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Documents authored by Jakoby, Andreas

Document
DOI: 10.4230/LIPIcs.STACS.2012.66
Algorithmic Meta Theorems for Circuit Classes of Constant and Logarithmic Depth

Authors: Michael Elberfeld, Andreas Jakoby, and Till Tantau

Published in: LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

Abstract
An algorithmic meta theorem for a logic and a class C of structures states that all problems expressible in this logic can be solved efficiently for inputs from $C$. The prime example is Courcelle's Theorem, which states that monadic second-order (MSO) definable problems are linear-time solvable on graphs of bounded tree width. We contribute new algorithmic meta theorems, which state that MSO-definable problems are (a) solvable by uniform constant-depth circuit families (AC0 for decision problems and TC0 for counting problems) when restricted to input structures of bounded tree depth and (b) solvable by uniform logarithmic-depth circuit families (NC1 for decision problems and #NC1 for counting problems) when a tree decomposition of bounded width in term representation is part of the input. Applications of our theorems include a TC0-completeness proof for the unary version of integer linear programming with a fixed number of equations and extensions of a recent result that counting the number of accepting paths of a visible pushdown automaton lies in #NC1. Our main technical contributions are a new tree automata model for unordered, unranked, labeled trees; a method for representing the tree automata's computations algebraically using convolution circuits; and a lemma on computing balanced width-3 tree decompositions of trees in TC0, which encapsulates most of the technical difficulties surrounding earlier results connecting tree automata and NC1.
Cite as

Michael Elberfeld, Andreas Jakoby, and Till Tantau. Algorithmic Meta Theorems for Circuit Classes of Constant and Logarithmic Depth. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 66-77, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{elberfeld_et_al:LIPIcs.STACS.2012.66,
  author =	{Elberfeld, Michael and Jakoby, Andreas and Tantau, Till},
  title =	{{Algorithmic Meta Theorems for Circuit Classes of Constant and Logarithmic Depth}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{66--77},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{D\"{u}rr, Christoph and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.66},
  URN =		{urn:nbn:de:0030-drops-34059},
  doi =		{10.4230/LIPIcs.STACS.2012.66},
  annote =	{Keywords: algorithmic meta theorem, monadic second-order logic, circuit complexity, tree width, tree depth}
}
Document
DOI: 10.4230/DagSemProc.06111.6
Computing Shortest Paths in Series-Parallel Graphs in Logarithmic Space

Authors: Andreas Jakoby and Till Tantau

Published in: Dagstuhl Seminar Proceedings, Volume 6111, Complexity of Boolean Functions (2006)

Abstract
Series-parallel graphs, which are built by repeatedly applying series or parallel composition operations to paths, play an important role in computer science as they model the flow of information in many types of programs. For directed series-parallel graphs, we study the problem of finding a shortest path between two given vertices. Our main result is that we can find such a path in logarithmic space, which shows that the distance problem for series-parallel graphs is L-complete. Previously, it was known that one can compute some path in logarithmic space; but for other graph types, like undirected graphs or tournament graphs, constructing some path between given vertices is possible in logarithmic space while constructing a shortest path is NL-complete.
Cite as

Andreas Jakoby and Till Tantau. Computing Shortest Paths in Series-Parallel Graphs in Logarithmic Space. In Complexity of Boolean Functions. Dagstuhl Seminar Proceedings, Volume 6111, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{jakoby_et_al:DagSemProc.06111.6,
  author =	{Jakoby, Andreas and Tantau, Till},
  title =	{{Computing Shortest Paths in Series-Parallel Graphs in Logarithmic Space}},
  booktitle =	{Complexity of Boolean Functions},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6111},
  editor =	{Matthias Krause and Pavel Pudl\'{a}k and R\"{u}diger Reischuk and Dieter van Melkebeek},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06111.6},
  URN =		{urn:nbn:de:0030-drops-6185},
  doi =		{10.4230/DagSemProc.06111.6},
  annote =	{Keywords: Series-parallel graphs, shortest path, logspace}
}
Document
DOI: 10.4230/DagSemProc.06111.21
Using Quantum Oblivious Transfer to Cheat Sensitive Quantum Bit Commitment

Authors: Andreas Jakoby, Maciej Liskiewicz, and Aleksander Madry

Published in: Dagstuhl Seminar Proceedings, Volume 6111, Complexity of Boolean Functions (2006)

Abstract
We define $(varepsilon,delta)$-secure quantum computations between two parties that can play dishonestly to maximise advantage $delta$, however keeping small the probability $varepsilon$ that the computation fails in evaluating correct value. We present a simple quantum protocol for computing one-out-of-two oblivious transfer that is $(O(sqrt{varepsilon}),varepsilon)$-secure. Using the protocol as a black box we construct a scheme for cheat sensitive quantum bit commitment which guarantee that a mistrustful party has a nonzero probability of detecting a cheating.
Cite as

Andreas Jakoby, Maciej Liskiewicz, and Aleksander Madry. Using Quantum Oblivious Transfer to Cheat Sensitive Quantum Bit Commitment. In Complexity of Boolean Functions. Dagstuhl Seminar Proceedings, Volume 6111, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{jakoby_et_al:DagSemProc.06111.21,
  author =	{Jakoby, Andreas and Liskiewicz, Maciej and Madry, Aleksander},
  title =	{{Using Quantum Oblivious Transfer to Cheat Sensitive Quantum Bit Commitment}},
  booktitle =	{Complexity of Boolean Functions},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6111},
  editor =	{Matthias Krause and Pavel Pudl\'{a}k and R\"{u}diger Reischuk and Dieter van Melkebeek},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06111.21},
  URN =		{urn:nbn:de:0030-drops-6223},
  doi =		{10.4230/DagSemProc.06111.21},
  annote =	{Keywords: Two-Party Computations, Quantum Protocols, Bit Commitment, Oblivious Transfer.}
}
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