10 Search Results for "Schuster, Peter"

Document
DOI: 10.4230/LIPIcs.CSL.2024.16
A General Constructive Form of Higman’s Lemma

Authors: Stefano Berardi, Gabriele Buriola, and Peter Schuster

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
In logic and computer science one often needs to constructivize a theorem ∀ f ∃ g.P(f,g), stating that for every infinite sequence f there is an infinite sequence g such that P(f,g). Here P is a computable predicate but g is not necessarily computable from f. In this paper we propose the following constructive version of ∀ f ∃ g.P(f,g): for every f there is a "long enough" finite prefix g₀ of g such that P(f,g₀), where "long enough" is expressed by membership to a bar which is a free parameter of the constructive version. Our approach with bars generalises the approaches to Higman’s lemma undertaken by Coquand-Fridlender, Murthy-Russell and Schwichtenberg-Seisenberger-Wiesnet. As a first test for our bar technique, we sketch a constructive theory of well-quasi orders. This includes yet another constructive version of Higman’s lemma: that every infinite sequence of words has an infinite ascending subsequence. As compared with the previous constructive versions of Higman’s lemma, our constructive proofs are closer to the original classical proofs.
Cite as

Stefano Berardi, Gabriele Buriola, and Peter Schuster. A General Constructive Form of Higman’s Lemma. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{berardi_et_al:LIPIcs.CSL.2024.16,
  author =	{Berardi, Stefano and Buriola, Gabriele and Schuster, Peter},
  title =	{{A General Constructive Form of Higman’s Lemma}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.16},
  URN =		{urn:nbn:de:0030-drops-196599},
  doi =		{10.4230/LIPIcs.CSL.2024.16},
  annote =	{Keywords: intuitionistic logic, constructive mathematics, formal proof, inductive predicate, bar induction, well quasi-order, Higman’s lemma}
}
Document
Artifact
DOI: 10.4230/DARTS.9.1.2
FusionClock: WCEC-Optimal Clock-Tree Reconfigurations (Artifact)

Authors: Eva Dengler, Phillip Raffeck, Simon Schuster, and Peter Wägemann

Published in: DARTS, Volume 9, Issue 1, Special Issue of the 35th Euromicro Conference on Real-Time Systems (ECRTS 2023)

Abstract
Numerous embedded real-time systems have, besides their worst-case execution time (WCET) requirements, strict worst-case energy consumption (WCEC) constraints that must be satisfied. The core hardware component of modern system-on-chip (SoC) platforms to configure the tradeoff between time and energy is the system’s clock tree, which provides the necessary clock source for each connected device (i.e., memory, sensors, transceivers). Existing energy-aware scheduling approaches have limitations with regard to these modern, feature-rich clock trees: These shortcomings concern the (re-)configuration of the clock tree with the associated penalties, which are a non-negligible part of dynamic frequency/voltage scaling or power-gating devices in addition to the influence of available sleep modes. This artifact evaluation covers the work on FusionClock, an approach that exploits a fine-grained model of the system’s temporal and energetic behavior. By means of our developed clock-tree model, FusionClock processes time-triggered schedules and finally generates optimized code for a system where offline-determined and online-applied reconfigurations lead to the worst-case-optimal energy demand while still meeting given timing-related deadlines. For statically determining these energy-optimal reconfigurations on task level, FusionClock builds a mathematical optimization problem based on the tasks' specifications and the system’s resource-consumption model. Specific components like transceivers of SoCs usually have strict requirements regarding the used clock source (e.g., phase-locked loop, RC network, oscillator). FusionClock accounts for these clock-tree requirements with its ability to exploit application-specific knowledge within an optimization problem. With our resource-consumption model for a modern SoC platform and our open-source prototype of FusionClock, we are able to achieve significant energy savings while still providing guarantees for timeliness, as our evaluations on a real hardware platform (i.e., ESP32-C3) show.
Cite as

Eva Dengler, Phillip Raffeck, Simon Schuster, and Peter Wägemann. FusionClock: WCEC-Optimal Clock-Tree Reconfigurations (Artifact). In Special Issue of the 35th Euromicro Conference on Real-Time Systems (ECRTS 2023). Dagstuhl Artifacts Series (DARTS), Volume 9, Issue 1, pp. 2:1-2:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{dengler_et_al:DARTS.9.1.2,
  author =	{Dengler, Eva and Raffeck, Phillip and Schuster, Simon and W\"{a}gemann, Peter},
  title =	{{FusionClock: WCEC-Optimal Clock-Tree Reconfigurations (Artifact)}},
  pages =	{2:1--2:3},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2023},
  volume =	{9},
  number =	{1},
  editor =	{Dengler, Eva and Raffeck, Phillip and Schuster, Simon and W\"{a}gemann, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.9.1.2},
  URN =		{urn:nbn:de:0030-drops-180238},
  doi =		{10.4230/DARTS.9.1.2},
  annote =	{Keywords: energy-constrained real-time systems, worst-case execution time (WCET), worst-case energy consumption (WCEC), energy-aware real-time scheduling, static whole-system analysis, time/energy tradeoff, clock tree, system on chip}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2023.6
FusionClock: Energy-Optimal Clock-Tree Reconfigurations for Energy-Constrained Real-Time Systems

Authors: Eva Dengler, Phillip Raffeck, Simon Schuster, and Peter Wägemann

Published in: LIPIcs, Volume 262, 35th Euromicro Conference on Real-Time Systems (ECRTS 2023)

Abstract
Numerous embedded real-time systems have, besides their timing requirements, strict energy constraints that must be satisfied. Examples of this class of real-time systems are implantable medical devices, where knowledge of the worst-case execution time (WCET) has the same importance as of the worst-case energy consumption (WCEC) in order to provide runtime guarantees. The core hardware component of modern system-on-chip (SoC) platforms to configure the tradeoff between time and energy is the system’s clock tree, which provides the necessary clock source to all connected devices (i.e., memory, sensors, transceivers). Existing energy-aware scheduling approaches have shortcomings with regard to these modern, feature-rich clock trees: First, with their reactive, dynamic (re-)configuration of the clock tree, they are not able to provide static guarantees of the system’s resource consumption (i.e., energy and time). Second, they only account for dynamic voltage/frequency scaling of the CPU and thereby miss the reconfiguration of clock sources and clock speed for the other connected devices on such SoCs. Third, they neglect the reconfiguration penalties of frequency scaling and clock/power gating in the presence of the CPU’s sleep modes. In this paper, we present FusionClock, an approach that exploits a fine-grained model of the system’s temporal and energetic behavior. By means of our developed clock-tree model, FusionClock processes time-triggered schedules and finally generates optimized code for a system where offline-determined and online-applied reconfigurations lead to the worst-case-optimal energy demand while still meeting given timing-related deadlines. For statically determining these energy-optimal reconfigurations on task level, FusionClock builds a mathematical optimization problem based on the tasks' specifications and the system’s resource-consumption model. Specific components like transceivers of SoCs usually have strict requirements regarding the used clock source (e.g., phase-locked loop, RC network, oscillator). FusionClock accounts for these clock-tree requirements with its ability to exploit application-specific knowledge within an optimization problem. With our resource-consumption model for a modern SoC platform and our open-source prototype of FusionClock, we are able to achieve significant energy savings while still providing guarantees for timeliness, as our evaluations on a real hardware platform (i.e., ESP32-C3) show.
Cite as

Eva Dengler, Phillip Raffeck, Simon Schuster, and Peter Wägemann. FusionClock: Energy-Optimal Clock-Tree Reconfigurations for Energy-Constrained Real-Time Systems. In 35th Euromicro Conference on Real-Time Systems (ECRTS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 262, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dengler_et_al:LIPIcs.ECRTS.2023.6,
  author =	{Dengler, Eva and Raffeck, Phillip and Schuster, Simon and W\"{a}gemann, Peter},
  title =	{{FusionClock: Energy-Optimal Clock-Tree Reconfigurations for Energy-Constrained Real-Time Systems}},
  booktitle =	{35th Euromicro Conference on Real-Time Systems (ECRTS 2023)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-280-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{262},
  editor =	{Papadopoulos, Alessandro V.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2023.6},
  URN =		{urn:nbn:de:0030-drops-180354},
  doi =		{10.4230/LIPIcs.ECRTS.2023.6},
  annote =	{Keywords: energy-aware scheduling, device-aware whole-system analysis, clock tree}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2021.7
Constructive Cut Elimination in Geometric Logic

Authors: Giulio Fellin, Sara Negri, and Eugenio Orlandelli

Published in: LIPIcs, Volume 239, 27th International Conference on Types for Proofs and Programs (TYPES 2021)

Abstract
A constructivisation of the cut-elimination proof for sequent calculi for classical and intuitionistic infinitary logic with geometric rules - given in earlier work by the second author - is presented. This is achieved through a procedure in which the non-constructive transfinite induction on the commutative sum of ordinals is replaced by two instances of Brouwer’s Bar Induction. Additionally, a proof of Barr’s Theorem for geometric theories that uses only constructively acceptable proof-theoretical tools is obtained.
Cite as

Giulio Fellin, Sara Negri, and Eugenio Orlandelli. Constructive Cut Elimination in Geometric Logic. In 27th International Conference on Types for Proofs and Programs (TYPES 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 239, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fellin_et_al:LIPIcs.TYPES.2021.7,
  author =	{Fellin, Giulio and Negri, Sara and Orlandelli, Eugenio},
  title =	{{Constructive Cut Elimination in Geometric Logic}},
  booktitle =	{27th International Conference on Types for Proofs and Programs (TYPES 2021)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-254-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{239},
  editor =	{Basold, Henning and Cockx, Jesper and Ghilezan, Silvia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2021.7},
  URN =		{urn:nbn:de:0030-drops-167763},
  doi =		{10.4230/LIPIcs.TYPES.2021.7},
  annote =	{Keywords: Geometric theories, sequent calculi, axioms-as-rules, infinitary logic, constructive cut elimination}
}
Document
DOI: 10.4230/DagRep.11.10.151
Geometric Logic, Constructivisation, and Automated Theorem Proving (Dagstuhl Seminar 21472)

Authors: Thierry Coquand, Hajime Ishihara, Sara Negri, and Peter M. Schuster

Published in: Dagstuhl Reports, Volume 11, Issue 10 (2022)

Abstract
At least from a practical and contemporary angle, the time-honoured question about the extent of intuitionistic mathematics rather is to which extent any given proof is effective, which proofs of which theorems can be rendered effective, and whether and how numerical information such as bounds and algorithms can be extracted from proofs. All this is ideally done by manipulating proofs mechanically or by adequate metatheorems, which includes proof translations, automated theorem proving, program extraction from proofs, proof analysis and proof mining. The question should thus be put as: What is the computational content of proofs? Guided by this central question, the present Dagstuhl seminar puts a special focus on coherent and geometric theories and their generalisations. These are not only widespread in mathematics and non-classical logics such as temporal and modal logics, but also a priori amenable for constructivisation, e.g., by Barr’s Theorem, and last but not least particularly suited as a basis for automated theorem proving. Specific topics include categorical semantics for geometric theories, complexity issues of and algorithms for geometrisation of theories including speed-up questions, the use of geometric theories in constructive mathematics including finding algorithms, proof-theoretic presentation of sheaf models and higher toposes, and coherent logic for automatically readable proofs.
Cite as

Thierry Coquand, Hajime Ishihara, Sara Negri, and Peter M. Schuster. Geometric Logic, Constructivisation, and Automated Theorem Proving (Dagstuhl Seminar 21472). In Dagstuhl Reports, Volume 11, Issue 10, pp. 151-172, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{coquand_et_al:DagRep.11.10.151,
  author =	{Coquand, Thierry and Ishihara, Hajime and Negri, Sara and Schuster, Peter M.},
  title =	{{Geometric Logic, Constructivisation, and Automated Theorem Proving (Dagstuhl Seminar 21472)}},
  pages =	{151--172},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{11},
  number =	{10},
  editor =	{Coquand, Thierry and Ishihara, Hajime and Negri, Sara and Schuster, Peter M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.11.10.151},
  URN =		{urn:nbn:de:0030-drops-159321},
  doi =		{10.4230/DagRep.11.10.151},
  annote =	{Keywords: automated theorem proving, categorical semantics, constructivisation, geometric logic, proof theory}
}
Document
DOI: 10.4230/OASIcs.WCET.2019.4
Worst-Case Energy-Consumption Analysis by Microarchitecture-Aware Timing Analysis for Device-Driven Cyber-Physical Systems

Authors: Phillip Raffeck, Christian Eichler, Peter Wägemann, and Wolfgang Schröder-Preikschat

Published in: OASIcs, Volume 72, 19th International Workshop on Worst-Case Execution Time Analysis (WCET 2019)

Abstract
Many energy-constrained cyber-physical systems require both timeliness and the execution of tasks within given energy budgets. That is, besides knowledge on worst-case execution time (WCET), the worst-case energy consumption (WCEC) of operations is essential. Unfortunately, WCET analysis approaches are not directly applicable for deriving WCEC bounds in device-driven cyber-physical systems: For example, a single memory operation can lead to a significant power-consumption increase when thereby switching on a device (e.g. transceiver, actuator) in the embedded system. However, as we demonstrate in this paper, existing approaches from microarchitecture-aware timing analysis (i.e. considering cache and pipeline effects) are beneficial for determining WCEC bounds: We extended our framework on whole-system analysis with microarchitecture-aware timing modeling to precisely account for the execution time that devices are kept (in)active. Our evaluations based on a benchmark generator, which is able to output benchmarks with known baselines (i.e. actual WCET and actual WCEC), and an ARM Cortex-M4 platform validate that the approach significantly reduces analysis pessimism in whole-system WCEC analyses.
Cite as

Phillip Raffeck, Christian Eichler, Peter Wägemann, and Wolfgang Schröder-Preikschat. Worst-Case Energy-Consumption Analysis by Microarchitecture-Aware Timing Analysis for Device-Driven Cyber-Physical Systems. In 19th International Workshop on Worst-Case Execution Time Analysis (WCET 2019). Open Access Series in Informatics (OASIcs), Volume 72, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{raffeck_et_al:OASIcs.WCET.2019.4,
  author =	{Raffeck, Phillip and Eichler, Christian and W\"{a}gemann, Peter and Schr\"{o}der-Preikschat, Wolfgang},
  title =	{{Worst-Case Energy-Consumption Analysis by Microarchitecture-Aware Timing Analysis for Device-Driven Cyber-Physical Systems}},
  booktitle =	{19th International Workshop on Worst-Case Execution Time Analysis (WCET 2019)},
  pages =	{4:1--4:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-118-4},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{72},
  editor =	{Altmeyer, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.WCET.2019.4},
  URN =		{urn:nbn:de:0030-drops-107699},
  doi =		{10.4230/OASIcs.WCET.2019.4},
  annote =	{Keywords: WCEC, WCRE, WCET, michroarchitecture analysis, whole-system analysis}
}
Document
DOI: 10.4230/OASIcs.GCB.2012.39
A Two-Step Soft Segmentation Procedure for MALDI Imaging Mass Spectrometry Data

Authors: Ilya Chernyavsky, Theodore Alexandrov, Peter Maass, and Sergey I. Nikolenko

Published in: OASIcs, Volume 26, German Conference on Bioinformatics 2012

Abstract
We propose a new method for soft spatial segmentation of matrix assisted laser desorption/ionization imaging mass spectrometry (MALDI-IMS) data which is based on probabilistic clustering with subsequent smoothing. Clustering of spectra is done with the Latent Dirichlet Allocation (LDA) model. Then, clustering results are smoothed with a Markov random field (MRF) resulting in a soft probabilistic segmentation map. We show several extensions of the basic MRF model specifically tuned for MALDI-IMS data segmentation. We describe a highly parallel implementation of the smoothing algorithm based on GraphLab framework and show experimental results.
Cite as

Ilya Chernyavsky, Theodore Alexandrov, Peter Maass, and Sergey I. Nikolenko. A Two-Step Soft Segmentation Procedure for MALDI Imaging Mass Spectrometry Data. In German Conference on Bioinformatics 2012. Open Access Series in Informatics (OASIcs), Volume 26, pp. 39-48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{chernyavsky_et_al:OASIcs.GCB.2012.39,
  author =	{Chernyavsky, Ilya and Alexandrov, Theodore and Maass, Peter and Nikolenko, Sergey I.},
  title =	{{A Two-Step Soft Segmentation Procedure for MALDI Imaging Mass Spectrometry Data}},
  booktitle =	{German Conference on Bioinformatics 2012},
  pages =	{39--48},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-44-6},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{26},
  editor =	{B\"{o}cker, Sebastian and Hufsky, Franziska and Scheubert, Kerstin and Schleicher, Jana and Schuster, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.GCB.2012.39},
  URN =		{urn:nbn:de:0030-drops-37163},
  doi =		{10.4230/OASIcs.GCB.2012.39},
  annote =	{Keywords: MALDI imaging mass spectrometry, hyperspectral image segmentation, probabilistic graphical models, latent Dirichlet allocation, Markov random field}
}
Document
DOI: 10.4230/OASIcs.CCA.2009.2265
Uniqueness, Continuity, and Existence of Implicit Functions in Constructive Analysis

Authors: Hannes Diener and Peter Schuster

Published in: OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009)

Abstract
We extract a quantitative variant of uniqueness from the usual hypotheses of the implicit functions theorem. This leads not only to an a priori proof of continuity, but also to an alternative, fully constructive existence proof.
Cite as

Hannes Diener and Peter Schuster. Uniqueness, Continuity, and Existence of Implicit Functions in Constructive Analysis. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 131-140, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{diener_et_al:OASIcs.CCA.2009.2265,
  author =	{Diener, Hannes and Schuster, Peter},
  title =	{{Uniqueness, Continuity, and Existence of Implicit Functions in Constructive Analysis}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  pages =	{131--140},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2265},
  URN =		{urn:nbn:de:0030-drops-22651},
  doi =		{10.4230/OASIcs.CCA.2009.2265},
  annote =	{Keywords: Implicit function, uniqueness, continuity, constructive analysis, countable choice}
}
Document
DOI: 10.4230/DagSemProc.05021.4
A Nilregular Element Property

Authors: Thierry Coquand, Henri Lombardi, and Peter Schuster

Published in: Dagstuhl Seminar Proceedings, Volume 5021, Mathematics, Algorithms, Proofs (2006)

Abstract
An element or an ideal of a commutative ring is nilregular if and only if it is regular modulo the nilradical. We prove that if the ring is Noetherian, then every nilregular ideal contains a nilregular element. In constructive mathematics, this proof can then be seen as an algorithm to produce nilregular elements of nilregular ideals whenever the ring is coherent, Noetherian, and discrete. As an application, we give a constructive proof of the Eisenbud--Evans--Storch theorem that every algebraic set in $n$--dimensional affine space is the intersection of $n$ hypersurfaces. The input of the algorithm is an arbitrary finite list of polynomials, which need not arrive in a special form such as a Gr"obner basis. We dispense with prime ideals when defining concepts or carrying out proofs.
Cite as

Thierry Coquand, Henri Lombardi, and Peter Schuster. A Nilregular Element Property. In Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, Volume 5021, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{coquand_et_al:DagSemProc.05021.4,
  author =	{Coquand, Thierry and Lombardi, Henri and Schuster, Peter},
  title =	{{A Nilregular Element Property}},
  booktitle =	{Mathematics, Algorithms, Proofs},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{5021},
  editor =	{Thierry Coquand and Henri Lombardi and Marie-Fran\c{c}oise Roy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.05021.4},
  URN =		{urn:nbn:de:0030-drops-2784},
  doi =		{10.4230/DagSemProc.05021.4},
  annote =	{Keywords: Lists of generators, polynomial ideals, Krull dimension, Zariski topology, commutative Noetherian rings, constructive algebra}
}
Document
DOI: 10.4230/DagSemProc.04351.9
Compactness in apartness spaces?

Authors: Douglas Bridges, Hajime Ishihara, Peter Schuster, and Luminita S. Vita

Published in: Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005)

Abstract
A major problem in the constructive theory of apartness spaces is that of finding a good notion of compactness. Such a notion should (i) reduce to ``complete plus totally bounded'' for uniform spaces and (ii) classically be equivalent to the usual Heine-Borel-Lebesgue property for the apartness topology. The constructive counterpart of the smallest uniform structure compatible with a given apartness, while not constructively a uniform structure, offers a possible solution to the compactness-definition problem. That counterpart turns out to be interesting in its own right, and reveals some additional properties of an apartness that may have uses elsewhere in the theory.
Cite as

Douglas Bridges, Hajime Ishihara, Peter Schuster, and Luminita S. Vita. Compactness in apartness spaces?. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{bridges_et_al:DagSemProc.04351.9,
  author =	{Bridges, Douglas and Ishihara, Hajime and Schuster, Peter and Vita, Luminita S.},
  title =	{{Compactness in apartness spaces?}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--7},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.9},
  URN =		{urn:nbn:de:0030-drops-1175},
  doi =		{10.4230/DagSemProc.04351.9},
  annote =	{Keywords: Apartness , constructive , compact uniform space}
}
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