3 Search Results for "van der Hoeven, Joris"

Document
DOI: 10.4230/LIPIcs.CONCUR.2024.18
Weighted Basic Parallel Processes and Combinatorial Enumeration

Authors: Lorenzo Clemente

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We study weighted basic parallel processes (WBPP), a nonlinear recursive generalisation of weighted finite automata inspired from process algebra and Petri net theory. Our main result is an algorithm of 2-EXPSPACE complexity for the WBPP equivalence problem. While (unweighted) BPP language equivalence is undecidable, we can use this algorithm to decide multiplicity equivalence of BPP and language equivalence of unambiguous BPP, with the same complexity. These are long-standing open problems for the related model of weighted context-free grammars. Our second contribution is a connection between WBPP, power series solutions of systems of polynomial differential equations, and combinatorial enumeration. To this end we consider constructible differentially finite power series (CDF), a class of multivariate differentially algebraic series introduced by Bergeron and Reutenauer in order to provide a combinatorial interpretation to differential equations. CDF series generalise rational, algebraic, and a large class of D-finite (holonomic) series, for which no complexity upper bound for equivalence was known. We show that CDF series correspond to commutative WBPP series. As a consequence of our result on WBPP and commutativity, we show that equivalence of CDF power series can be decided with 2-EXPTIME complexity. In order to showcase the CDF equivalence algorithm, we show that CDF power series naturally arise from combinatorial enumeration, namely as the exponential generating series of constructible species of structures. Examples of such species include sequences, binary trees, ordered trees, Cayley trees, set partitions, series-parallel graphs, and many others. As a consequence of this connection, we obtain an algorithm to decide multiplicity equivalence of constructible species, decidability of which was not known before. The complexity analysis is based on effective bounds from algebraic geometry, namely on the length of chains of polynomial ideals constructed by repeated application of finitely many, not necessarily commuting derivations of a multivariate polynomial ring. This is obtained by generalising a result of Novikov and Yakovenko in the case of a single derivation, which is noteworthy since generic bounds on ideal chains are non-primitive recursive in general. On the way, we develop the theory of WBPP series and CDF power series, exposing several of their appealing properties.
Cite as

Lorenzo Clemente. Weighted Basic Parallel Processes and Combinatorial Enumeration. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{clemente:LIPIcs.CONCUR.2024.18,
  author =	{Clemente, Lorenzo},
  title =	{{Weighted Basic Parallel Processes and Combinatorial Enumeration}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.18},
  URN =		{urn:nbn:de:0030-drops-207903},
  doi =		{10.4230/LIPIcs.CONCUR.2024.18},
  annote =	{Keywords: weighted automata, combinatorial enumeration, shuffle, algebraic differential equations, process algebra, basic parallel processes, species of structures}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.20
Better Space-Time-Robustness Trade-Offs for Set Reconciliation

Authors: Djamal Belazzougui, Gregory Kucherov, and Stefan Walzer

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider the problem of reconstructing the symmetric difference between similar sets from their representations (sketches) of size linear in the number of differences. Exact solutions to this problem are based on error-correcting coding techniques and suffer from a large decoding time. Existing probabilistic solutions based on Invertible Bloom Lookup Tables (IBLTs) are time-efficient but offer insufficient success guarantees for many applications. Here we propose a tunable trade-off between the two approaches combining the efficiency of IBLTs with exponentially decreasing failure probability. The proof relies on a refined analysis of IBLTs proposed in (Bæk Tejs Houen et al. SOSA 2023) which has an independent interest. We also propose a modification of our algorithm that enables telling apart the elements of each set in the symmetric difference.
Cite as

Djamal Belazzougui, Gregory Kucherov, and Stefan Walzer. Better Space-Time-Robustness Trade-Offs for Set Reconciliation. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{belazzougui_et_al:LIPIcs.ICALP.2024.20,
  author =	{Belazzougui, Djamal and Kucherov, Gregory and Walzer, Stefan},
  title =	{{Better Space-Time-Robustness Trade-Offs for Set Reconciliation}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{20:1--20:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.20},
  URN =		{urn:nbn:de:0030-drops-201639},
  doi =		{10.4230/LIPIcs.ICALP.2024.20},
  annote =	{Keywords: data structures, hashing, set reconciliation, invertible Bloom lookup tables, random hypergraphs, BCH codes}
}
Document
DOI: 10.4230/DagSemProc.06271.10
GNU TeXmacs

Authors: Joris van der Hoeven

Published in: Dagstuhl Seminar Proceedings, Volume 6271, Challenges in Symbolic Computation Software (2006)

Abstract
GNU TeXmacs is a free scientific editing platform with special features for mathematicians. The editor can be used to produce documents with a professional typesetting quality (better than TeX/LaTeX) via a user-friendly front-end. The editor can be used as a front-end to several computer algebra systems and includes a lot of additional facilities, like a presentation mode, a technical picture editor, a typed linking tool, etc. The editor can be extended by users in several ways: using style files, plug-ins or via the Scheme extension language. Converters exist for LaTeX, Xhtml and MathML.
Cite as

Joris van der Hoeven. GNU TeXmacs. In Challenges in Symbolic Computation Software. Dagstuhl Seminar Proceedings, Volume 6271, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{vanderhoeven:DagSemProc.06271.10,
  author =	{van der Hoeven, Joris},
  title =	{{GNU TeXmacs}},
  booktitle =	{Challenges in Symbolic Computation Software},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6271},
  editor =	{Wolfram Decker and Mike Dewar and Erich Kaltofen and Stephen Watt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06271.10},
  URN =		{urn:nbn:de:0030-drops-7672},
  doi =		{10.4230/DagSemProc.06271.10},
  annote =	{Keywords: Scientific text editor, Mathematics, Computer algebra system, Front-end}
}
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