5 Search Results for "Angluin, Dana"


Document
Approximate Majority with Catalytic Inputs

Authors: Talley Amir, James Aspnes, and John Lazarsfeld

Published in: LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)


Abstract
Population protocols [Dana Angluin et al., 2006] are a class of algorithms for modeling distributed computation in networks of finite-state agents communicating through pairwise interactions. Their suitability for analyzing numerous chemical processes has motivated the adaptation of the original population protocol framework to better model these chemical systems. In this paper, we further the study of two such adaptations in the context of solving approximate majority: persistent-state agents (or catalysts) and spontaneous state changes (or leaks). Based on models considered in recent protocols for populations with persistent-state agents [Bartlomiej Dudek and Adrian Kosowski, 2018; Alistarh et al., 2017; Dan Alistarh et al., 2020], we assume a population with n catalytic input agents and m worker agents, and the goal of the worker agents is to compute some predicate over the states of the catalytic inputs. We call this model the Catalytic Input (CI) model. For m = Θ(n), we show that computing the parity of the input population with high probability requires at least Ω(n²) total interactions, demonstrating a strong separation between the CI model and the standard population protocol model. On the other hand, we show that the simple third-state dynamics [Angluin et al., 2008; Perron et al., 2009] for approximate majority in the standard model can be naturally adapted to the CI model: we present such a constant-state protocol for the CI model that solves approximate majority in O(n log n) total steps with high probability when the input margin is Ω(√{n log n}). We then show the robustness of third-state dynamics protocols to the transient leaks events introduced by [Alistarh et al., 2017; Dan Alistarh et al., 2020]. In both the original and CI models, these protocols successfully compute approximate majority with high probability in the presence of leaks occurring at each step with probability β ≤ O(√{n log n}/n). The resilience of these dynamics to leaks exhibits similarities to previous work involving Byzantine agents, and we define and prove a notion of equivalence between the two.

Cite as

Talley Amir, James Aspnes, and John Lazarsfeld. Approximate Majority with Catalytic Inputs. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{amir_et_al:LIPIcs.OPODIS.2020.19,
  author =	{Amir, Talley and Aspnes, James and Lazarsfeld, John},
  title =	{{Approximate Majority with Catalytic Inputs}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Bramas, Quentin and Oshman, Rotem and Romano, Paolo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.19},
  URN =		{urn:nbn:de:0030-drops-135040},
  doi =		{10.4230/LIPIcs.OPODIS.2020.19},
  annote =	{Keywords: population protocols, approximate majority, catalysts, leaks, lower bound}
}
Document
Succinct Population Protocols for Presburger Arithmetic

Authors: Michael Blondin, Javier Esparza, Blaise Genest, Martin Helfrich, and Stefan Jaax

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)


Abstract
In [Dana Angluin et al., 2006], Angluin et al. proved that population protocols compute exactly the predicates definable in Presburger arithmetic (PA), the first-order theory of addition. As part of this result, they presented a procedure that translates any formula φ of quantifier-free PA with remainder predicates (which has the same expressive power as full PA) into a population protocol with 2^?(poly(|φ|)) states that computes φ. More precisely, the number of states of the protocol is exponential in both the bit length of the largest coefficient in the formula, and the number of nodes of its syntax tree. In this paper, we prove that every formula φ of quantifier-free PA with remainder predicates is computable by a leaderless population protocol with ?(poly(|φ|)) states. Our proof is based on several new constructions, which may be of independent interest. Given a formula φ of quantifier-free PA with remainder predicates, a first construction produces a succinct protocol (with ?(|φ|³) leaders) that computes φ; this completes the work initiated in [Michael Blondin et al., 2018], where we constructed such protocols for a fragment of PA. For large enough inputs, we can get rid of these leaders. If the input is not large enough, then it is small, and we design another construction producing a succinct protocol with one leader that computes φ. Our last construction gets rid of this leader for small inputs.

Cite as

Michael Blondin, Javier Esparza, Blaise Genest, Martin Helfrich, and Stefan Jaax. Succinct Population Protocols for Presburger Arithmetic. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 40:1-40:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{blondin_et_al:LIPIcs.STACS.2020.40,
  author =	{Blondin, Michael and Esparza, Javier and Genest, Blaise and Helfrich, Martin and Jaax, Stefan},
  title =	{{Succinct Population Protocols for Presburger Arithmetic}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{40:1--40:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.40},
  URN =		{urn:nbn:de:0030-drops-119018},
  doi =		{10.4230/LIPIcs.STACS.2020.40},
  annote =	{Keywords: Population protocols, Presburger arithmetic, state complexity}
}
Document
Strongly Unambiguous Büchi Automata Are Polynomially Predictable With Membership Queries

Authors: Dana Angluin, Timos Antonopoulos, and Dana Fisman

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)


Abstract
A Büchi automaton is strongly unambiguous if every word w ∈ Σ^ω has at most one final path. Many properties of strongly unambiguous Büchi automata (SUBAs) are known. They are fully expressive: every regular ω-language can be represented by a SUBA. Equivalence and containment of SUBAs can be decided in polynomial time. SUBAs may be exponentially smaller than deterministic Muller automata and may be exponentially bigger than deterministic Büchi automata. In this work we show that SUBAs can be learned in polynomial time using membership and certain non-proper equivalence queries, which implies that they are polynomially predictable with membership queries. In contrast, under plausible cryptographic assumptions, non-deterministic Büchi automata are not polynomially predictable with membership queries.

Cite as

Dana Angluin, Timos Antonopoulos, and Dana Fisman. Strongly Unambiguous Büchi Automata Are Polynomially Predictable With Membership Queries. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{angluin_et_al:LIPIcs.CSL.2020.8,
  author =	{Angluin, Dana and Antonopoulos, Timos and Fisman, Dana},
  title =	{{Strongly Unambiguous B\"{u}chi Automata Are Polynomially Predictable With Membership Queries}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.8},
  URN =		{urn:nbn:de:0030-drops-116519},
  doi =		{10.4230/LIPIcs.CSL.2020.8},
  annote =	{Keywords: Polynomially predictable languages, Automata learning, Strongly unambiguous B\"{u}chi automata, Automata succinctness, Regular \omega-languages, Grammatical inference}
}
Document
Query Learning of Derived Omega-Tree Languages in Polynomial Time

Authors: Dana Angluin, Timos Antonopoulos, and Dana Fisman

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)


Abstract
We present the first polynomial time algorithm to learn nontrivial classes of languages of infinite trees. Specifically, our algorithm uses membership and equivalence queries to learn classes of omega-tree languages derived from weak regular omega-word languages in polynomial time. The method is a general polynomial time reduction of learning a class of derived omega-tree languages to learning the underlying class of omega-word languages, for any class of omega-word languages recognized by a deterministic Büchi acceptor. Our reduction, combined with the polynomial time learning algorithm of Maler and Pnueli [Maler and Pneuli, Inform. Comput., 1995] for the class of weak regular omega-word languages yields the main result. We also show that subset queries that return counterexamples can be implemented in polynomial time using subset queries that return no counterexamples for deterministic or non-deterministic finite word acceptors, and deterministic or non-deterministic Büchi omega-word acceptors. A previous claim of an algorithm to learn regular omega-trees due to Jayasrirani, Begam and Thomas [Jayasrirani et al., ICGI, 2008] is unfortunately incorrect, as shown in [Angluin, YALEU/DCS/TR-1528, 2016].

Cite as

Dana Angluin, Timos Antonopoulos, and Dana Fisman. Query Learning of Derived Omega-Tree Languages in Polynomial Time. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{angluin_et_al:LIPIcs.CSL.2017.10,
  author =	{Angluin, Dana and Antonopoulos, Timos and Fisman, Dana},
  title =	{{Query Learning of Derived Omega-Tree Languages in Polynomial Time}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.10},
  URN =		{urn:nbn:de:0030-drops-77022},
  doi =		{10.4230/LIPIcs.CSL.2017.10},
  annote =	{Keywords: Learning, queries, infinite trees, derived tree languages, reactive systems}
}
Document
Families of DFAs as Acceptors of omega-Regular Languages

Authors: Dana Angluin, Udi Boker, and Dana Fisman

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)


Abstract
Families of DFAs (FDFAs) provide an alternative formalism for recognizing omega-regular languages. The motivation for introducing them was a desired correlation between the automaton states and right congruence relations, in a manner similar to the Myhill-Nerode theorem for regular languages. This correlation is beneficial for learning algorithms, and indeed it was recently shown that omega-regular languages can be learned from membership and equivalence queries, using FDFAs as the acceptors. In this paper, we look into the question of how suitable FDFAs are for defining omega-regular languages. Specifically, we look into the complexity of performing Boolean operations, such as complementation and intersection, on FDFAs, the complexity of solving decision problems, such as emptiness and language containment, and the succinctness of FDFAs compared to standard deterministic and nondeterministic omega-automata. We show that FDFAs enjoy the benefits of deterministic automata with respect to Boolean operations and decision problems. Namely, they can all be performed in nondeterministic logarithmic space. We provide polynomial translations of deterministic Buchi and coBuchi automata to FDFAs and of FDFAs to nondeterministic Buchi automata (NBAs). We show that translation of an NBA to an FDFA may involve an exponential blowup. Last, we show that FDFAs are more succinct than deterministic parity automata (DPAs) in the sense that translating a DPA to an FDFA can always be done with only a polynomial increase, yet the other direction involves an inevitable exponential blowup in the worst case.

Cite as

Dana Angluin, Udi Boker, and Dana Fisman. Families of DFAs as Acceptors of omega-Regular Languages. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{angluin_et_al:LIPIcs.MFCS.2016.11,
  author =	{Angluin, Dana and Boker, Udi and Fisman, Dana},
  title =	{{Families of DFAs as Acceptors of omega-Regular Languages}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{11:1--11:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.11},
  URN =		{urn:nbn:de:0030-drops-64274},
  doi =		{10.4230/LIPIcs.MFCS.2016.11},
  annote =	{Keywords: finite automata, omega regular languages}
}
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