Understanding the algorithmic behaviors that are in principle realizable in a chemical system is necessary for a rigorous understanding of the design principles of biological regulatory networks. Further, advances in synthetic biology herald the time when we'll be able to rationally engineer complex chemical systems, and when idealized formal models will become blueprints for engineering. Coupled chemical interactions in a well-mixed solution are commonly formalized as chemical reaction networks (CRNs). However, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. Here we study the following problem: what functions f : ∪k → ∪ can be computed by a chemical reaction network, in which the CRN eventually produces the correct amount of the "output" ∣ molecule, no matter the rate at which reactions proceed? This captures a previously unexplored, but very natural class of computations: for example, the reaction X1 + X2 → Y can be thought to compute the function y = min(x1, x2). Such a CRN is robust in the sense that it is correct whether its evolution is governed by the standard model of mass-action kinetics, alternatives such as Hill-function or Michaelis-Menten kinetics, or other arbitrary models of chemistry that respect the (fundamentally digital) stoichiometric constraints (what are the reactants and products?). We develop a formal definition of such computation using a novel notion of reachability, and prove that a function is computable in this manner if and only if it is continuous piecewise linear.
{"title":"Rate-independent computation in continuous chemical reaction networks","authors":"Ho-Lin Chen, David Doty, D. Soloveichik","doi":"10.1145/2554797.2554827","DOIUrl":"https://doi.org/10.1145/2554797.2554827","url":null,"abstract":"Understanding the algorithmic behaviors that are in principle realizable in a chemical system is necessary for a rigorous understanding of the design principles of biological regulatory networks. Further, advances in synthetic biology herald the time when we'll be able to rationally engineer complex chemical systems, and when idealized formal models will become blueprints for engineering. Coupled chemical interactions in a well-mixed solution are commonly formalized as chemical reaction networks (CRNs). However, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. Here we study the following problem: what functions f : ∪k → ∪ can be computed by a chemical reaction network, in which the CRN eventually produces the correct amount of the \"output\" ∣ molecule, no matter the rate at which reactions proceed? This captures a previously unexplored, but very natural class of computations: for example, the reaction X1 + X2 → Y can be thought to compute the function y = min(x1, x2). Such a CRN is robust in the sense that it is correct whether its evolution is governed by the standard model of mass-action kinetics, alternatives such as Hill-function or Michaelis-Menten kinetics, or other arbitrary models of chemistry that respect the (fundamentally digital) stoichiometric constraints (what are the reactants and products?). We develop a formal definition of such computation using a novel notion of reachability, and prove that a function is computable in this manner if and only if it is continuous piecewise linear.","PeriodicalId":382856,"journal":{"name":"Proceedings of the 5th conference on Innovations in theoretical computer science","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126954386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the price of anarchy of coordination mechanisms for a scheduling problem where each job j has a weight wj, processing time pij, assignment cost hij, and communication delay (or release date) rij, on machine i. Each machine is free to declare its own scheduling policy. Each job is a selfish agent and selects a machine that minimizes its own disutility, which is equal to its weighted completion time plus its assignment cost. The goal is to minimize the total disutility incurred by all the jobs. Our model is general enough to capture scheduling jobs in a distributed environment with heterogeneous machines (or data centers) that are situated across different locations. Our main result is a characterization of scheduling policies that give a small (robust) Price of Anarchy. More precisely, we show that whenever each machine independently declares any scheduling policy that satisfies a certain bounded stretch condition introduced in this paper, the game induced between the jobs has a small Price of Anarchy. Our characterization is powerful enough to test almost all popular scheduling policies. On the technical side, to derive our results, we use a potential function whose derivative leads to an instantaneous smoothness condition, and linear programming and dual fitting. To the best of our knowledge, this is a novel application of these techniques in the context of coordination mechanisms, and we believe these tools will find more applications in analyzing PoA of games. We also extend our results to the lk-norms and l∞ norm (makespan) objectives.
{"title":"Coordination mechanisms from (almost) all scheduling policies","authors":"Sayan Bhattacharya, Sungjin Im, Janardhan Kulkarni, Kamesh Munagala","doi":"10.1145/2554797.2554811","DOIUrl":"https://doi.org/10.1145/2554797.2554811","url":null,"abstract":"We study the price of anarchy of coordination mechanisms for a scheduling problem where each job j has a weight wj, processing time pij, assignment cost hij, and communication delay (or release date) rij, on machine i. Each machine is free to declare its own scheduling policy. Each job is a selfish agent and selects a machine that minimizes its own disutility, which is equal to its weighted completion time plus its assignment cost. The goal is to minimize the total disutility incurred by all the jobs. Our model is general enough to capture scheduling jobs in a distributed environment with heterogeneous machines (or data centers) that are situated across different locations. Our main result is a characterization of scheduling policies that give a small (robust) Price of Anarchy. More precisely, we show that whenever each machine independently declares any scheduling policy that satisfies a certain bounded stretch condition introduced in this paper, the game induced between the jobs has a small Price of Anarchy. Our characterization is powerful enough to test almost all popular scheduling policies. On the technical side, to derive our results, we use a potential function whose derivative leads to an instantaneous smoothness condition, and linear programming and dual fitting. To the best of our knowledge, this is a novel application of these techniques in the context of coordination mechanisms, and we believe these tools will find more applications in analyzing PoA of games. We also extend our results to the lk-norms and l∞ norm (makespan) objectives.","PeriodicalId":382856,"journal":{"name":"Proceedings of the 5th conference on Innovations in theoretical computer science","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114462558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Session 7: 14:00--14:10","authors":"S. Irani","doi":"10.1145/3255059","DOIUrl":"https://doi.org/10.1145/3255059","url":null,"abstract":"","PeriodicalId":382856,"journal":{"name":"Proceedings of the 5th conference on Innovations in theoretical computer science","volume":"239 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132372889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The papers in this volume were presented at the 5th Innovations in Theoretical Computer Science (ITCS 2014) conference, sponsored by the ACM Special Interest Group on Algorithms and Computation Theory (SIGACT). The conference was held in Princeton, New Jersey, USA, January 11--14, 2014. ITCS (previously known as ICS) seeks to promote research that carries a strong conceptual message, for instance, introducing a new concept or model, opening a new line of inquiry within traditional or cross-interdisciplinary areas, or introducing new techniques or new applications of known techniques). The call for papers welcomed all submissions, whether aligned with current theory of computation research directions or deviating from them. Altogether 116 submissions were received worldwide. Of these the program committee selected 48 papers. The accepted papers cover a wide range of topics in theoretical computer science, including algorithms, complexity, cryptography, learning, data privacy, quantum, physical and biological computing and relations between computing and social sciences. In addition to the selected papers the committee invited Professor Peter Winkler of Dartmouth to give an evening talk and we are grateful for his acceptance. Another evening was devoted to "Graduating Bits" - short talks by recent graduates. The program committee consisted of 24 members (plus the chair): Deeparnab Chakrabarty (Microsoft Research India), Timothy Chan (University of Waterloo), Costis Daskalakis (MIT), Yuval Emek (ETH and Technion), Kousha Etessami (University of Edinburgh), Yuval Filmus (University of Toronto and Simons Institute, Berkeley), Arpita Ghosh (Cornell University), Monika Henzinger (University of Vienna), Sandy Irani (University of California Irvine), Michael nKearns (University of Pennsylvania), Lap Chi Lau (The Chinese University of Hong Kong), Nati Linial (Hebrew University of Jerusalem), Kobbi Nissim (Ben-Gurion University), Rasmus Pagh (IT University of Copenhagen), Shubhangi Saraf (Rutgers University), Ola Svensson (EPFL), Vinod Vaikuntanathan (University of Toronto and MIT), Jan Vondrak (IBM Almaden Research Center), Manfred Warmuth (University of California, Santa Cruz), Daniel Wichs (Northeastern University), Udi Wieder (Microsoft Research SVC), Ryan Williams (Stanford University), Ronald de Wolf (CWI and University of Amsterdam), David Xiao (CNRS and Universite Paris 7). I wish to express my admiration for their hard work of reading, evaluating and debating the merits of the submissions. The many individuals who assisted the reviewing process as subreviewers and extended the expertise of the committee deserve acknowledgments as well.
{"title":"Proceedings of the 5th conference on Innovations in theoretical computer science","authors":"M. Naor","doi":"10.1145/2554797","DOIUrl":"https://doi.org/10.1145/2554797","url":null,"abstract":"The papers in this volume were presented at the 5th Innovations in Theoretical Computer Science (ITCS 2014) conference, sponsored by the ACM Special Interest Group on Algorithms and Computation Theory (SIGACT). The conference was held in Princeton, New Jersey, USA, January 11--14, 2014. ITCS (previously known as ICS) seeks to promote research that carries a strong conceptual message, for instance, introducing a new concept or model, opening a new line of inquiry within traditional or cross-interdisciplinary areas, or introducing new techniques or new applications of known techniques). \u0000 \u0000The call for papers welcomed all submissions, whether aligned with current theory of computation research directions or deviating from them. Altogether 116 submissions were received worldwide. Of these the program committee selected 48 papers. The accepted papers cover a wide range of topics in theoretical computer science, including algorithms, complexity, cryptography, learning, data privacy, quantum, physical and biological computing and relations between computing and social sciences. In addition to the selected papers the committee invited Professor Peter Winkler of Dartmouth to give an evening talk and we are grateful for his acceptance. Another evening was devoted to \"Graduating Bits\" - short talks by recent graduates. \u0000 \u0000The program committee consisted of 24 members (plus the chair): Deeparnab Chakrabarty (Microsoft Research India), Timothy Chan (University of Waterloo), Costis Daskalakis (MIT), Yuval Emek (ETH and Technion), Kousha Etessami (University of Edinburgh), Yuval Filmus (University of Toronto and Simons Institute, Berkeley), Arpita Ghosh (Cornell University), Monika Henzinger (University of Vienna), Sandy Irani (University of California Irvine), Michael nKearns (University of Pennsylvania), Lap Chi Lau (The Chinese University of Hong Kong), Nati Linial (Hebrew University of Jerusalem), Kobbi Nissim (Ben-Gurion University), Rasmus Pagh (IT University of Copenhagen), Shubhangi Saraf (Rutgers University), Ola Svensson (EPFL), Vinod Vaikuntanathan (University of Toronto and MIT), Jan Vondrak (IBM Almaden Research Center), Manfred Warmuth (University of California, Santa Cruz), Daniel Wichs (Northeastern University), Udi Wieder (Microsoft Research SVC), Ryan Williams (Stanford University), Ronald de Wolf (CWI and University of Amsterdam), David Xiao (CNRS and Universite Paris 7). I wish to express my admiration for their hard work of reading, evaluating and debating the merits of the submissions. The many individuals who assisted the reviewing process as subreviewers and extended the expertise of the committee deserve acknowledgments as well.","PeriodicalId":382856,"journal":{"name":"Proceedings of the 5th conference on Innovations in theoretical computer science","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133415411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Session 3: 14:00--14:10","authors":"Michael Kearns","doi":"10.1145/3255055","DOIUrl":"https://doi.org/10.1145/3255055","url":null,"abstract":"","PeriodicalId":382856,"journal":{"name":"Proceedings of the 5th conference on Innovations in theoretical computer science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115764640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a new notion called tester of a class M of functions f : A → C that maps the elements α ∈ A in the domain A of the function to a finite number (the size of the tester) of elements b1,...,bt in a smaller sub-domain B ⊂ A where the property f(α) ≠ 0 is preserved for all f ∈ M. I.e., for all f ∈ M and - ∈ A if f(α) ≠ 0 then f(bi) ≠ 0 for some i. We use tools from elementary algebra and algebraic function fields to construct testers of almost optimal size in deterministic polynomial time in the size of the tester. We then apply testers to deterministically construct new set of objects with some combinatorial and algebraic properties that can be used to derandomize some algorithms. We show that those new constructions are almost optimal and for many of them meet the union bound of the problem. Constructions include, d-restriction problems, perfect hash, universal sets, cover-free families, separating hash functions, polynomial restriction problems, black box polynomial identity testing for polynomials and circuits over small fields and hitting sets.
{"title":"Testers and their applications","authors":"N. Bshouty","doi":"10.1145/2554797.2554828","DOIUrl":"https://doi.org/10.1145/2554797.2554828","url":null,"abstract":"We develop a new notion called tester of a class M of functions f : A → C that maps the elements α ∈ A in the domain A of the function to a finite number (the size of the tester) of elements b1,...,bt in a smaller sub-domain B ⊂ A where the property f(α) ≠ 0 is preserved for all f ∈ M. I.e., for all f ∈ M and - ∈ A if f(α) ≠ 0 then f(bi) ≠ 0 for some i. We use tools from elementary algebra and algebraic function fields to construct testers of almost optimal size in deterministic polynomial time in the size of the tester. We then apply testers to deterministically construct new set of objects with some combinatorial and algebraic properties that can be used to derandomize some algorithms. We show that those new constructions are almost optimal and for many of them meet the union bound of the problem. Constructions include, d-restriction problems, perfect hash, universal sets, cover-free families, separating hash functions, polynomial restriction problems, black box polynomial identity testing for polynomials and circuits over small fields and hitting sets.","PeriodicalId":382856,"journal":{"name":"Proceedings of the 5th conference on Innovations in theoretical computer science","volume":"94 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129826508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Session 8: 16:00--16:10","authors":"Yuval Filmus","doi":"10.1145/3255060","DOIUrl":"https://doi.org/10.1145/3255060","url":null,"abstract":"","PeriodicalId":382856,"journal":{"name":"Proceedings of the 5th conference on Innovations in theoretical computer science","volume":"82 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123142660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We derive structural constraints on the automorphism groups of strongly regular (s.r.) graphs, giving a surprisingly strong answer to a decades-old problem, with tantalizing implications to testing isomorphism of s.r. graphs, and raising new combinatorial challenges. S.r. graphs, while not believed to be Graph Isomorphism (GI) complete, have long been recognized as hard cases for GI, and, in this author's view, present some of the core difficulties of the general GI problem. Progress on the complexity of testing their isomorphism has been intermittent (Babai 1980, Spielman 1996, BW & CST (STOC'13) and BCSTW (FOCS'13)), and the current best bound is exp(Õ(n1/5)) (n is the number of vertices). Our main result is that if X is a s.r. graph then, with straightforward exceptions, the degree of the largest alternating group involved in the automorphism group Aut(X) (as a quotient of a subgroup) is O((ln n)2ln ln n). (The exceptions admit trivial linear-time GI testing.) The design of isomorphism tests for various classes of structures is intimately connected with the study of the automorphism groups of those structures. We include a brief survey of these connections, starting with an 1869 paper by Jordan on trees. In particular, our result amplifies the potential of Luks's divide-and-conquer methods (1980) to be applicable to testing isomorphism of s.r. graphs in quasipolynomial time. The challenge remains to find a hierarchy of combinatorial substructures through which this potential can be realized. We expect that the generality of our result will help in this regard; the result applies not only to s.r. graphs but to all graphs with strong spectral expansion and with a relatively small number of common neighbors for every pair of vertices. We state a purely mathematical conjecture that could bring us closer to finding the right kind of hierarchy. We also outline the broader GI context, and state conjectures in terms of "primitive coherent configurations." These are generalizations of s.r. graphs, relevant to the general GI problem. Another consequence of the main result is the strongest argument to date against GI-completeness of s.r. graphs: we prove that no polynomial-time categorical reduction of GI to isomorphism of s.r. graphs is possible. All known reductions between isomorphism problems of various classes of structures fit into our notion of "categorical reduction." The proof of the main result is elementary; it is based on known results in spectral graph theory and on a 1987 lemma on permutations by Ákos Seress and the author.
{"title":"On the automorphism groups of strongly regular graphs I","authors":"L. Babai","doi":"10.1145/2554797.2554830","DOIUrl":"https://doi.org/10.1145/2554797.2554830","url":null,"abstract":"We derive structural constraints on the automorphism groups of strongly regular (s.r.) graphs, giving a surprisingly strong answer to a decades-old problem, with tantalizing implications to testing isomorphism of s.r. graphs, and raising new combinatorial challenges. S.r. graphs, while not believed to be Graph Isomorphism (GI) complete, have long been recognized as hard cases for GI, and, in this author's view, present some of the core difficulties of the general GI problem. Progress on the complexity of testing their isomorphism has been intermittent (Babai 1980, Spielman 1996, BW & CST (STOC'13) and BCSTW (FOCS'13)), and the current best bound is exp(Õ(n1/5)) (n is the number of vertices). Our main result is that if X is a s.r. graph then, with straightforward exceptions, the degree of the largest alternating group involved in the automorphism group Aut(X) (as a quotient of a subgroup) is O((ln n)2ln ln n). (The exceptions admit trivial linear-time GI testing.) The design of isomorphism tests for various classes of structures is intimately connected with the study of the automorphism groups of those structures. We include a brief survey of these connections, starting with an 1869 paper by Jordan on trees. In particular, our result amplifies the potential of Luks's divide-and-conquer methods (1980) to be applicable to testing isomorphism of s.r. graphs in quasipolynomial time. The challenge remains to find a hierarchy of combinatorial substructures through which this potential can be realized. We expect that the generality of our result will help in this regard; the result applies not only to s.r. graphs but to all graphs with strong spectral expansion and with a relatively small number of common neighbors for every pair of vertices. We state a purely mathematical conjecture that could bring us closer to finding the right kind of hierarchy. We also outline the broader GI context, and state conjectures in terms of \"primitive coherent configurations.\" These are generalizations of s.r. graphs, relevant to the general GI problem. Another consequence of the main result is the strongest argument to date against GI-completeness of s.r. graphs: we prove that no polynomial-time categorical reduction of GI to isomorphism of s.r. graphs is possible. All known reductions between isomorphism problems of various classes of structures fit into our notion of \"categorical reduction.\" The proof of the main result is elementary; it is based on known results in spectral graph theory and on a 1987 lemma on permutations by Ákos Seress and the author.","PeriodicalId":382856,"journal":{"name":"Proceedings of the 5th conference on Innovations in theoretical computer science","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114299442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joshua Brody, S. K. Jakobsen, Dominik Scheder, P. Winkler
We consider the following cryptographic secret leaking problem. A group of players communicate with the goal of learning (and perhaps revealing) a secret held initially by one of them. Their conversation is monitored by a computationally unlimited eavesdropper, who wants to learn the identity of the secret-holder. Despite the unavailability of key, some protection can be provided to the identity of the secret-holder. We call the study of such communication problems, either from the group's or the eavesdropper's point of view, cryptogenography. We introduce a basic cryptogenography problem and show that two players can force the eavesdropper to missguess the origin of a secret bit with probability 1/3; we complement this with a hardness result showing that they cannot do better than than 3/8. We prove that larger numbers of players can do better than 0.5644, but no group of any size can achieve 0.75.
{"title":"Cryptogenography","authors":"Joshua Brody, S. K. Jakobsen, Dominik Scheder, P. Winkler","doi":"10.1145/2554797.2554800","DOIUrl":"https://doi.org/10.1145/2554797.2554800","url":null,"abstract":"We consider the following cryptographic secret leaking problem. A group of players communicate with the goal of learning (and perhaps revealing) a secret held initially by one of them. Their conversation is monitored by a computationally unlimited eavesdropper, who wants to learn the identity of the secret-holder. Despite the unavailability of key, some protection can be provided to the identity of the secret-holder. We call the study of such communication problems, either from the group's or the eavesdropper's point of view, cryptogenography. We introduce a basic cryptogenography problem and show that two players can force the eavesdropper to missguess the origin of a secret bit with probability 1/3; we complement this with a hardness result showing that they cannot do better than than 3/8. We prove that larger numbers of players can do better than 0.5644, but no group of any size can achieve 0.75.","PeriodicalId":382856,"journal":{"name":"Proceedings of the 5th conference on Innovations in theoretical computer science","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115003892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Session details: Session 9: 08:30--08:40","authors":"D. Wichs","doi":"10.1145/3255061","DOIUrl":"https://doi.org/10.1145/3255061","url":null,"abstract":"","PeriodicalId":382856,"journal":{"name":"Proceedings of the 5th conference on Innovations in theoretical computer science","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122916922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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