Dagstuhl Seminar Proceedings, Volume 6451
Dagstuhl Seminar Proceedings
DagSemProc
https://www.dagstuhl.de/dagpub/1862-4405
https://dblp.org/db/series/dagstuhl
1862-4405
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
6451
2007
https://drops.dagstuhl.de/entities/volume/DagSemProc-volume-6451
06451 Abstracts Collection – Circuits, Logic, and Games
From 08.11.06 to 10.11.06, the Dagstuhl Seminar 06451 ``Circuits, Logic, and Games'' was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.
Computational complexity theory
finite model theory
Boolean circuits
regular languages
finite monoids
Ehrenfeucht-Fra\"{\i}ss\'{e} games
1-10
Regular Paper
Thomas
Schwentick
Thomas Schwentick
Denis
Thérien
Denis Thérien
Heribert
Vollmer
Heribert Vollmer
10.4230/DagSemProc.06451.1
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06451 Executive Summary – Circuits, Logic, and Games
In this document we describe the original motivation and goals of the seminar as well as the sequence of talks given during the seminar.
Circuits
Logics
Games
1-3
Regular Paper
Thomas
Schwentick
Thomas Schwentick
Denis
Thérien
Denis Thérien
Heribert
Vollmer
Heribert Vollmer
10.4230/DagSemProc.06451.2
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A note on the size of Craig Interpolants
Mundici considered the question of whether the interpolant of two
propositional formulas of the form $F
ightarrow G$ can always have
a short circuit description, and showed that if this is the case then
every problem in NP $cap$ co-NP would have polynomial size circuits.
In this note we observe further consequences of the interpolant having
short circuit descriptions, namely that
UP $subseteq$ P$/$poly, and that every single valued NP function has a
total extension in FP$/$poly. We also relate
this question with other
Complexity Theory assumptions.
Interpolant
non-uniform complexity
1-9
Regular Paper
Uwe
Schöning
Uwe Schöning
Jacobo
Torán
Jacobo Torán
10.4230/DagSemProc.06451.3
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Counting Results in Weak Formalisms
The counting ability of weak formalisms is of interest as a measure of their expressive
power. The question was investigated in the 1980's in several papers in complexity theory and in weak arithmetic. In each case, the considered formalism (AC$^0$--circuits, first--order logic, $Delta_0$, respectively) was shown to be able to count precisely up to a polylogarithmic number. An essential part of each of the proofs is the construction of a 1--1
mapping from a small subset of ${0,ldots,N-1}$ into a small initial segment. In each case the expressibility of such a mapping depends on some strong argument (group theoretic device or prime number theorem) or intricate construction. We present a coding device based on a collision-free hashing technique, leading to a completely elementary proof for the polylog counting capability of first--order logic (with built--in arithmetic), $AC^0$--circuits, rudimentary arithmetic, the Linear Hierarchy, and monadic--second order logic with addition.
Small complexity classes
logic
polylog counting
1-11
Regular Paper
Arnaud
Durand
Arnaud Durand
Clemens
Lautemann
Clemens Lautemann
Malika
More
Malika More
10.4230/DagSemProc.06451.4
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Some Algebraic Problems with Connections to Circuit Complexity of Dynamic Data Structures
While researching dynamic data structures of polynomial size that
are updated by extremely simple circuits, we have come across
many interesting algebraic problems. Some of these simple
questions about small sums and products in an algebra would
give lower bounds on the complexity of dynamic data structures.
Boolean Functions
auxiliary data
circuit complexity
lower bounds
1-3
Regular Paper
William
Hesse
William Hesse
10.4230/DagSemProc.06451.5
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Structure Theorem and Strict Alternation Hierarchy for FOÃ‚Â² on Words
It is well-known that every first-order property on words is
expressible using at most three variables. The subclass of properties
expressible with only two variables is also quite interesting and
well-studied. We prove precise structure
theorems that characterize the exact expressive power of first-order
logic with two variables on words. Our results apply to
FO$^2[<]$ and FO$^2[<,suc]$, the latter of which includes the
binary successor relation in addition to the linear ordering on
string positions.
For both languages, our structure theorems show exactly what is
expressible using a given quantifier depth, $n$, and using $m$ blocks
of alternating quantifiers, for any $mleq n$. Using these
characterizations, we prove, among other results, that there is a
strict hierarchy of alternating quantifiers for both languages. The
question whether there was such a hierarchy had been completely open
since it was asked in [Etessami, Vardi, and Wilke 1997].
Descriptive complexity
finite model theory
alternation hierarchy
Ehrenfeucht-Fraisse games
1-22
Regular Paper
Philipp
Weis
Philipp Weis
Neil
Immerman
Neil Immerman
10.4230/DagSemProc.06451.6
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