Document

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

For k ≥ 0, k-partial (k+1)-coloring asks to color the nodes of an n-node graph using a palette of k+1 colors such that every node v has at least min{k,deg(v)} neighbors colored with colors different from its own color. Hence, proper (Δ+1)-coloring is the special case of k-partial (k+1)-coloring when k = Δ. Ghaffari and Kuhn [FOCS 2021] recently proved that there exists a deterministic distributed algorithm that solves proper (Δ+1)-coloring of n-node graphs with maximum degree Δ in O(log n ⋅ log²Δ) rounds under the LOCAL model of distributed computing. This breakthrough result is achieved via an original iterated rounding approach. Using the same technique, Ghaffari and Kuhn also showed that there exists a deterministic algorithm that solves proper O(a)-coloring of n-node graphs with arboricity a in O(log n ⋅ log³a) rounds. It directly follows from this latter result that k-partial O(k)-coloring can be solved deterministically in O(log n ⋅ log³k) rounds.
We develop an extension of the Ghaffari and Kuhn algorithm for proper (Δ+1)-coloring, and show that it solves k-partial (k+1)-coloring, thus generalizing their main result. Our algorithm runs in O(log n ⋅ log³k) rounds, like the algorithm that follows from Ghaffari and Kuhn’s algorithm for graphs with bounded arboricity, but uses only k+1 color, i.e., the smallest number c of colors such that every graph has a k-partial c-coloring. Like all the previously mentioned algorithms, our algorithm actually solves the general list-coloring version of the problem. Specifically, every node v receives as input an integer demand d(v) ≤ deg(v), and a list of at least d(v)+1 colors. Every node must then output a color from its list such that the resulting coloring satisfies that every node v has at least d(v) neighbors with colors different from its own. Our algorithm solves this problem in O(log n ⋅ log³k) rounds where k = max_v d(v). Moreover, in the specific case where all lists of colors given to the nodes as input share a common colors c^* known to all nodes, one can save one log k factor. In particular, for standard k-partial (k+1)-coloring, which corresponds to the case where all nodes are given the same list {1,… ,k+1}, one can modify our algorithm so that it runs in O(log n ⋅ log²k) rounds, and thus matches the complexity of Ghaffari and Kuhn’s algorithm for (Δ+1)-coloring for k = Δ.

Avinandan Das, Pierre Fraigniaud, and Adi Rosén. Distributed Partial Coloring via Gradual Rounding. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 30:1-30:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{das_et_al:LIPIcs.OPODIS.2023.30, author = {Das, Avinandan and Fraigniaud, Pierre and Ros\'{e}n, Adi}, title = {{Distributed Partial Coloring via Gradual Rounding}}, booktitle = {27th International Conference on Principles of Distributed Systems (OPODIS 2023)}, pages = {30:1--30:22}, 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.2023.30}, URN = {urn:nbn:de:0030-drops-195205}, doi = {10.4230/LIPIcs.OPODIS.2023.30}, annote = {Keywords: Distributed graph coloring, partial coloring, weak coloring} }

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

The paper compares two generic techniques for deriving lower bounds and impossibility results in distributed computing. First, we prove a speedup theorem (a-la Brandt, 2019), for wait-free colorless algorithms, aiming at capturing the essence of the seminal round-reduction proof establishing a lower bound on the number of rounds for 3-coloring a cycle (Linial, 1992), and going by backward induction. Second, we consider FLP-style proofs, aiming at capturing the essence of the seminal consensus impossibility proof (Fischer, Lynch, and Paterson, 1985) and using forward induction.
We show that despite their very different natures, these two forms of proof are tightly connected. In particular, we show that for every colorless task Π, if there is a round-reduction proof establishing the impossibility of solving Π using wait-free colorless algorithms, then there is an FLP-style proof establishing the same impossibility. For 1-dimensional colorless tasks (for an arbitrarily number n ≥ 2 of processes), we prove that the two proof techniques have exactly the same power, and more importantly, both are complete: if a 1-dimensional colorless task is not wait-free solvable by n ≥ 2 processes, then the impossibility can be proved by both proof techniques. Moreover, a round-reduction proof can be automatically derived, and an FLP-style proof can be automatically generated from it.
Finally, we illustrate the use of these two techniques by establishing the impossibility of solving any colorless covering task of arbitrary dimension by wait-free algorithms.

Hagit Attiya, Pierre Fraigniaud, Ami Paz, and Sergio Rajsbaum. One Step Forward, One Step Back: FLP-Style Proofs and the Round-Reduction Technique for Colorless Tasks. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{attiya_et_al:LIPIcs.DISC.2023.4, author = {Attiya, Hagit and Fraigniaud, Pierre and Paz, Ami and Rajsbaum, Sergio}, title = {{One Step Forward, One Step Back: FLP-Style Proofs and the Round-Reduction Technique for Colorless Tasks}}, booktitle = {37th International Symposium on Distributed Computing (DISC 2023)}, pages = {4:1--4:23}, 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.2023.4}, URN = {urn:nbn:de:0030-drops-191304}, doi = {10.4230/LIPIcs.DISC.2023.4}, annote = {Keywords: Wait-free computing, lower bounds} }

Document

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

A proof-labeling scheme (PLS) for a boolean predicate Π on labeled graphs is a mechanism used for certifying the legality with respect to Π of global network states in a distributed manner. In a PLS, a certificate is assigned to each processing node of the network, and the nodes are in charge of checking that the collection of certificates forms a global proof that the system is in a correct state, by exchanging the certificates once, between neighbors only. The main measure of complexity is the size of the certificates. Many PLSs have been designed for certifying specific predicates, including cycle-freeness, minimum-weight spanning tree, planarity, etc.
In 2021, a breakthrough has been obtained, as a "meta-theorem" stating that a large set of properties have compact PLSs in a large class of networks. Namely, for every MSO₂ property Π on labeled graphs, there exists a PLS for Π with O(log n)-bit certificates for all graphs of bounded tree-depth. This result has been extended to the larger class of graphs with bounded tree-width, using certificates on O(log² n) bits.
We extend this result even further, to the larger class of graphs with bounded clique-width, which, as opposed to the other two aforementioned classes, includes dense graphs. We show that, for every MSO₁ property Π on labeled graphs, there exists a PLS for Π with O(log² n)-bit certificates for all graphs of bounded clique-width. As a consequence, certifying families of graphs such as distance-hereditary graphs and (induced) P₄-free graphs (a.k.a., cographs) can be done using a PLS with O(log² n)-bit certificates, merely because each of these two classes can be specified in MSO₁. In fact, we show that certifying P₄-free graphs can be done with certificates on O(log n) bits only. This is in contrast to the class of C₄-free graphs (which does not have bounded clique-width) which requires Ω̃(√n)-bit certificates.

Pierre Fraigniaud, Frédéric Mazoit, Pedro Montealegre, Ivan Rapaport, and Ioan Todinca. Distributed Certification for Classes of Dense Graphs. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2023.20, author = {Fraigniaud, Pierre and Mazoit, Fr\'{e}d\'{e}ric and Montealegre, Pedro and Rapaport, Ivan and Todinca, Ioan}, title = {{Distributed Certification for Classes of Dense Graphs}}, booktitle = {37th International Symposium on Distributed Computing (DISC 2023)}, pages = {20:1--20:17}, 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.2023.20}, URN = {urn:nbn:de:0030-drops-191467}, doi = {10.4230/LIPIcs.DISC.2023.20}, annote = {Keywords: CONGEST, Proof Labelling Schemes, clique-width, MSO} }

Document

**Published in:** LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

During the last two decades, a small set of distributed computing models for networks have emerged, among which LOCAL, CONGEST, and Broadcast Congested Clique (BCC) play a prominent role. We consider hybrid models resulting from combining these three models. That is, we analyze the computing power of models allowing to, say, perform a constant number of rounds of CONGEST, then a constant number of rounds of LOCAL, then a constant number of rounds of BCC, possibly repeating this figure a constant number of times. We specifically focus on 2-round models, and we establish the complete picture of the relative powers of these models. That is, for every pair of such models, we determine whether one is (strictly) stronger than the other, or whether the two models are incomparable. The separation results are obtained by approaching communication complexity through an original angle, which may be of an independent interest. The two players are not bounded to compute the value of a binary function, but the combined outputs of the two players are constrained by this value. In particular, we introduce the XOR-Index problem, in which Alice is given a binary vector x ∈ {0,1}ⁿ together with an index i ∈ [n], Bob is given a binary vector y ∈ {0,1}ⁿ together with an index j ∈ [n], and, after a single round of 2-way communication, Alice must output a boolean out_A, and Bob must output a boolean out_B, such that out_A ∧ out_B = x_j⊕ y_i. We show that the communication complexity of XOR-Index is Ω(n) bits.

Pierre Fraigniaud, Pedro Montealegre, Pablo Paredes, Ivan Rapaport, Martín Ríos-Wilson, and Ioan Todinca. Computing Power of Hybrid Models in Synchronous Networks. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fraigniaud_et_al:LIPIcs.OPODIS.2022.20, author = {Fraigniaud, Pierre and Montealegre, Pedro and Paredes, Pablo and Rapaport, Ivan and R{\'\i}os-Wilson, Mart{\'\i}n and Todinca, Ioan}, title = {{Computing Power of Hybrid Models in Synchronous Networks}}, booktitle = {26th International Conference on Principles of Distributed Systems (OPODIS 2022)}, pages = {20:1--20:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-265-5}, ISSN = {1868-8969}, year = {2023}, volume = {253}, editor = {Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.20}, URN = {urn:nbn:de:0030-drops-176401}, doi = {10.4230/LIPIcs.OPODIS.2022.20}, annote = {Keywords: hybrid model, synchronous networks, LOCAL, CONGEST, Broadcast Congested Clique} }

Document

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

We present a wait-free algorithm for proper coloring the n nodes of the asynchronous cycle C_n, where each crash-prone node starts with its (unique) identifier as input. The algorithm is independent of n ≥ 3, and runs in O(log^*n) rounds in C_n. This round-complexity is optimal thanks to a known matching lower bound, which applies even to synchronous (failure-free) executions. The range of colors used by our algorithm, namely {0,…,4}, is optimal too, thanks to a known lower bound on the minimum number of names for which renaming is solvable wait-free in shared-memory systems, whenever n is a power of a prime. Indeed, our model coincides with the shared-memory model whenever n = 3, and the minimum number of names for which renaming is possible in 3-process shared-memory systems is 5.

Pierre Fraigniaud, Patrick Lambein-Monette, and Mikaël Rabie. Fault Tolerant Coloring of the Asynchronous Cycle. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2022.23, author = {Fraigniaud, Pierre and Lambein-Monette, Patrick and Rabie, Mika\"{e}l}, title = {{Fault Tolerant Coloring of the Asynchronous Cycle}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {23:1--23:22}, 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.2022.23}, URN = {urn:nbn:de:0030-drops-172147}, doi = {10.4230/LIPIcs.DISC.2022.23}, annote = {Keywords: graph coloring, LOCAL model, shared-memory model, immediate snapshot, renaming, wait-free algorithms} }

Document

Brief Announcement

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

During the last two decades, a small set of distributed computing models for networks have emerged, among which LOCAL, CONGEST, and Broadcast Congested Clique (BCC) play a prominent role. We consider hybrid models resulting from combining these three models. That is, we analyze the computing power of models allowing to, say, perform a constant number of rounds of CONGEST, then a constant number of rounds of LOCAL, then a constant number of rounds of BCC, possibly repeating this figure a constant number of times. We specifically focus on 2-round models, and we establish the complete picture of the relative powers of these models. That is, for every pair of such models, we determine whether one is (strictly) stronger than the other, or whether the two models are incomparable.

Pierre Fraigniaud, Pedro Montealegre, Pablo Paredes, Ivan Rapaport, Martín Ríos-Wilson, and Ioan Todinca. Brief Announcement: Computing Power of Hybrid Models in Synchronous Networks. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 43:1-43:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2022.43, author = {Fraigniaud, Pierre and Montealegre, Pedro and Paredes, Pablo and Rapaport, Ivan and R{\'\i}os-Wilson, Mart{\'\i}n and Todinca, Ioan}, title = {{Brief Announcement: Computing Power of Hybrid Models in Synchronous Networks}}, booktitle = {36th International Symposium on Distributed Computing (DISC 2022)}, pages = {43:1--43:3}, 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.2022.43}, URN = {urn:nbn:de:0030-drops-172345}, doi = {10.4230/LIPIcs.DISC.2022.43}, annote = {Keywords: hybrid model, synchronous networks, LOCAL, CONGEST, Broadcast Congested Clique} }

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Complete Volume

**Published in:** LIPIcs, Volume 226, 11th International Conference on Fun with Algorithms (FUN 2022)

LIPIcs, Volume 226, FUN 2022, Complete Volume

11th International Conference on Fun with Algorithms (FUN 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 226, pp. 1-450, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Proceedings{fraigniaud_et_al:LIPIcs.FUN.2022, title = {{LIPIcs, Volume 226, FUN 2022, Complete Volume}}, booktitle = {11th International Conference on Fun with Algorithms (FUN 2022)}, pages = {1--450}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-232-7}, ISSN = {1868-8969}, year = {2022}, volume = {226}, editor = {Fraigniaud, Pierre and Uno, Yushi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2022}, URN = {urn:nbn:de:0030-drops-159693}, doi = {10.4230/LIPIcs.FUN.2022}, annote = {Keywords: LIPIcs, Volume 226, FUN 2022, Complete Volume} }

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Front Matter

**Published in:** LIPIcs, Volume 226, 11th International Conference on Fun with Algorithms (FUN 2022)

Front Matter, Table of Contents, Preface, Conference Organization

11th International Conference on Fun with Algorithms (FUN 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 226, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fraigniaud_et_al:LIPIcs.FUN.2022.0, author = {Fraigniaud, Pierre and Uno, Yushi}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {11th International Conference on Fun with Algorithms (FUN 2022)}, pages = {0:i--0:xii}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-232-7}, ISSN = {1868-8969}, year = {2022}, volume = {226}, editor = {Fraigniaud, Pierre and Uno, Yushi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2022.0}, URN = {urn:nbn:de:0030-drops-159703}, doi = {10.4230/LIPIcs.FUN.2022.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

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Brief Announcement

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

Given any task Π, Brandt’s speedup theorem (PODC 2019) provides a mechanical way to design another task Π' on the same input-set as Π such that, for any t ≥ 1, Π is solvable in t rounds in the LOCAL model if and only if Π' is solvable in t-1 rounds in the LOCAL model. We dissect the construction in Brandt’s speedup theorem for expressing it in the broader framework of all round-based models supporting full information protocols, which includes models as different as asynchronous wait-free shared-memory computing with iterated immediate snapshots, and synchronous failure-free network computing.

Paul Bastide and Pierre Fraigniaud. Brief Annoucement: On Extending Brandt’s Speedup Theorem from LOCAL to Round-Based Full-Information Models. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 47:1-47:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bastide_et_al:LIPIcs.DISC.2021.47, author = {Bastide, Paul and Fraigniaud, Pierre}, title = {{Brief Annoucement: On Extending Brandt’s Speedup Theorem from LOCAL to Round-Based Full-Information Models}}, booktitle = {35th International Symposium on Distributed Computing (DISC 2021)}, pages = {47:1--47:4}, 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.2021.47}, URN = {urn:nbn:de:0030-drops-148492}, doi = {10.4230/LIPIcs.DISC.2021.47}, annote = {Keywords: Local Checkability, Distributed Complexity and Computability} }

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**Published in:** LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

This paper tackles the issue of checking that all copies of a large data set replicated at several nodes of a network are identical. The fact that the replicas may be located at distant nodes prevents the system from verifying their equality locally, i.e., by having each node consult only nodes in its vicinity. On the other hand, it remains possible to assign certificates to the nodes, so that verifying the consistency of the replicas can be achieved locally. However, we show that, as the replicated data is large, classical certification mechanisms, including distributed Merlin-Arthur protocols, cannot guarantee good completeness and soundness simultaneously, unless they use very large certificates. The main result of this paper is a distributed quantum Merlin-Arthur protocol enabling the nodes to collectively check the consistency of the replicas, based on small certificates, and in a single round of message exchange between neighbors, with short messages. In particular, the certificate-size is logarithmic in the size of the data set, which gives an exponential advantage over classical certification mechanisms. We propose yet another usage of a fundamental quantum primitive, called the SWAP test, in order to show our main result.

Pierre Fraigniaud, François Le Gall, Harumichi Nishimura, and Ami Paz. Distributed Quantum Proofs for Replicated Data. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{fraigniaud_et_al:LIPIcs.ITCS.2021.28, author = {Fraigniaud, Pierre and Le Gall, Fran\c{c}ois and Nishimura, Harumichi and Paz, Ami}, title = {{Distributed Quantum Proofs for Replicated Data}}, booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)}, pages = {28:1--28:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-177-1}, ISSN = {1868-8969}, year = {2021}, volume = {185}, editor = {Lee, James R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.28}, URN = {urn:nbn:de:0030-drops-135679}, doi = {10.4230/LIPIcs.ITCS.2021.28}, annote = {Keywords: Quantum Computing, Distributed Network Computing, Algorithmic Aspects of Networks} }

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Brief Announcement

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

This paper tackles the issue of checking that all copies of a large data set replicated at several nodes of a network are identical. The fact that the replicas may be located at distant nodes prevents the system from verifying their equality locally, i.e., by having each node consult only nodes in its vicinity. On the other hand, it remains possible to assign certificates to the nodes, so that verifying the consistency of the replicas can be achieved locally. However, we show that, as the replicated data is large, classical certification mechanisms, including distributed Merlin-Arthur protocols, cannot guarantee good completeness and soundness simultaneously, unless they use very large certificates. The main result of this paper is a distributed quantum Merlin-Arthur protocol enabling the nodes to collectively check the consistency of the replicas, based on small certificates, and in a single round of message exchange between neighbors, with short messages. In particular, the certificate-size is logarithmic in the size of the data set, which gives an exponential advantage over classical certification mechanisms.

Pierre Fraigniaud, François Le Gall, Harumichi Nishimura, and Ami Paz. Brief Announcement: Distributed Quantum Proofs for Replicated Data. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 43:1-43:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fraigniaud_et_al:LIPIcs.DISC.2020.43, author = {Fraigniaud, Pierre and Le Gall, Fran\c{c}ois and Nishimura, Harumichi and Paz, Ami}, title = {{Brief Announcement: Distributed Quantum Proofs for Replicated Data}}, booktitle = {34th International Symposium on Distributed Computing (DISC 2020)}, pages = {43:1--43:3}, 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.2020.43}, URN = {urn:nbn:de:0030-drops-131217}, doi = {10.4230/LIPIcs.DISC.2020.43}, annote = {Keywords: Quantum Computing, Distributed Network Computing, Algorithmic Aspects of Networks} }

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Track B: Automata, Logic, Semantics, and Theory of Programming

**Published in:** LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed algebraic topology. In both cases, the considered computational model generally assumes communication via shared objects (typically a shared memory consisting of a collection of read-write registers), or message-passing enabling direct communication between any pair of processes. Our paper is concerned with network computing, where the processes are located at the nodes of a network, and communicate by exchanging messages along the edges of that network (only neighboring processes can communicate directly).
Applying the topological approach for verification in network computing is a considerable challenge, mainly because the presence of identifiers assigned to the nodes yields protocol complexes whose size grows exponentially with the size of the underlying network. However, many of the problems studied in this context are of local nature, and their definitions do not depend on the identifiers or on the size of the network. We leverage this independence in order to meet the above challenge, and present local protocol complexes, whose sizes do not depend on the size of the network. As an application of the design of "compacted" protocol complexes, we reformulate the celebrated lower bound of Ω(log^*n) rounds for 3-coloring the n-node ring, in the algebraic topology framework.

Pierre Fraigniaud and Ami Paz. The Topology of Local Computing in Networks. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 128:1-128:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fraigniaud_et_al:LIPIcs.ICALP.2020.128, author = {Fraigniaud, Pierre and Paz, Ami}, title = {{The Topology of Local Computing in Networks}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {128:1--128:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.128}, URN = {urn:nbn:de:0030-drops-125358}, doi = {10.4230/LIPIcs.ICALP.2020.128}, annote = {Keywords: Distributed computing, distributed graph algorithms, combinatorial topology} }

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**Published in:** LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

The study of interactive proofs in the context of distributed network computing is a novel topic, recently introduced by Kol, Oshman, and Saxena [PODC 2018]. In the spirit of sequential interactive proofs theory, we study the power of distributed interactive proofs. This is achieved via a series of results establishing trade-offs between various parameters impacting the power of interactive proofs, including the number of interactions, the certificate size, the communication complexity, and the form of randomness used. Our results also connect distributed interactive proofs with the established field of distributed verification. In general, our results contribute to providing structure to the landscape of distributed interactive proofs.

Pierluigi Crescenzi, Pierre Fraigniaud, and Ami Paz. Trade-Offs in Distributed Interactive Proofs. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{crescenzi_et_al:LIPIcs.DISC.2019.13, author = {Crescenzi, Pierluigi and Fraigniaud, Pierre and Paz, Ami}, title = {{Trade-Offs in Distributed Interactive Proofs}}, booktitle = {33rd International Symposium on Distributed Computing (DISC 2019)}, pages = {13:1--13:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-126-9}, ISSN = {1868-8969}, year = {2019}, volume = {146}, editor = {Suomela, Jukka}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.13}, URN = {urn:nbn:de:0030-drops-113202}, doi = {10.4230/LIPIcs.DISC.2019.13}, annote = {Keywords: Distributed interactive proofs, Distributed verification} }

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**Published in:** LIPIcs, Volume 125, 22nd International Conference on Principles of Distributed Systems (OPODIS 2018)

Distributed tasks such as constructing a maximal independent set (MIS) in a network, or properly coloring the nodes or the edges of a network with reasonably few colors, are known to admit efficient distributed randomized algorithms. Those algorithms essentially proceed according to some simple generic rules, by letting each node choosing a temptative value at random, and checking whether this choice is consistent with the choices of the nodes in its vicinity. If this is the case, then the node outputs the chosen value, else it repeats the same process. Although such algorithms are, with high probability, running in a polylogarithmic number of rounds, they are not robust against actions performed by rational but selfish nodes. Indeed, such nodes may prefer specific individual outputs over others, e.g., because the formers suit better with some individual constraints. For instance, a node may prefer not being placed in a MIS as it is not willing to serve as a relay node. Similarly, a node may prefer not being assigned some radio frequencies (i.e., colors) as these frequencies would interfere with other devices running at that node. In this paper, we show that the probability distribution governing the choices of the output values in the generic algorithm can be tuned such that no nodes will rationally deviate from this distribution. More formally, and more generally, we prove that the large class of so-called LCL tasks, including MIS and coloring, admit simple "Luby's style" algorithms where the probability distribution governing the individual choices of the output values forms a Nash equilibrium. In fact, we establish the existence of a stronger form of equilibria, called symmetric trembling-hand perfect equilibria for those games.

Simon Collet, Pierre Fraigniaud, and Paolo Penna. Equilibria of Games in Networks for Local Tasks. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{collet_et_al:LIPIcs.OPODIS.2018.6, author = {Collet, Simon and Fraigniaud, Pierre and Penna, Paolo}, title = {{Equilibria of Games in Networks for Local Tasks}}, booktitle = {22nd International Conference on Principles of Distributed Systems (OPODIS 2018)}, pages = {6:1--6:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-098-9}, ISSN = {1868-8969}, year = {2019}, volume = {125}, editor = {Cao, Jiannong and Ellen, Faith and Rodrigues, Luis and Ferreira, Bernardo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2018.6}, URN = {urn:nbn:de:0030-drops-100668}, doi = {10.4230/LIPIcs.OPODIS.2018.6}, annote = {Keywords: Local distributed computing, Locally checkable labelings} }

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**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Distributed proofs are mechanisms enabling the nodes of a network to collectively and efficiently check the correctness of Boolean predicates on the structure of the network (e.g. having a specific diameter), or on data structures distributed over the nodes (e.g. a spanning tree). We consider well known mechanisms consisting of two components: a prover that assigns a certificate to each node, and a distributed algorithm called verifier that is in charge of verifying the distributed proof formed by the collection of all certificates. We show that many network predicates have distributed proofs offering a high level of redundancy, explicitly or implicitly. We use this remarkable property of distributed proofs to establish perfect tradeoffs between the size of the certificate stored at every node, and the number of rounds of the verification protocol.

Laurent Feuilloley, Pierre Fraigniaud, Juho Hirvonen, Ami Paz, and Mor Perry. Redundancy in Distributed Proofs. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{feuilloley_et_al:LIPIcs.DISC.2018.24, author = {Feuilloley, Laurent and Fraigniaud, Pierre and Hirvonen, Juho and Paz, Ami and Perry, Mor}, title = {{Redundancy in Distributed Proofs}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {24:1--24:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.24}, URN = {urn:nbn:de:0030-drops-98139}, doi = {10.4230/LIPIcs.DISC.2018.24}, annote = {Keywords: Distributed verification, Distributed graph algorithms, Proof-labeling schemes, Space-time tradeoffs, Non-determinism} }

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**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

On the one hand, the correctness of routing protocols in networks is an issue of utmost importance for guaranteeing the delivery of messages from any source to any target. On the other hand, a large collection of routing schemes have been proposed during the last two decades, with the objective of transmitting messages along short routes, while keeping the routing tables small. Regrettably, all these schemes share the property that an adversary may modify the content of the routing tables with the objective of, e.g., blocking the delivery of messages between some pairs of nodes, without being detected by any node.
In this paper, we present a simple certification mechanism which enables the nodes to locally detect any alteration of their routing tables. In particular, we show how to locally verify the stretch 3 routing scheme by Thorup and Zwick [SPAA 2001] by adding certificates of ~O(sqrt(n)) bits at each node in n-node networks, that is, by keeping the memory size of the same order of magnitude as the original routing tables. We also propose a new name-independent routing scheme using routing tables of size ~O(sqrt(n)) bits. This new routing scheme can be locally verified using certificates on ~O(sqrt(n)) bits. Its stretch is 3 if using handshaking, and 5 otherwise.

Alkida Balliu and Pierre Fraigniaud. Certification of Compact Low-Stretch Routing Schemes. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{balliu_et_al:LIPIcs.DISC.2017.6, author = {Balliu, Alkida and Fraigniaud, Pierre}, title = {{Certification of Compact Low-Stretch Routing Schemes}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {6:1--6:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.6}, URN = {urn:nbn:de:0030-drops-79807}, doi = {10.4230/LIPIcs.DISC.2017.6}, annote = {Keywords: Distributed verification, compact routing, local computing} }

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**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

In this paper we present distributed property-testing algorithms for graph properties in the CONGEST model, with emphasis on testing subgraph-freeness. Testing a graph property P means distinguishing graphs G = (V,E) having property P from graphs that are epsilon-far from having it, meaning that epsilon|E| edges must be added or removed from G to obtain a graph satisfying P.
We present a series of results, including:
- Testing H-freeness in O(1/epsilon) rounds, for any constant-sized graph H containing an edge (u,v) such that any cycle in H contain either u or v (or both). This includes all connected graphs over five vertices except K_5. For triangles, we can do even better when epsilon is not too small.
- A deterministic CONGEST protocol determining whether a graph contains a given tree as a subgraph in constant time.
- For cliques K_s with s >= 5, we show that K_s-freeness can be tested in O(m^(1/2-1/(s-2)) epsilon^(-1/2-1/(s-2))) rounds, where m is the number of edges in the network graph.
- We describe a general procedure for converting epsilon-testers with f(D) rounds, where D denotes the diameter of the graph, to work in O((log n)/epsilon)+f((log n)/epsilon) rounds, where n is the number of processors of the network. We then apply this procedure to obtain an epsilon-tester for testing whether a graph is bipartite and testing whether a graph is cycle-free. Moreover, for cycle-freeness, we obtain a corrector of the graph that locally corrects the graph so that the corrected graph is acyclic. Note that, unlike a tester, a corrector needs to mend the graph in many places in the case that the graph is far from having the property.
These protocols extend and improve previous results of [Censor-Hillel et al. 2016] and [Fraigniaud et al. 2016].

Guy Even, Orr Fischer, Pierre Fraigniaud, Tzlil Gonen, Reut Levi, Moti Medina, Pedro Montealegre, Dennis Olivetti, Rotem Oshman, Ivan Rapaport, and Ioan Todinca. Three Notes on Distributed Property Testing. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 15:1-15:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{even_et_al:LIPIcs.DISC.2017.15, author = {Even, Guy and Fischer, Orr and Fraigniaud, Pierre and Gonen, Tzlil and Levi, Reut and Medina, Moti and Montealegre, Pedro and Olivetti, Dennis and Oshman, Rotem and Rapaport, Ivan and Todinca, Ioan}, title = {{Three Notes on Distributed Property Testing}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {15:1--15:30}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.15}, URN = {urn:nbn:de:0030-drops-79847}, doi = {10.4230/LIPIcs.DISC.2017.15}, annote = {Keywords: Property testing, Property correcting, Distributed algorithms, CONGEST model} }

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**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Proof-labeling schemes are known mechanisms providing nodes of networks with certificates that can be verified locally by distributed algorithms. Given a boolean predicate on network states, such schemes enable to check whether the predicate is satisfied by the actual state of the network, by having nodes interacting with their neighbors only. Proof-labeling schemes are typically designed for enforcing fault-tolerance, by making sure that if the current state of the network is illegal with respect to some given predicate, then at least one node will detect it. Such a node can raise an alarm, or launch a recovery procedure enabling the system to return to a legal state. In this paper, we introduce error-sensitive proof-labeling schemes. These are proof-labeling schemes which guarantee that the number of nodes detecting illegal states is linearly proportional to the edit-distance between the current state and the set of legal states. By using error-sensitive proof-labeling schemes, states which are far from satisfying the predicate will be detected by many nodes, enabling fast return to legality. We provide a structural characterization of the set of boolean predicates on network states for which there exist error-sensitive proof-labeling schemes. This characterization allows us to show that classical predicates such as, e.g., acyclicity, and leader admit error-sensitive proof-labeling schemes, while others like regular subgraphs don't. We also focus on compact error-sensitive proof-labeling schemes. In particular, we show that the known proof-labeling schemes for spanning tree and minimum spanning tree, using certificates on O(log n) bits, and on O(log^2 n) bits, respectively, are error-sensitive, as long as the trees are locally represented by adjacency lists, and not just by parent pointers.

Laurent Feuilloley and Pierre Fraigniaud. Error-Sensitive Proof-Labeling Schemes. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{feuilloley_et_al:LIPIcs.DISC.2017.16, author = {Feuilloley, Laurent and Fraigniaud, Pierre}, title = {{Error-Sensitive Proof-Labeling Schemes}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {16:1--16:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.16}, URN = {urn:nbn:de:0030-drops-80180}, doi = {10.4230/LIPIcs.DISC.2017.16}, annote = {Keywords: Fault-tolerance, distributed decision, distributed property testing} }

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**Published in:** LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

We are considering distributed network computing, in which computing entities are connected by a network modeled as a connected graph. These entities are located at the nodes of the graph, and they exchange information by message-passing along its edges. In this context, we are adopting the classical framework for local distributed decision, in which nodes must collectively decide whether their network configuration satisfies some given boolean predicate, by having each node interacting with the nodes in its vicinity only. A network configuration is accepted if and only if every node individually accepts. It is folklore that not every Turing-decidable network property (e.g., whether the network is planar) can be decided locally whenever the computing entities are Turing machines (TM). On the other hand, it is known that every Turing-decidable network property can be decided locally if nodes are running non-deterministic Turing machines (NTM). However, this holds only if the nodes have the ability to guess the identities of the nodes currently in the network. That is, for different sets of identities assigned to the nodes, the correct guesses of the nodes might be different. If one asks the nodes to use the same guess in the same network configuration even with different identity assignments, i.e., to perform identity-oblivious guesses, then it is known that not every Turing-decidable network property can be decided locally.
In this paper, we show that every Turing-decidable network property can be decided locally if nodes are running alternating Turing machines (ATM), and this holds even if nodes are bounded to perform identity-oblivious guesses. More specifically, we show that, for every network property, there is a local algorithm for ATMs, with at most 2 alternations, that decides that property. To this aim, we define a hierarchy of classes of decision tasks where the lowest level contains tasks solvable with TMs, the first level those solvable with NTMs, and level k contains those tasks solvable with ATMs with k alternations. We characterize the entire hierarchy, and show that it collapses in the second level. In addition, we show separation results between the classes of network properties that are locally decidable with TMs, NTMs, and ATMs. Finally, we establish the existence of completeness results for each of these classes, using novel notions of local reduction.

Alkida Balliu, Gianlorenzo D'Angelo, Pierre Fraigniaud, and Dennis Olivetti. What Can Be Verified Locally?. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{balliu_et_al:LIPIcs.STACS.2017.8, author = {Balliu, Alkida and D'Angelo, Gianlorenzo and Fraigniaud, Pierre and Olivetti, Dennis}, title = {{What Can Be Verified Locally?}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {8:1--8:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.8}, URN = {urn:nbn:de:0030-drops-70253}, doi = {10.4230/LIPIcs.STACS.2017.8}, annote = {Keywords: Distributed Network Computing, Distributed Algorithm, Distributed Decision, Locality} }

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**Published in:** LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

Runtime Verification (RV) is a lightweight method for monitoring the formal specification of a system during its execution. It has recently been shown that a given state predicate can be monitored consistently by a set of crash-prone asynchronous distributed monitors, only if sufficiently many different verdicts can be emitted by each monitor. We revisit this impossibility result in the context of LTL semantics for RV. We show that employing the four-valued logic Rv-LTL will result in inconsistent distributed monitoring for some formulas. Our first main contribution is a family of logics, called Ltl2k+4, that refines Rv-Ltl incorporating 2k + 4 truth values, for each k >= 0. The truth values of Ltl2k+4 can be effectively used by each monitor to reach a consistent global set of verdicts for each given formula, provided k is sufficiently large. Our second main contribution is an algorithm for monitor construction enabling fault-tolerant distributed monitoring based on the aggregation of the individual verdicts by each monitor.

Borzoo Bonakdarpour, Pierre Fraigniaud, Sergio Rajsbaum, David A. Rosenblueth, and Corentin Travers. Decentralized Asynchronous Crash-Resilient Runtime Verification. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bonakdarpour_et_al:LIPIcs.CONCUR.2016.16, author = {Bonakdarpour, Borzoo and Fraigniaud, Pierre and Rajsbaum, Sergio and Rosenblueth, David A. and Travers, Corentin}, title = {{Decentralized Asynchronous Crash-Resilient Runtime Verification}}, booktitle = {27th International Conference on Concurrency Theory (CONCUR 2016)}, pages = {16:1--16:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-017-0}, ISSN = {1868-8969}, year = {2016}, volume = {59}, editor = {Desharnais, Jos\'{e}e and Jagadeesan, Radha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.16}, URN = {urn:nbn:de:0030-drops-61856}, doi = {10.4230/LIPIcs.CONCUR.2016.16}, annote = {Keywords: Runtime monitoring, Distributed algorithms, Fault-tolerance} }

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**Published in:** LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

We extend the notion of distributed decision in the framework of distributed network computing, inspired by recent results on so-called distributed graph automata. We show that, by using distributed decision mechanisms based on the interaction between a prover and a disprover, the size of the certificates distributed to the nodes for certifying a given network property can be drastically reduced. For instance, we prove that minimum spanning tree can be certified with O(log(n))-bit certificates in n-node graphs, with just one interaction between the prover and the disprover, while it is known that certifying MST requires Omega(log^2(n))-bit certificates if only the prover can act. The improvement can even be exponential for some simple graph properties.
For instance, it is known that certifying the existence of a nontrivial automorphism requires Omega(n^2) bits if only the prover can act. We show that there is a protocol with two interactions between the prover and the disprover enabling to certify nontrivial automorphism with O(log(n))- bit certificates. These results are achieved by defining and analysing a local hierarchy of decision which generalizes the classical notions of proof-labelling schemes and locally checkable proofs.

Laurent Feuilloley, Pierre Fraigniaud, and Juho Hirvonen. A Hierarchy of Local Decision. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 118:1-118:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{feuilloley_et_al:LIPIcs.ICALP.2016.118, author = {Feuilloley, Laurent and Fraigniaud, Pierre and Hirvonen, Juho}, title = {{A Hierarchy of Local Decision}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {118:1--118:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.118}, URN = {urn:nbn:de:0030-drops-62536}, doi = {10.4230/LIPIcs.ICALP.2016.118}, annote = {Keywords: Distributed Network Computing, Distributed Algorithm, Distributed Decision, Locality} }

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**Published in:** Dagstuhl Reports, Volume 3, Issue 1 (2013)

This report documents the program and the outcomes of Dagstuhl Seminar 13042 "Epidemic Algorithms and Processes: From Theory to Applications", which took place from January 20 to 25, 2013 at Schloss Dagstuhl - Leibniz Center for
Informatics. Several research topics were covered by the seminar participants, including scientists working in Theoretical Computer Science, as well as researchers from the more practical area of Computer Systems. Most of the participants presented their recent results on the topic of the seminar, as well as some challenging new directions and open problems. The presentations contained a description of the main research area for a wide audience. During the seminar, ample time was reserved for informal discussions between participants working on different topics. In our executive summary, we describe the main field of the seminar, as well as our goals in general. Then, we present the abstracts of the presentations given during the seminar.

Benjamin Doerr, Robert Elsässer, and Pierre Fraigniaud. Epidemic Algorithms and Processes: From Theory to Applications (Dagstuhl Seminar 13042). In Dagstuhl Reports, Volume 3, Issue 1, pp. 94-110, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@Article{doerr_et_al:DagRep.3.1.94, author = {Doerr, Benjamin and Els\"{a}sser, Robert and Fraigniaud, Pierre}, title = {{Epidemic Algorithms and Processes: From Theory to Applications (Dagstuhl Seminar 13042)}}, pages = {94--110}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2013}, volume = {3}, number = {1}, editor = {Doerr, Benjamin and Els\"{a}sser, Robert and Fraigniaud, Pierre}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.3.1.94}, URN = {urn:nbn:de:0030-drops-40104}, doi = {10.4230/DagRep.3.1.94}, annote = {Keywords: Message dissemination, Epidemic spreading, Dynamic spreading processes} }

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**Published in:** Dagstuhl Reports, Volume 1, Issue 2 (2011)

From February 14, 2012 to February 18, 2012, the Dagstuhl Seminar 11071
``Theory and Applications of Graph Searching Problems (GRASTA 2011)''
was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, 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 open problems are put together in this paper. The first section describes the seminar topics and goals in general.
The second section contains the abstracts of the talks and the third section
includes the open problems presented during the seminar.

Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer, and Dimitrios M. Thilikos. Theory and Applications of Graph Searching Problems (GRASTA 2011) (Dagstuhl Seminar 11071). In Dagstuhl Reports, Volume 1, Issue 2, pp. 30-46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@Article{fomin_et_al:DagRep.1.2.30, author = {Fomin, Fedor V. and Fraigniaud, Pierre and Kreutzer, Stephan and Thilikos, Dimitrios M.}, title = {{Theory and Applications of Graph Searching Problems (GRASTA 2011) (Dagstuhl Seminar 11071)}}, pages = {30--46}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2011}, volume = {1}, number = {2}, editor = {Fomin, Fedor V. and Fraigniaud, Pierre and Kreutzer, Stephan and Thilikos, Dimitrios M.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.1.2.30}, URN = {urn:nbn:de:0030-drops-31534}, doi = {10.4230/DagRep.1.2.30}, annote = {Keywords: Graph Searching, Pursuit Evasion Games, Cop and Robers Games, Fugitive Search Games} }

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