DROPS

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DOI: 10.4230/OASIcs.AEiC.2026.6

Task-Based Constant Bandwidth Server in the Zephyr Operating System

Authors: Alexander Paschoaletto, Paulo Baltarejo Sousa, Luis Miguel Pinho, and Tiago Carvalho

Published in: OASIcs, Volume 143, 30th Ada-Europe International Conference on Reliable Software Technologies (AEiC 2026)

Abstract

The Constant Bandwidth Server (CBS) is a widely used method to support aperiodic soft real-time tasks in a system that uses dynamic scheduling algorithms, such as Earliest Deadline First (EDF), while providing end-to-end temporal guarantees through bandwidth reservation. We have recently proposed an approach to integrate CBS with the open-source real-time operating system, Zephyr, which involves developing CBS as a separate kernel component that can be shared by multiple execution contexts. In this paper, we propose an alternative approach, which provides each task with a dedicated CBS instance, which enables fine-grained control over task execution. The paper also presents a richer support for EDF scheduling in Zephyr, which is used to support the Task-Based CBS. The proposed method is validated through test cases, demonstrating its efficiency in supporting aperiodic real-time tasks with bandwidth constraints in Zephyr.

Cite as

Alexander Paschoaletto, Paulo Baltarejo Sousa, Luis Miguel Pinho, and Tiago Carvalho. Task-Based Constant Bandwidth Server in the Zephyr Operating System. In 30th Ada-Europe International Conference on Reliable Software Technologies (AEiC 2026). Open Access Series in Informatics (OASIcs), Volume 143, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{paschoaletto_et_al:OASIcs.AEiC.2026.6,
  author =	{Paschoaletto, Alexander and Sousa, Paulo Baltarejo and Pinho, Luis Miguel and Carvalho, Tiago},
  title =	{{Task-Based Constant Bandwidth Server in the Zephyr Operating System}},
  booktitle =	{30th Ada-Europe International Conference on Reliable Software Technologies (AEiC 2026)},
  pages =	{6:1--6:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-425-3},
  ISSN =	{2190-6807},
  year =	{2026},
  volume =	{143},
  editor =	{Filieri, Antonio and Backeman, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.AEiC.2026.6},
  URN =		{urn:nbn:de:0030-drops-259246},
  doi =		{10.4230/OASIcs.AEiC.2026.6},
  annote =	{Keywords: Constant Bandwidth Server, Zephyr Operating System}
}

Document

DOI: 10.4230/LITES.11.1.1

A Survey of Real-Time Support, Analysis, and Advancements in ROS 2

Authors: Daniel Casini, Jian-Jia Chen, Jing Li, Federico Reghenzani, and Harun Teper

Published in: LITES, Volume 11, Issue 1 (2026). Leibniz Transactions on Embedded Systems, Volume 11, Issue 1

Abstract

The Robot Operating System 2 (ROS 2) has emerged as a relevant middleware framework for robotic applications, offering modularity, distributed execution, and communication. In the last six years, ROS 2 has drawn increasing attention from the real-time systems community and industry. This survey presents a comprehensive overview of research efforts that analyze, enhance, and extend ROS 2 to support real-time execution. We first provide a detailed description of the internal scheduling mechanisms of ROS 2 and its layered architecture, including the interaction with DDS-based communication and other communication middleware. We then review key contributions from the literature, covering timing analysis for both single- and multi-threaded executors, metrics such as response time, reaction time, and data age, and different communication modes. The survey also discusses community-driven enhancements to the ROS 2 runtime, including new executor algorithm designs, real-time GPU management, and microcontroller support via micro-ROS. Furthermore, we summarize techniques for bounding DDS communication delays, message filters, and profiling tools that have been developed to support analysis and experimentation. To help systematize this growing body of work, we introduce taxonomies that classify the surveyed contributions based on different criteria. This survey aims to guide both researchers and practitioners in understanding and improving the real-time capabilities of ROS 2.

Cite as

Daniel Casini, Jian-Jia Chen, Jing Li, Federico Reghenzani, and Harun Teper. A Survey of Real-Time Support, Analysis, and Advancements in ROS 2. In LITES, Volume 11, Issue 1 (2026). Leibniz Transactions on Embedded Systems, Volume 11, Issue 1, pp. 1:1-1:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{casini_et_al:LITES.11.1.1,
  author =	{Casini, Daniel and Chen, Jian-Jia and Li, Jing and Reghenzani, Federico and Teper, Harun},
  title =	{{A Survey of Real-Time Support, Analysis, and Advancements in ROS 2}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{1:1--1:37},
  ISSN =	{2199-2002},
  year =	{2026},
  volume =	{11},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES.11.1.1},
  URN =		{urn:nbn:de:0030-drops-257914},
  doi =		{10.4230/LITES.11.1.1},
  annote =	{Keywords: ROS 2, middleware, real-time, timing predictability, publish-subscribe}
}

Document

DOI: 10.4230/LIPIcs.ESA.2025.89

A Simple Algorithm for Trimmed Multipoint Evaluation

Authors: Nick Fischer, Melvin Kallmayer, and Leo Wennmann

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract

Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an n-variate polynomial with bounded individual degree d and total degree D, the goal is to evaluate it on a natural class of input points. This problem arises as a key subroutine in recent algorithmic results [Dinur; SODA '21], [Dell, Haak, Kallmayer, Wennmann; SODA '25]. It is known that trimmed multipoint evaluation can be solved in near-linear time [van der Hoeven, Schost; AAECC '13] by a clever yet somewhat involved algorithm. We give a simple recursive algorithm that avoids heavy computer-algebraic machinery, and can be readily understood by researchers without specialized background.

Cite as

Nick Fischer, Melvin Kallmayer, and Leo Wennmann. A Simple Algorithm for Trimmed Multipoint Evaluation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 89:1-89:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fischer_et_al:LIPIcs.ESA.2025.89,
  author =	{Fischer, Nick and Kallmayer, Melvin and Wennmann, Leo},
  title =	{{A Simple Algorithm for Trimmed Multipoint Evaluation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{89:1--89:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.89},
  URN =		{urn:nbn:de:0030-drops-245574},
  doi =		{10.4230/LIPIcs.ESA.2025.89},
  annote =	{Keywords: Algebraic Algorithms, Multipoint Evaluation, Interpolation, LU Decomposition}
}

Document

RANDOM

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.29

A Simplified Reduction for Error Correcting Matrix Multiplication Algorithms

Authors: Igor Shinkar and Harsimran Singh

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract

We study the problem of transforming an algorithm for matrix multiplication, whose output has a small fraction of the entries correct into a matrix multiplication algorithm, whose output is fully correct for all inputs. In this work, we provide a new and simple way to transform an average-case algorithm that takes two matrices A,B ∈ 𝔽_p^{n×n} for a prime p, and outputs a matrix that agrees with the matrix product AB on a 1/p + ε fraction of entries on average for a small ε > 0, into a worst-case algorithm that correctly computes the matrix product for all possible inputs. Our reduction employs list-decodable codes to transform an average-case algorithm into an algorithm with one-sided error, which are known to admit efficient reductions from the work of Gola, Shinkar, and Singh [Gola et al., 2024]. Our reduction is more concise and straightforward compared to the recent work of Hirahara and Shimizu [Hirahara and Shimizu, 2025], and improves the overhead in the running time incurred during the reduction.

Cite as

Igor Shinkar and Harsimran Singh. A Simplified Reduction for Error Correcting Matrix Multiplication Algorithms. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{shinkar_et_al:LIPIcs.APPROX/RANDOM.2025.29,
  author =	{Shinkar, Igor and Singh, Harsimran},
  title =	{{A Simplified Reduction for Error Correcting Matrix Multiplication Algorithms}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.29},
  URN =		{urn:nbn:de:0030-drops-243953},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.29},
  annote =	{Keywords: Matrix Multiplication, Reductions, Worst case to average case reductions}
}

Document

DOI: 10.4230/LIPIcs.ECRTS.2025.3

Enabling Containerisation of Distributed Applications with Real-Time Constraints

Authors: Nasim Samimi, Luca Abeni, Daniel Casini, Mauro Marinoni, Twan Basten, Mitra Nasri, Marc Geilen, and Alessandro Biondi

Published in: LIPIcs, Volume 335, 37th Euromicro Conference on Real-Time Systems (ECRTS 2025)

Abstract

Containerisation is becoming a cornerstone of modern distributed systems, thanks to their lightweight virtualisation, high portability, and seamless integration with orchestration tools such as Kubernetes. The usage of containers has also gained traction in real-time cyber-physical systems, such as software-defined vehicles, which are characterised by strict timing requirements to ensure safety and performance. Nevertheless, ensuring real-time execution of co-located containers is challenging because of mutual interference due to the sharing of the same processing hardware. Existing parallel computing frameworks such as Ray and its Kubernetes-enabled variant, KubeRay, excel in distributed computation but lack support for scheduling policies that allow guaranteeing real-time timing constraints and CPU resource isolation between containers, such as the SCHED_DEADLINE policy of Linux. To fill this gap, this paper extends Ray to support real-time containers that leverage SCHED_DEADLINE. To this end, we propose KubeDeadline, a novel, modular Kubernetes extension to support SCHED_DEADLINE. We evaluate our approach through extensive experiments, using synthetic workloads and a case study based on the MobileNet and EfficientNet deep neural networks. Our evaluation shows that KubeDeadline ensures deadline compliance in all synthetic workloads, adds minimal deployment overhead (in the order of milliseconds), and achieves lower worst-case response times, up to 4 times lower, than vanilla Kubernetes under background interference.

Cite as

Nasim Samimi, Luca Abeni, Daniel Casini, Mauro Marinoni, Twan Basten, Mitra Nasri, Marc Geilen, and Alessandro Biondi. Enabling Containerisation of Distributed Applications with Real-Time Constraints. In 37th Euromicro Conference on Real-Time Systems (ECRTS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 335, pp. 3:1-3:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{samimi_et_al:LIPIcs.ECRTS.2025.3,
  author =	{Samimi, Nasim and Abeni, Luca and Casini, Daniel and Marinoni, Mauro and Basten, Twan and Nasri, Mitra and Geilen, Marc and Biondi, Alessandro},
  title =	{{Enabling Containerisation of Distributed Applications with Real-Time Constraints}},
  booktitle =	{37th Euromicro Conference on Real-Time Systems (ECRTS 2025)},
  pages =	{3:1--3:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-377-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{335},
  editor =	{Mancuso, Renato},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2025.3},
  URN =		{urn:nbn:de:0030-drops-235816},
  doi =		{10.4230/LIPIcs.ECRTS.2025.3},
  annote =	{Keywords: Kubernetes, real-time containers, SCHED\underlineDEADLINE, KubeRay}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2025.131

Deterministic Complexity Analysis of Hermitian Eigenproblems

Authors: Aleksandros Sobczyk

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract

In this work we revisit the arithmetic and bit complexity of Hermitian eigenproblems. Recently, [BGVKS, FOCS 2020] proved that a (non-Hermitian) matrix A can be diagonalized with a randomized algorithm in O(n^{ω}log²(n/ε)) arithmetic operations, where ω≲ 2.371 is the square matrix multiplication exponent, and [Shah, SODA 2025] significantly improved the bit complexity for the Hermitian case. Our main goal is to obtain similar deterministic complexity bounds for various Hermitian eigenproblems. In the Real RAM model, we show that a Hermitian matrix can be diagonalized deterministically in O(n^{ω}log(n)+n²polylog(n/ε)) arithmetic operations, improving the classic deterministic Õ(n³) algorithms, and derandomizing the aforementioned state-of-the-art. The main technical step is a complete, detailed analysis of a well-known divide-and-conquer tridiagonal eigensolver of Gu and Eisenstat [GE95], when accelerated with the Fast Multipole Method, asserting that it can accurately diagonalize a symmetric tridiagonal matrix in nearly-O(n²) operations. In finite precision, we show that an algorithm by Schönhage [Sch72] to reduce a Hermitian matrix to tridiagonal form is stable in the floating point model, using O(log(n/ε)) bits of precision. This leads to a deterministic algorithm to compute all the eigenvalues of a Hermitian matrix in O(n^{ω}ℱ(log(n/ε)) + n²polylog(n/ε)) bit operations, where ℱ(b) ∈ Õ(b) is the bit complexity of a single floating point operation on b bits. This improves the best known Õ(n³) deterministic and O(n^{ω}log²(n/ε)ℱ(log(n/ε))) randomized complexities. We conclude with some other useful subroutines such as computing spectral gaps, condition numbers, and spectral projectors, and with some open problems.

Cite as

Aleksandros Sobczyk. Deterministic Complexity Analysis of Hermitian Eigenproblems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 131:1-131:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sobczyk:LIPIcs.ICALP.2025.131,
  author =	{Sobczyk, Aleksandros},
  title =	{{Deterministic Complexity Analysis of Hermitian Eigenproblems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{131:1--131:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.131},
  URN =		{urn:nbn:de:0030-drops-235081},
  doi =		{10.4230/LIPIcs.ICALP.2025.131},
  annote =	{Keywords: Hermitian eigenproblem, eigenvalues, SVD, tridiagonal reduction, matrix multiplication time, diagonalization, bit complexity}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.18

Finite Matrix Multiplication Algorithms from Infinite Groups

Authors: Jonah Blasiak, Henry Cohn, Joshua A. Grochow, Kevin Pratt, and Chris Umans

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

The Cohn-Umans (FOCS '03) group-theoretic framework for matrix multiplication produces fast matrix multiplication algorithms from three subsets of a finite group G satisfying a simple combinatorial condition (the Triple Product Property). The complexity of such an algorithm then depends on the representation theory of G. In this paper we extend the group-theoretic framework to the setting of infinite groups. In particular, this allows us to obtain constructions in Lie groups, with favorable parameters, that are provably impossible in finite groups of Lie type (Blasiak, Cohn, Grochow, Pratt, and Umans, ITCS '23). Previously the Lie group setting was investigated purely as an analogue of the finite group case; a key contribution in this paper is a fully developed framework for obtaining bona fide matrix multiplication algorithms directly from Lie group constructions. As part of this framework, we introduce "separating functions" as a necessary new design component, and show that when the underlying group is G = GL_n, these functions are polynomials with their degree being the key parameter. In particular, we show that a construction with "half-dimensional" subgroups and optimal degree would imply ω = 2. We then build up machinery that reduces the problem of constructing optimal-degree separating polynomials to the problem of constructing a single polynomial (and a corresponding set of group elements) in a ring of invariant polynomials determined by two out of the three subgroups that satisfy the Triple Product Property. This machinery combines border rank with the Lie algebras associated with the Lie subgroups in a critical way. We give several constructions illustrating the main components of the new framework, culminating in a construction in a special unitary group that achieves separating polynomials of optimal degree, meeting one of the key challenges. The subgroups in this construction have dimension approaching half the ambient dimension, but (just barely) too slowly. We argue that features of the classical Lie groups make it unlikely that constructions in these particular groups could produce nontrivial bounds on ω unless they prove ω = 2. One way to get ω = 2 via our new framework would be to lift our existing construction from the special unitary group to GL_n, and improve the dimension of the subgroups from (dim G)/2 - Θ(n) to (dim G)/2 - o(n).

Cite as

Jonah Blasiak, Henry Cohn, Joshua A. Grochow, Kevin Pratt, and Chris Umans. Finite Matrix Multiplication Algorithms from Infinite Groups. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 18:1-18:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{blasiak_et_al:LIPIcs.ITCS.2025.18,
  author =	{Blasiak, Jonah and Cohn, Henry and Grochow, Joshua A. and Pratt, Kevin and Umans, Chris},
  title =	{{Finite Matrix Multiplication Algorithms from Infinite Groups}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{18:1--18:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.18},
  URN =		{urn:nbn:de:0030-drops-226460},
  doi =		{10.4230/LIPIcs.ITCS.2025.18},
  annote =	{Keywords: Fast matrix multiplication, representation theory, infinite groups}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.64

A Universal Sequence of Tensors for the Asymptotic Rank Conjecture

Authors: Petteri Kaski and Mateusz Michałek

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

The exponent σ(T) of a tensor T ∈ 𝔽^d⊗𝔽^d⊗𝔽^d over a field 𝔽 captures the base of the exponential growth rate of the tensor rank of T under Kronecker powers. Tensor exponents are fundamental from the standpoint of algorithms and computational complexity theory; for example, the exponent ω of square matrix multiplication can be characterized as ω = 2σ(MM₂), where MM₂ ∈ 𝔽⁴⊗𝔽⁴⊗𝔽⁴ is the tensor that represents 2×2 matrix multiplication. Strassen [FOCS 1986] initiated a duality theory for spaces of tensors that enables one to characterize the exponent of a tensor via objects in a dual space, called the asymptotic spectrum of the primal (tensor) space. While Strassen’s theory has considerable generality beyond the setting of tensors - Wigderson and Zuiddam [Asymptotic Spectra: Theory, Applications, and Extensions, preprint, 2023] give a recent exposition - progress in characterizing the dual space in the tensor setting has been slow, with the first universal points in the dual identified by Christandl, Vrana, and Zuiddam [J. Amer. Math. Soc. 36 (2023)]. In parallel to Strassen’s theory, the algebraic geometry community has developed a geometric theory of tensors aimed at characterizing the structure of the primal space and tensor exponents therein; the latter study was motivated in particular by an observation of Strassen (implicit in [J. Reine Angew. Math. 384 (1988)]) that matrix-multiplication tensors have limited universality in the sense that σ(𝔽^d⊗𝔽^d⊗𝔽^d) ≤ 2ω/3 = 4/3σ(MM₂) holds for all d ≥ 1. In particular, this limited universality of the tensor MM₂ puts forth the question whether one could construct explicit universal tensors that exactly characterize the worst-case tensor exponent in the primal space. Such explicit universal objects would, among others, give means towards a proof or a disproof of Strassen’s asymptotic rank conjecture [Progr. Math. 120 (1994)]; the former would immediately imply ω = 2 and, among others, refute the Set Cover Conjecture (cf. Björklund and Kaski [STOC 2024] and Pratt [STOC 2024]). Our main result is an explicit construction of a sequence 𝒰_d of zero-one-valued tensors that is universal for the worst-case tensor exponent; more precisely, we show that σ(𝒰_d) = σ(d) where σ(d) = sup_{T ∈ 𝔽^d⊗𝔽^d⊗𝔽^d}σ(T). We also supply an explicit universal sequence 𝒰_Δ localised to capture the worst-case exponent σ(Δ) of tensors with support contained in Δ ⊆ [d]×[d]×[d]; by combining such sequences, we obtain a universal sequence 𝒯_d such that σ(𝒯_d) = 1 holds if and only if Strassen’s asymptotic rank conjecture holds for d. Finally, we show that the limit lim_{d → ∞}σ(d) exists and can be captured as lim_{d → ∞} σ(D_d) for an explicit sequence (D_d)_{d = 1}^∞ of tensors obtained by diagonalisation of the sequences 𝒰_d. As our second result we relate the absence of polynomials of fixed degree vanishing on tensors of low rank, or more generally asymptotic rank, with upper bounds on the exponent σ(d). Using this technique, one may bound asymptotic rank for all tensors of a given format, knowing enough specific tensors of low asymptotic rank.

Cite as

Petteri Kaski and Mateusz Michałek. A Universal Sequence of Tensors for the Asymptotic Rank Conjecture. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 64:1-64:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kaski_et_al:LIPIcs.ITCS.2025.64,
  author =	{Kaski, Petteri and Micha{\l}ek, Mateusz},
  title =	{{A Universal Sequence of Tensors for the Asymptotic Rank Conjecture}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{64:1--64:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.64},
  URN =		{urn:nbn:de:0030-drops-226925},
  doi =		{10.4230/LIPIcs.ITCS.2025.64},
  annote =	{Keywords: asymptotic rank conjecture, secant variety, Specht module, tensor rank, tensor exponent}
}

Document

DOI: 10.4230/LITES-v005-i001-a001

Risk-Aware Scheduling of Dual Criticality Job Systems Using Demand Distributions

Authors: Bader Naim Alahmad and Sathish Gopalakrishnan

Published in: LITES, Volume 5, Issue 1 (2018). Leibniz Transactions on Embedded Systems, Volume 5, Issue 1

Abstract

We pose the problem of scheduling Mixed Criticality (MC) job systems when there are only two criticality levels, Lo and Hi -referred to as Dual Criticality job systems- on a single processing platform, when job demands are probabilistic and their distributions are known. The current MC models require that the scheduling policy allocate as little execution time as possible to Lo-criticality jobs if the scenario of execution is of Hi criticality, and drop Lo-criticality jobs entirely as soon as the execution scenario's criticality level can be inferred and is Hi. The work incurred by "incorrectly" scheduling Lo-criticality jobs in cases of Hi realized scenarios might affect the feasibility of Hi criticality jobs; we quantify this work and call it Work Threatening Feasibility (WTF). Our objective is to construct online scheduling policies that minimize the expected WTF for the given instance, and under which the instance is feasible in a probabilistic sense that is consistent with the traditional deterministic definition of MC feasibility. We develop a probabilistic framework for MC scheduling, where feasibility is defined in terms of (chance) constraints on the probabilities that Lo and Hi jobs meet their deadlines. The probabilities are computed over the set of sample paths, or trajectories, induced by executing the policy, and those paths are dependent upon the set of execution scenarios and the given demand distributions. Our goal is to exploit the information provided by job distributions to compute the minimum expected WTF below which the given instance is not feasible in probability, and to compute a (randomized) "efficiently implementable" scheduling policy that realizes the latter quantity. We model the problem as a Constrained Markov Decision Process (CMDP) over a suitable state space and a finite planning horizon, and show that an optimal (non-stationary) Markov randomized scheduling policy exists. We derive an optimal policy by solving a Linear Program (LP). We also carry out quantitative evaluations on select probabilistic MC instances to demonstrate that our approach potentially outperforms current MC scheduling policies.

Cite as

Bader Naim Alahmad and Sathish Gopalakrishnan. Risk-Aware Scheduling of Dual Criticality Job Systems Using Demand Distributions. In LITES, Volume 5, Issue 1 (2018). Leibniz Transactions on Embedded Systems, Volume 5, Issue 1, pp. 01:1-01:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Article{alahmad_et_al:LITES-v005-i001-a001,
  author =	{Alahmad, Bader Naim and Gopalakrishnan, Sathish},
  title =	{{Risk-Aware Scheduling of Dual Criticality Job Systems Using Demand Distributions}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{01:1--01:30},
  ISSN =	{2199-2002},
  year =	{2018},
  volume =	{5},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES-v005-i001-a001},
  URN =		{urn:nbn:de:0030-drops-192720},
  doi =		{10.4230/LITES-v005-i001-a001},
  annote =	{Keywords: Mixed criticalities, Probability distribution, Real time systems, Scheduling, Chance constrained Markov decision process, Linear programming, Randomized policy}
}

Document

DOI: 10.4230/LITES-v004-i002-a003

Per Processor Spin-Based Protocols for Multiprocessor Real-Time Systems

Authors: Sara Afshar, Moris Behnam, Reinder J. Bril, and Thomas Nolte

Published in: LITES, Volume 4, Issue 2 (2017). Leibniz Transactions on Embedded Systems, Volume 4, Issue 2

Abstract

This paper investigates preemptive spin-based global resource sharing protocols for resource-constrained real-time embedded multi-core systems based on partitioned fixed-priority preemptive scheduling. We present preemptive spin-based protocols that feature (i) an increased schedulability ratio of task sets and reduced response jitter of tasks compared to the classical non-preemptive spin-based protocol, (ii) similar memory requirements for the administration of waiting tasks as for the non-preemptive protocol whilst only causing (iii) a minimal increase of the minimal number of required stacks per core from one to at most two, and (iv) strong progress guarantees to tasks. We complement these protocols with a unified worst-case response time analysis that specializes to the classical analysis for the non-preemptive protocol. The paper includes a comparative evaluation of the preemptive protocols and the non-preemptive protocol based on synthetic data.

Cite as

Sara Afshar, Moris Behnam, Reinder J. Bril, and Thomas Nolte. Per Processor Spin-Based Protocols for Multiprocessor Real-Time Systems. In LITES, Volume 4, Issue 2 (2017). Leibniz Transactions on Embedded Systems, Volume 4, Issue 2, pp. 03:1-03:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Article{afshar_et_al:LITES-v004-i002-a003,
  author =	{Afshar, Sara and Behnam, Moris and Bril, Reinder J. and Nolte, Thomas},
  title =	{{Per Processor Spin-Based Protocols for Multiprocessor Real-Time Systems}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{03:1--03:30},
  ISSN =	{2199-2002},
  year =	{2018},
  volume =	{4},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES-v004-i002-a003},
  URN =		{urn:nbn:de:0030-drops-192708},
  doi =		{10.4230/LITES-v004-i002-a003},
  annote =	{Keywords: Resource sharing, Real-time systems, Multiprocessors, Spin-locks}
}

Document

DOI: 10.4230/DagSemProc.07461.1

07461 Abstracts Collection – Numerical Methods for Structured Markov Chains

Authors: Dario A. Bini, Beatrice Meini, Vaidyanathan Ramaswami, Marie-Ange Remiche, and Peter Taylor

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract

From 11.11. to 14.11.07, the Dagstuhl Seminar 07461 ``Numerical Methods for Structured Markov Chains'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

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Dario A. Bini, Beatrice Meini, Vaidyanathan Ramaswami, Marie-Ange Remiche, and Peter Taylor. 07461 Abstracts Collection – Numerical Methods for Structured Markov Chains. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bini_et_al:DagSemProc.07461.1,
  author =	{Bini, Dario A. and Meini, Beatrice and Ramaswami, Vaidyanathan and Remiche, Marie-Ange and Taylor, Peter},
  title =	{{07461 Abstracts Collection – Numerical Methods for Structured Markov Chains}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.1},
  URN =		{urn:nbn:de:0030-drops-14046},
  doi =		{10.4230/DagSemProc.07461.1},
  annote =	{Keywords: Matrix analytic methods, markov processes, queuing theory, numerical methods, structured matrices, telecommunication modeling, performance evaluation}
}

Document

DOI: 10.4230/DagSemProc.07461.2

07461 Executive Summary – Numerical Methods for Structured Markov Chains

Authors: Dario A. Bini, Beatrice Meini, Vaidyanathan Ramaswami, Marie-Ange Remiche, and Peter Taylor

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract

This Dagstuhl seminar has brought together leaders and young researchers in the fields of analysis of numerical algorithms, applied stochastic modeling and statistical inference, with the result of stimulating exchange of methodologies and experiences and generating synergetic collaborations. This has favored a better communication between these worlds where problems from the applications feed the theoretical research and where advanced numerical tools can be utilized in applications with reciprocal advantages.

Cite as

Dario A. Bini, Beatrice Meini, Vaidyanathan Ramaswami, Marie-Ange Remiche, and Peter Taylor. 07461 Executive Summary – Numerical Methods for Structured Markov Chains. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bini_et_al:DagSemProc.07461.2,
  author =	{Bini, Dario A. and Meini, Beatrice and Ramaswami, Vaidyanathan and Remiche, Marie-Ange and Taylor, Peter},
  title =	{{07461 Executive Summary – Numerical Methods for Structured Markov Chains}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.2},
  URN =		{urn:nbn:de:0030-drops-14006},
  doi =		{10.4230/DagSemProc.07461.2},
  annote =	{Keywords: Matrix analytic methods, Markov processes, queuing theory, numerical methods, structured matrices, telecommunication modeling, performance evaluation.}
}

@InProceedings{bini_et_al:DagSemProc.07461.2,
  author =	{Bini, Dario A. and Meini, Beatrice and Ramaswami, Vaidyanathan and Remiche, Marie-Ange and Taylor, Peter},
  title =	{{07461 Executive Summary – Numerical Methods for Structured Markov Chains}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.2},
  URN =		{urn:nbn:de:0030-drops-14006},
  doi =		{10.4230/DagSemProc.07461.2},
  annote =	{Keywords: Matrix analytic methods, Markov processes, queuing theory, numerical methods, structured matrices, telecommunication modeling, performance evaluation.}
}

Document

DOI: 10.4230/DagSemProc.07461.3

A policy iteration algorithm for Markov decision processes skip-free in one direction

Authors: Joke Lambert, Benny van Houdt, and Chris Blondia

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract

In this paper we present a new algorithm for policy iteration for Markov decision processes (MDP) skip-free in one direction. This algorithm, which is based on matrix analytic methods, is in the same spirit as the algorithm of White (Stochastic Models, 21:785-797, 2005) which was limited to matrices that are skip-free in both directions. Optimization problems that can be solved using Markov decision processes arise in the domain of optical buffers, when trying to improve loss rates of fibre delay line (FDL) buffers. Based on the analysis of such an FDL buffer we present a comparative study between the different techniques available to solve an MDP. The results illustrate that the exploitation of the structure of the transition matrices places us in a position to deal with larger systems, while reducing the computation times.

Cite as

Joke Lambert, Benny van Houdt, and Chris Blondia. A policy iteration algorithm for Markov decision processes skip-free in one direction. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{lambert_et_al:DagSemProc.07461.3,
  author =	{Lambert, Joke and van Houdt, Benny and Blondia, Chris},
  title =	{{A policy iteration algorithm for Markov decision processes skip-free in one direction}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.3},
  URN =		{urn:nbn:de:0030-drops-14032},
  doi =		{10.4230/DagSemProc.07461.3},
  annote =	{Keywords: Markov Decision Process, Policy Evaluation, Skip-Free, Optical buffers, Fibre Delay Lines}
}

Document

DOI: 10.4230/DagSemProc.07461.4

Characterizing Coxian Distributions of Algebraic Degree q and Triangular Order p

Authors: Mark Fackrell

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract

In this research note we present a procedure to characterize the set of all Coxian distributions of algebraic degree q that have Coxian representations of order p where p > q.

Cite as

Mark Fackrell. Characterizing Coxian Distributions of Algebraic Degree q and Triangular Order p. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{fackrell:DagSemProc.07461.4,
  author =	{Fackrell, Mark},
  title =	{{Characterizing Coxian Distributions of Algebraic Degree q and Triangular Order p}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--10},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.4},
  URN =		{urn:nbn:de:0030-drops-13916},
  doi =		{10.4230/DagSemProc.07461.4},
  annote =	{Keywords: Phase-type distribution, Coxian distribution, algebraic degree, triangular order, rational Laplace-Stieltjes transform}
}

Document

DOI: 10.4230/DagSemProc.07461.5

Current results and open questions on PH and MAP characterization

Authors: Levente Bodrog, Armin Heindl, Gábor Horváth, Miklós Telek, and András Horváth

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract

Stochastic processes with matrix exponential kernels have a wide range of applications due to the availability of efficient matrix analytic methods. The characterization of these processes is in progress in recent years. Basic questions like the flexibility, the degree of freedom, the most efficient (canonical) representation of these models are under study. The presentation collects a set of available results and related open questions.

Cite as

Levente Bodrog, Armin Heindl, Gábor Horváth, Miklós Telek, and András Horváth. Current results and open questions on PH and MAP characterization. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bodrog_et_al:DagSemProc.07461.5,
  author =	{Bodrog, Levente and Heindl, Armin and Horv\'{a}th, G\'{a}bor and Telek, Mikl\'{o}s and Horv\'{a}th, Andr\'{a}s},
  title =	{{Current results and open questions on PH and MAP characterization}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--6},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.5},
  URN =		{urn:nbn:de:0030-drops-14010},
  doi =		{10.4230/DagSemProc.07461.5},
  annote =	{Keywords: PH distribution, ME distribution, MAP, MEP}
}

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