and continuous system elements, one promising application area for KeYmaeraX are closed-loop control systems. A closed-loop control system consists of a plant and a controller. While the plant is basically an aggregation of continuous variables whose values change over time accordingly to physical laws, the controller can be seen as an algorithm formulated in a classical programming language. In this paper, we review some recent extensions of the proof calculus applied by KeYmaeraX that make formal proofs on the stability of dynamic systems more feasible. Based on an example, we first introduce to the topic and prove asymptotic stability of a given system in a hand-written mathematical style. This approach is then compared with a formal encoding of the problem and a formal proof established in KeYmaeraX. We also discuss open problems such as the formalization of asymptotic stability.


2021 ◽  
Author(s):  
Xuwei Wu ◽  
Christian Ott ◽  
Alin Albu-Schäffer ◽  
Alexander Dietrich

Kinematic redundancy in robots makes it possible to execute several control tasks simultaneously. As some tasks are usually more important than others, it is reasonable to dynamically decouple them in order to ensure their execution in a hierarchical way or even without any interference at all. The most widely used technique is to decouple the system by feedback linearization. However, that requires to actively shape the inertia and consequently modify the natural dynamics of the robot. Here we propose a passivity-based multi-task tracking controller that preserves these inertial properties but fully compensates for task-space cross-couplings using external force feedback. Additionally, three formal proofs are provided: uniform exponential stability for trajectory tracking, passivity during physical interaction, and input-to-state-stability. The controller is validated in simulations and experiments and directly compared with the hierarchical PD+ approach and the feedback linearization. The proposed approach is well suited for safe physical human-robot interaction and dynamic trajectory tracking if measurements or estimations of the external forces are available.


2021 ◽  
Author(s):  
Xuwei Wu ◽  
Christian Ott ◽  
Alin Albu-Schäffer ◽  
Alexander Dietrich

Kinematic redundancy in robots makes it possible to execute several control tasks simultaneously. As some tasks are usually more important than others, it is reasonable to dynamically decouple them in order to ensure their execution in a hierarchical way or even without any interference at all. The most widely used technique is to decouple the system by feedback linearization. However, that requires to actively shape the inertia and consequently modify the natural dynamics of the robot. Here we propose a passivity-based multi-task tracking controller that preserves these inertial properties but fully compensates for task-space cross-couplings using external force feedback. Additionally, three formal proofs are provided: uniform exponential stability for trajectory tracking, passivity during physical interaction, and input-to-state-stability. The controller is validated in simulations and experiments and directly compared with the hierarchical PD+ approach and the feedback linearization. The proposed approach is well suited for safe physical human-robot interaction and dynamic trajectory tracking if measurements or estimations of the external forces are available.


2021 ◽  
Vol 5 (OOPSLA) ◽  
pp. 1-27
Author(s):  
Ori Lahav ◽  
Egor Namakonov ◽  
Jonas Oberhauser ◽  
Anton Podkopaev ◽  
Viktor Vafeiadis

Liveness properties, such as termination, of even the simplest shared-memory concurrent programs under sequential consistency typically require some fairness assumptions about the scheduler. Under weak memory models, we observe that the standard notions of thread fairness are insufficient, and an additional fairness property, which we call memory fairness, is needed. In this paper, we propose a uniform definition for memory fairness that can be integrated into any declarative memory model enforcing acyclicity of the union of the program order and the reads-from relation. For the well-known models, SC, x86-TSO, RA, and StrongCOH, that have equivalent operational and declarative presentations, we show that our declarative memory fairness condition is equivalent to an intuitive model-specific operational notion of memory fairness, which requires the memory system to fairly execute its internal propagation steps. Our fairness condition preserves the correctness of local transformations and the compilation scheme from RC11 to x86-TSO, and also enables the first formal proofs of termination of mutual exclusion lock implementations under declarative weak memory models.


2021 ◽  
Vol 37 (3) ◽  
pp. 185-200
Author(s):  
Robert Cori

The aim of this paper is to come back to a data structure representation of graph by permutations. This originated in the years 1960-1970 by contributions due to J. Edmonds [7], A. Jacques [11], W. Tutte [22] in order to consider the embedding of a graph in a surface as a combinatorial object. Some algebraic developments where suggested in [4] and [12]. It was also used for implementation in different situation, like planarity testing by H. de Fraysseix and P. Rosenstiehl [6], computer vision by G. Damiand  and A. Dupas [5] or formal proofs by G. Gonthier [9].


2021 ◽  
Vol 22 (3) ◽  
Author(s):  
Chabane Djeddi ◽  
Nacer-eddine Zarour ◽  
Pierre-Jean Charrel

Identifying all the right requirements is indispensable for the success of anysystem. These requirements need to be engineered with precision in the earlyphases. Principally, late corrections costs are estimated to be more than 200times as much as corrections during requirements engineering (RE). EspeciallyBig data area, it becomes more and more crucial due to its importance andcharacteristics. In fact, and after literature analyzing, we note that currentsRE methods do not support the elicitation of Big data projects requirements. Inthis study, we propose the BiStar novel method as extension of iStar to under-take some Big data characteristics such as (volume, variety ...etc). As a firststep, we identify some missing concepts that currents requirements engineeringmethods do not support. Next, BiStar, an extension of iStar is developed totake into account Big data specifics characteristics while dealing with require-ments. In order to ensure the integrity property of BiStar, formal proofs weremade, we perform a bigraph based description on iStar and BiStar. Finally, anapplication is conducted on iStar and BiStar for the same illustrative scenario.The BiStar shows important results to be more suitable for eliciting Big dataprojects requirements.


Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2310
Author(s):  
Qiao-Ping Zhang ◽  
Ngai-Ying Wong

The topic of similarity plays an essential role in developing students’ deductive reasoning. However, knowing how to teach similarity and understanding how to incorporate deductive reasoning and proof along with plane geometry remain a challenge to both school curriculum creators and teachers. This study identified the problems and characteristics regarding how similarity is treated in secondary mathematics textbooks in Hong Kong in the past half century. The content analysis method was used to analyze six secondary mathematics textbook series published in different periods. From the epistemological perspective of the textbook contents, our analysis shows the historical context and learning trajectories of how similarity was treated in school curriculum. The natural axiomatic geometry paradigm is not emphasized too much at different stages and most of the textbooks did not provide formal proofs of similarity. The intuitive idea was gradually consolidated into a formal definition of similarity. Furthermore, the way that rigorous geometric deduction can be performed from intuitive concepts and experimental geometry to the idea of proofs and formal proofs is also discussed.


CONVERTER ◽  
2021 ◽  
pp. 449-458
Author(s):  
Junwei Yang, Xiangkun Tong, Chenglian Liu, Sonia C-I Chen

Formal verification is to use mathematical methods to prove that our scheme is correct. This scheme is just a pronoun. It may be expressed as a hardware, a software or an algorithm. Errors in hardware are more difficult to modify than errors in software, so formal proofs and inspections often appear in the argument for hardware design. But, it does not mean that the software does not need to be formally verified. In addition to digital circuits or combinational circuits, cryptographic protocols also need to be formally verified. Formal proof can only ensure whether the result of logical inference is consistent with the previous stage, and can not guarantee whether there are defects in the process of logical inference. In this article the authors take as an example of Zhang-Wang's digital signature algorithm, and point out two formal proof methods of Boolean algebra and Galois field respectively.


Author(s):  
Carlos Andrés Ramos-Paja ◽  
Daniel Gonzalez-Motoya ◽  
Juan Pablo Villegas-Seballos ◽  
Sergio Ignacio Serna-Garces ◽  
Roberto Giral

The wide range of step-up and step-down input-output voltage characteristic of the Cuk converter makes it a good candidate to interface photovoltaic arrays in both classical and distributed maximum power point tracking systems. Because its two inductor structure, Cuk converters have continuous input and output currents, which reduce the additional filtering elements usually required for interfacing dc/dc converter topologies. However, PV systems based on Cuk converters usually do not provide formal proofs of global stability under realistic conditions, which makes impossible to ensure a safe operation of the PV installation. Therefore, this paper proposes a high performance sliding-mode controller for PV systems based on Cuk converters, which regulates the PV voltage in agreement with the commands imposed by a MPPT algorithm, rejecting both load and environmental perturbations, and ensuring global stability for real operation conditions. Finally, the performance of the regulated PV system is tested using both simulations and experiments.


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