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DOI: 10.4230/LIPIcs.STACS.2018.31

Automata Theory on Sliding Windows

Authors: Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract

In a recent paper we analyzed the space complexity of streaming algorithms whose goal is to decide membership of a sliding window to a fixed language. For the class of regular languages we proved a space trichotomy theorem: for every regular language the optimal space bound is either constant, logarithmic or linear. In this paper we continue this line of research: We present natural characterizations for the constant and logarithmic space classes and establish tight relationships to the concept of language growth. We also analyze the space complexity with respect to automata size and prove almost matching lower and upper bounds. Finally, we consider the decision problem whether a language given by a DFA/NFA admits a sliding window algorithm using logarithmic/constant space.

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Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras. Automata Theory on Sliding Windows. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2018.31,
  author =	{Ganardi, Moses and Hucke, Danny and K\"{o}nig, Daniel and Lohrey, Markus and Mamouras, Konstantinos},
  title =	{{Automata Theory on Sliding Windows}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.31},
  URN =		{urn:nbn:de:0030-drops-84851},
  doi =		{10.4230/LIPIcs.STACS.2018.31},
  annote =	{Keywords: regular languages, sliding window algorithms}
}

Document

DOI: 10.4230/LIPIcs.ICALP.2017.112

Automata-Based Stream Processing

Authors: Rajeev Alur, Konstantinos Mamouras, and Caleb Stanford

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract

We propose an automata-theoretic framework for modularly expressing computations on streams of data. With weighted automata as a starting point, we identify three key features that are useful for an automaton model for stream processing: expressing the regular decomposition of streams whose data items are elements of a complex type (e.g., tuple of values), allowing the hierarchical nesting of several different kinds of aggregations, and specifying modularly the parallel execution and combination of various subcomputations. The combination of these features leads to subtle efficiency considerations that concern the interaction between nondeterminism, hierarchical nesting, and parallelism. We identify a syntactic restriction where the nondeterminism is unambiguous and parallel subcomputations synchronize their outputs. For automata satisfying these restrictions, we show that there is a space- and time-efficient streaming evaluation algorithm. We also prove that when these restrictions are relaxed, the evaluation problem becomes inherently computationally expensive.

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Rajeev Alur, Konstantinos Mamouras, and Caleb Stanford. Automata-Based Stream Processing. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{alur_et_al:LIPIcs.ICALP.2017.112,
  author =	{Alur, Rajeev and Mamouras, Konstantinos and Stanford, Caleb},
  title =	{{Automata-Based Stream Processing}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{112:1--112:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.112},
  URN =		{urn:nbn:de:0030-drops-74720},
  doi =		{10.4230/LIPIcs.ICALP.2017.112},
  annote =	{Keywords: weighted automata, Quantitative Regular Expressions, stream processing}
}

Document

DOI: 10.4230/LIPIcs.CSL.2013.415

Kleene Algebra with Products and Iteration Theories

Authors: Dexter Kozen and Konstantinos Mamouras

Published in: LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)

Abstract

We develop a typed equational system that subsumes both iteration theories and typed Kleene algebra in a common framework. Our approach is based on cartesian categories endowed with commutative strong monads to handle nondeterminism.

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Dexter Kozen and Konstantinos Mamouras. Kleene Algebra with Products and Iteration Theories. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 415-431, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{kozen_et_al:LIPIcs.CSL.2013.415,
  author =	{Kozen, Dexter and Mamouras, Konstantinos},
  title =	{{Kleene Algebra with Products and Iteration Theories}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{415--431},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Ronchi Della Rocca, Simona},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.415},
  URN =		{urn:nbn:de:0030-drops-42111},
  doi =		{10.4230/LIPIcs.CSL.2013.415},
  annote =	{Keywords: Kleene algebra, typed Kleene algebra, iteration theories}
}

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Documents authored by Mamouras, Konstantinos

Automata Theory on Sliding Windows

Abstract

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Automata-Based Stream Processing

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Kleene Algebra with Products and Iteration Theories

Abstract

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