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

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.

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

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

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.

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

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

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.

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.} }