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A Theory of Reliable Hardware

Total Cost €


EC-Contrib. €






Project "ToRH" data sheet

The following table provides information about the project.


Organization address
city: Munich
postcode: 80539

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Total cost 1˙472˙000 €
 EC max contribution 1˙472˙000 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-08-01   to  2022-07-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

The complexity of computing hardware keeps increasing at a rapid pace, with no end in sight. With growing number of components and ongoing miniaturization, hardware engineers struggle with an increasing number and variety of faults, yet must guarantee correct operation of the system as a whole. This is hindered by a concurrent increase in design complexity, i.e., the trend of integrating ever more diverse circuits into larger systems, which results in a higher complexity of verifying the correctness of a given design -- especially when providing for the possibility that some components may fail.

The goal of this project is to develop a holistic mathematical approach to modeling fault-tolerant circuits and demonstrate its usefulness in practice. Such a framework will exhibit several advantages over the present methods, which are largely based on simulation and experimentation:

(i) mathematical proofs offer parametrized guarantees, which implies that the derived building blocks can easily be re-used in varying configurations and translated to different technologies; (ii) it permits statements about general fault types, entailing that claimed properties do not rely on specific fault behavior (which depends on operational parameters and technology); and (iii) abstract, parametrized reasoning enables to design and optimize for long-term scalability.

While this approach to fault-tolerance has been successfully applied in the area of distributed computing for decades, transferring it to low-level hardware design introduces new obstacles, such as very limited computational capabilities of the basic components and the potential for metastability. Overcoming these challenges will pave the way for highly dependable and scalable systems, and thus help in further sustaining the exponential growth in available computing power commonly referred to as Moore's Law.


List of deliverables.
Data Management Plan Open Research Data Pilot 2019-05-31 11:59:00

Take a look to the deliverables list in detail:  detailed list of ToRH deliverables.


year authors and title journal last update
List of publications.
2020 Johannes Bund, Matthias Fuegger, Christoph Lenzen, Moti Medina, Will Rosenbaum
PALS: Plesiochronous and Locally Synchronous Systems
published pages: , ISSN: , DOI:
2020 Johannes Bund, Christoph Lenzen, Moti Medina
Optimal Metastability-Containing Sorting via Parallel Prefix Computation
published pages: 198-211, ISSN: 0018-9340, DOI: 10.1109/tc.2019.2939818
IEEE Transactions on Computers 69/2 2020-03-11
2019 Christoph Lenzen, Joel Rybicki
Self-Stabilising Byzantine Clock Synchronisation Is Almost as Easy as Consensus
published pages: 1-56, ISSN: 0004-5411, DOI: 10.1145/3339471
Journal of the ACM 66/5 2020-03-11
2019 Christoph Lenzen, Joel Rybicki
Near-optimal self-stabilising counting and firing squads
published pages: 339-360, ISSN: 0178-2770, DOI: 10.1007/s00446-018-0342-6
Distributed Computing 32/4 2020-03-11
2019 Christian Ikenmeyer, Balagopal Komarath, Christoph Lenzen, Vladimir Lysikov, Andrey Mokhov, Karteek Sreenivasaiah
On the Complexity of Hazard-free Circuits
published pages: 1-20, ISSN: 0004-5411, DOI: 10.1145/3320123
Journal of the ACM 66/4 2020-03-11
2018 Stephan Friedrichs, Matthias Fugger, Christoph Lenzen
Metastability-Containing Circuits
published pages: 1-1, ISSN: 0018-9340, DOI: 10.1109/TC.2018.2808185
IEEE Transactions on Computers 2019-06-13
2018 Johannes Bund, Christoph Lenzen, Moti Medina
Small Hazard-free Transducers
published pages: , ISSN: , DOI:
2019 Johannes Bund, Christoph Lenzen, Will Rosenbaum
Fault Tolerant Gradient Clock Synchronization
published pages: , ISSN: , DOI:

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