10 Search Results for "Moses, Yoram"


Document
Epistemic and Topological Reasoning in Distributed Systems (Dagstuhl Seminar 23272)

Authors: Armando Castañeda, Hans van Ditmarsch, Roman Kuznets, Yoram Moses, and Ulrich Schmid

Published in: Dagstuhl Reports, Volume 13, Issue 7 (2024)


Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23272 "Epistemic and Topological Reasoning in Distributed Systems." The seminar brought together experts in combinatorial topology and epistemic logic interested in distributed systems, with the aim of exploring the directions that the recent interaction between those approaches can take, identifying challenges and opportunities.

Cite as

Armando Castañeda, Hans van Ditmarsch, Roman Kuznets, Yoram Moses, and Ulrich Schmid. Epistemic and Topological Reasoning in Distributed Systems (Dagstuhl Seminar 23272). In Dagstuhl Reports, Volume 13, Issue 7, pp. 34-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@Article{castaneda_et_al:DagRep.13.7.34,
  author =	{Casta\~{n}eda, Armando and van Ditmarsch, Hans and Kuznets, Roman and Moses, Yoram and Schmid, Ulrich},
  title =	{{Epistemic and Topological Reasoning in Distributed Systems (Dagstuhl Seminar 23272)}},
  pages =	{34--65},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{7},
  editor =	{Casta\~{n}eda, Armando and van Ditmarsch, Hans and Kuznets, Roman and Moses, Yoram and Schmid, Ulrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.7.34},
  URN =		{urn:nbn:de:0030-drops-197742},
  doi =		{10.4230/DagRep.13.7.34},
  annote =	{Keywords: combinatorial topology, distributed systems, epistemic logic, multi-agent systems, interpreted systems, dynamic epistemic logic, simplicial semantics, knowledge-based approach, distributed computing}
}
Document
Probable Approximate Coordination

Authors: Ariel Livshits and Yoram Moses

Published in: LIPIcs, Volume 286, 27th International Conference on Principles of Distributed Systems (OPODIS 2023)


Abstract
We study the problem of how to coordinate the actions of independent agents in a distributed system where message arrival times are unbounded, but are determined by an exponential probability distribution. Asynchronous protocols executed in such a model are guaranteed to succeed with probability 1. We demonstrate a case in which the best asynchronous protocol can be improved on significantly. Specifically, we focus on the task of performing actions by different agents in a linear temporal order - a problem known in the literature as Ordered Response. In asynchronous systems, ensuring such an ordering requires the construction of a message chain that passes through each acting agent, in order. Solving Ordered Response in this way in our model will terminate in time that grows linearly in the number of participating agents n, in expectation. We show that relaxing the specification slightly allows for a significant saving in time. Namely, if Ordered Response should be guaranteed with high probability (arbitrarily close to 1), it is possible to significantly shorten the expected execution time of the protocol. We present two protocols that adhere to the relaxed specification. One of our protocols executes exponentially faster than a message chain, when the number of participating agents n is large, while the other is roughly quadratically faster. For small values of n, it is also possible to achieve similar results by using a hybrid protocol.

Cite as

Ariel Livshits and Yoram Moses. Probable Approximate Coordination. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{livshits_et_al:LIPIcs.OPODIS.2023.19,
  author =	{Livshits, Ariel and Moses, Yoram},
  title =	{{Probable Approximate Coordination}},
  booktitle =	{27th International Conference on Principles of Distributed Systems (OPODIS 2023)},
  pages =	{19:1--19:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-308-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{286},
  editor =	{Bessani, Alysson and D\'{e}fago, Xavier and Nakamura, Junya and Wada, Koichi and Yamauchi, Yukiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2023.19},
  URN =		{urn:nbn:de:0030-drops-195090},
  doi =		{10.4230/LIPIcs.OPODIS.2023.19},
  annote =	{Keywords: Distributed coordination, ordered response, exponentially distributed delay}
}
Document
Null Messages, Information and Coordination

Authors: Raïssa Nataf, Guy Goren, and Yoram Moses

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)


Abstract
This paper investigates the role that null messages play in synchronous systems with and without failures, and provides necessary and sufficient conditions on the structure of protocols for information transfer and coordination there. We start by introducing a new and more refined definition of null messages. A generalization of message chains that allow these null messages is provided, and is shown to be necessary and sufficient for information transfer in reliable systems. Coping with crash failures requires a much richer structure, since not receiving a message may be the result of the sender’s failure. We introduce a class of communication patterns called resilient message blocks, which impose a stricter condition on protocols than the silent choirs of Goren and Moses (2020). Such blocks are shown to be necessary for information transfer in crash-prone systems. Moreover, they are sufficient in several cases of interest, in which silent choirs are not. Finally, a particular combination of resilient message blocks is shown to be necessary and sufficient for solving the Ordered Response coordination problem.

Cite as

Raïssa Nataf, Guy Goren, and Yoram Moses. Null Messages, Information and Coordination. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 30:1-30:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{nataf_et_al:LIPIcs.DISC.2023.30,
  author =	{Nataf, Ra\"{i}ssa and Goren, Guy and Moses, Yoram},
  title =	{{Null Messages, Information and Coordination}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{30:1--30:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.30},
  URN =		{urn:nbn:de:0030-drops-191564},
  doi =		{10.4230/LIPIcs.DISC.2023.30},
  annote =	{Keywords: null messages, fault tolerance, coordination, information flow, knowledge analysis}
}
Document
Brief Announcement
Brief Announcement: Null Messages, Information and Coordination

Authors: Raïssa Nataf, Guy Goren, and Yoram Moses

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)


Abstract
This paper investigates how null messages can transfer information in fault-prone synchronous systems. The notion of an f-resilient message block is defined and is shown to capture the fundamental communication pattern for knowledge transfer. In general, this pattern combines both null messages and explicit messages. It thus provides a fault-tolerant extension of the classic notion of a message-chain. Based on the above, we provide tight necessary and sufficient characterizations of the generalized communication patterns that can serve to solve the distributed tasks of (nice-run) Signalling and Ordered Response.

Cite as

Raïssa Nataf, Guy Goren, and Yoram Moses. Brief Announcement: Null Messages, Information and Coordination. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 49:1-49:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{nataf_et_al:LIPIcs.DISC.2022.49,
  author =	{Nataf, Ra\"{i}ssa and Goren, Guy and Moses, Yoram},
  title =	{{Brief Announcement: Null Messages, Information and Coordination}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{49:1--49:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.49},
  URN =		{urn:nbn:de:0030-drops-172409},
  doi =		{10.4230/LIPIcs.DISC.2022.49},
  annote =	{Keywords: null messages, fault tolerance, coordination, information flow}
}
Document
Brief Announcement
Brief Announcement: Probabilistic Indistinguishability and The Quality of Validity in Byzantine Agreement

Authors: Guy Goren, Yoram Moses, and Alexander Spiegelman

Published in: LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)


Abstract
Lower bounds and impossibility results in distributed computing are both intellectually challenging and practically important. Hundreds if not thousands of proofs appear in the literature, but surprisingly, the vast majority of them apply to deterministic algorithms only. Probabilistic protocols have been around for at least four decades and are receiving a lot of attention with the emergence of blockchain systems. Nonetheless, we are aware of only a handful of randomized lower bounds. In this work we provide a formal framework for reasoning about randomized distributed algorithms. We generalize the notion of indistinguishability, the most useful tool in deterministic lower bounds, to apply to a probabilistic setting. We apply this framework to prove a result of independent interest. Namely, we completely characterize the quality of decisions that protocols for a randomized multi-valued Consensus problem can guarantee in an asynchronous environment with Byzantine faults. We use the new notion to prove a lower bound on the guaranteed probability that honest parties will not decide on a possibly bogus value proposed by a malicious party. Finally, we show that the bound is tight by providing a protocol that matches it. This brief announcement consists of an introduction to the full paper [Guy Goren et al., 2020] by the same title. The interested reader is advised to consult the full paper for a detailed exposition.

Cite as

Guy Goren, Yoram Moses, and Alexander Spiegelman. Brief Announcement: Probabilistic Indistinguishability and The Quality of Validity in Byzantine Agreement. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 57:1-57:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{goren_et_al:LIPIcs.DISC.2021.57,
  author =	{Goren, Guy and Moses, Yoram and Spiegelman, Alexander},
  title =	{{Brief Announcement: Probabilistic Indistinguishability and The Quality of Validity in Byzantine Agreement}},
  booktitle =	{35th International Symposium on Distributed Computing (DISC 2021)},
  pages =	{57:1--57:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-210-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{209},
  editor =	{Gilbert, Seth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.57},
  URN =		{urn:nbn:de:0030-drops-148596},
  doi =		{10.4230/LIPIcs.DISC.2021.57},
  annote =	{Keywords: Indistinguishability, probabilistic lower bounds, Byzantine agreement}
}
Document
Brief Announcement
Brief Announcement: Simple Majority Consensus in Networks with Unreliable Communication

Authors: Ariel Livshits, Yonatan Shadmi, and Ran Tamir (Averbuch)

Published in: LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)


Abstract
In this work, we consider a synchronous model of n faultless agents, with a complete communication graph and messages that are lost with some constant probability q ∈ (0,1). In this model we show that there exists a protocol, called the Simple Majority Protocol, that solves consensus in 3 communication rounds with probability of agreement converging to 1 as n → ∞. We also prove that 3 communication rounds are necessary for the SMP to achieve consensus, with high probability.

Cite as

Ariel Livshits, Yonatan Shadmi, and Ran Tamir (Averbuch). Brief Announcement: Simple Majority Consensus in Networks with Unreliable Communication. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 59:1-59:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{livshits_et_al:LIPIcs.DISC.2021.59,
  author =	{Livshits, Ariel and Shadmi, Yonatan and Tamir (Averbuch), Ran},
  title =	{{Brief Announcement: Simple Majority Consensus in Networks with Unreliable Communication}},
  booktitle =	{35th International Symposium on Distributed Computing (DISC 2021)},
  pages =	{59:1--59:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-210-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{209},
  editor =	{Gilbert, Seth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.59},
  URN =		{urn:nbn:de:0030-drops-148617},
  doi =		{10.4230/LIPIcs.DISC.2021.59},
  annote =	{Keywords: Majority consensus, probabilistic message loss, distributed systems}
}
Document
Distributed Dispatching in the Parallel Server Model

Authors: Guy Goren, Shay Vargaftik, and Yoram Moses

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)


Abstract
With the rapid increase in the size and volume of cloud services and data centers, architectures with multiple job dispatchers are quickly becoming the norm. Load balancing is a key element of such systems. Nevertheless, current solutions to load balancing in such systems admit a paradoxical behavior in which more accurate information regarding server queue lengths degrades performance due to herding and detrimental incast effects. Indeed, both in theory and in practice, there is a common doubt regarding the value of information in the context of multi-dispatcher load balancing. As a result, both researchers and system designers resort to more straightforward solutions, such as the power-of-two-choices to avoid worst-case scenarios, potentially sacrificing overall resource utilization and system performance. A principal focus of our investigation concerns the value of information about queue lengths in the multi-dispatcher setting. We argue that, at its core, load balancing with multiple dispatchers is a distributed computing task. In that light, we propose a new job dispatching approach, called Tidal Water Filling, which addresses the distributed nature of the system. Specifically, by incorporating the existence of other dispatchers into the decision-making process, our protocols outperform previous solutions in many scenarios. In particular, when the dispatchers have complete and accurate information regarding the server queue lengths, our policies significantly outperform all existing solutions.

Cite as

Guy Goren, Shay Vargaftik, and Yoram Moses. Distributed Dispatching in the Parallel Server Model. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{goren_et_al:LIPIcs.DISC.2020.14,
  author =	{Goren, Guy and Vargaftik, Shay and Moses, Yoram},
  title =	{{Distributed Dispatching in the Parallel Server Model}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.14},
  URN =		{urn:nbn:de:0030-drops-130929},
  doi =		{10.4230/LIPIcs.DISC.2020.14},
  annote =	{Keywords: Distributed load balancing, Join the Shortest Queue, Tidal Water Filling,  Parallel Server Model}
}
Document
A Characterization of Consensus Solvability for Closed Message Adversaries

Authors: Kyrill Winkler, Ulrich Schmid, and Yoram Moses

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)


Abstract
Distributed computations in a synchronous system prone to message loss can be modeled as a game between a (deterministic) distributed algorithm versus an omniscient message adversary. The latter determines, for each round, the directed communication graph that specifies which messages can reach their destination. Message adversary definitions range from oblivious ones, which pick the communication graphs arbitrarily from a given set of candidate graphs, to general message adversaries, which are specified by the set of sequences of communication graphs (called admissible communication patterns) that they may generate. This paper provides a complete characterization of consensus solvability for closed message adversaries, where every inadmissible communication pattern has a finite prefix that makes all (infinite) extensions of this prefix inadmissible. Whereas every oblivious message adversary is closed, there are also closed message adversaries that are not oblivious. We provide a tight non-topological, purely combinatorial characterization theorem, which reduces consensus solvability to a simple condition on prefixes of the communication patterns. Our result not only non-trivially generalizes the known combinatorial characterization of the consensus solvability for oblivious message adversaries by Coulouma, Godard, and Peters (Theor. Comput. Sci., 2015), but also provides the first combinatorial characterization for this important class of message adversaries that is formulated directly on the prefixes of the communication patterns.

Cite as

Kyrill Winkler, Ulrich Schmid, and Yoram Moses. A Characterization of Consensus Solvability for Closed Message Adversaries. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{winkler_et_al:LIPIcs.OPODIS.2019.17,
  author =	{Winkler, Kyrill and Schmid, Ulrich and Moses, Yoram},
  title =	{{A Characterization of Consensus Solvability for Closed Message Adversaries}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.17},
  URN =		{urn:nbn:de:0030-drops-118038},
  doi =		{10.4230/LIPIcs.OPODIS.2019.17},
  annote =	{Keywords: Dynamic networks, Consensus, Message Adversary}
}
Document
The Computational Cost of Asynchronous Neural Communication

Authors: Yael Hitron, Merav Parter, and Gur Perri

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)


Abstract
Biological neural computation is inherently asynchronous due to large variations in neuronal spike timing and transmission delays. So-far, most theoretical work on neural networks assumes the synchronous setting where neurons fire simultaneously in discrete rounds. In this work we aim at understanding the barriers of asynchronous neural computation from an algorithmic perspective. We consider an extension of the widely studied model of synchronized spiking neurons [Maass, Neural Networks 97] to the asynchronous setting by taking into account edge and node delays. - Edge Delays: We define an asynchronous model for spiking neurons in which the latency values (i.e., transmission delays) of non self-loop edges vary adversarially over time. This extends the recent work of [Hitron and Parter, ESA'19] in which the latency values are restricted to be fixed over time. Our first contribution is an impossibility result that implies that the assumption that self-loop edges have no delays (as assumed in Hitron and Parter) is indeed necessary. Interestingly, in real biological networks self-loop edges (a.k.a. autapse) are indeed free of delays, and the latter has been noted by neuroscientists to be crucial for network synchronization. To capture the computational challenges in this setting, we first consider the implementation of a single NOT gate. This simple function already captures the fundamental difficulties in the asynchronous setting. Our key technical results are space and time upper and lower bounds for the NOT function, our time bounds are tight. In the spirit of the distributed synchronizers [Awerbuch and Peleg, FOCS'90] and following [Hitron and Parter, ESA'19], we then provide a general synchronizer machinery. Our construction is very modular and it is based on efficient circuit implementation of threshold gates. The complexity of our scheme is measured by the overhead in the number of neurons and the computation time, both are shown to be polynomial in the largest latency value, and the largest incoming degree Δ of the original network. - Node Delays: We introduce the study of asynchronous communication due to variations in the response rates of the neurons in the network. In real brain networks, the round duration varies between different neurons in the network. Our key result is a simulation methodology that allows one to transform the above mentioned synchronized solution under edge delays into a synchronized under node delays while incurring a small overhead w.r.t space and time.

Cite as

Yael Hitron, Merav Parter, and Gur Perri. The Computational Cost of Asynchronous Neural Communication. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 48:1-48:47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{hitron_et_al:LIPIcs.ITCS.2020.48,
  author =	{Hitron, Yael and Parter, Merav and Perri, Gur},
  title =	{{The Computational Cost of Asynchronous Neural Communication}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{48:1--48:47},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.48},
  URN =		{urn:nbn:de:0030-drops-117330},
  doi =		{10.4230/LIPIcs.ITCS.2020.48},
  annote =	{Keywords: asynchronous communication, asynchronous computation, spiking neurons, synchronizers}
}
Document
Instance Complexity and Unlabeled Certificates in the Decision Tree Model

Authors: Tomer Grossman, Ilan Komargodski, and Moni Naor

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)


Abstract
Instance complexity is a measure of goodness of an algorithm in which the performance of one algorithm is compared to others per input. This is in sharp contrast to worst-case and average-case complexity measures, where the performance is compared either on the worst input or on an average one, respectively. We initiate the systematic study of instance complexity and optimality in the query model (a.k.a. the decision tree model). In this model, instance optimality of an algorithm for computing a function is the requirement that the complexity of an algorithm on any input is at most a constant factor larger than the complexity of the best correct algorithm. That is we compare the decision tree to one that receives a certificate and its complexity is measured only if the certificate is correct (but correctness should hold on any input). We study both deterministic and randomized decision trees and provide various characterizations and barriers for more general results. We introduce a new measure of complexity called unlabeled-certificate complexity, appropriate for graph properties and other functions with symmetries, where only information about the structure of the graph is known to the competing algorithm. More precisely, the certificate is some permutation of the input (rather than the input itself) and the correctness should be maintained even if the certificate is wrong. First we show that such an unlabeled certificate is sometimes very helpful in the worst-case. We then study instance optimality with respect to this measure of complexity, where an algorithm is said to be instance optimal if for every input it performs roughly as well as the best algorithm that is given an unlabeled certificate (but is correct on every input). We show that instance optimality depends on the group of permutations in consideration. Our proofs rely on techniques from hypothesis testing and analysis of random graphs.

Cite as

Tomer Grossman, Ilan Komargodski, and Moni Naor. Instance Complexity and Unlabeled Certificates in the Decision Tree Model. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 56:1-56:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{grossman_et_al:LIPIcs.ITCS.2020.56,
  author =	{Grossman, Tomer and Komargodski, Ilan and Naor, Moni},
  title =	{{Instance Complexity and Unlabeled Certificates in the Decision Tree Model}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{56:1--56:38},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.56},
  URN =		{urn:nbn:de:0030-drops-117418},
  doi =		{10.4230/LIPIcs.ITCS.2020.56},
  annote =	{Keywords: decision tree complexity, instance complexity, instance optimality, query complexity, unlabeled certificates}
}
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