227 research outputs found
Probabilistic Model Counting with Short XORs
The idea of counting the number of satisfying truth assignments (models) of a
formula by adding random parity constraints can be traced back to the seminal
work of Valiant and Vazirani, showing that NP is as easy as detecting unique
solutions. While theoretically sound, the random parity constraints in that
construction have the following drawback: each constraint, on average, involves
half of all variables. As a result, the branching factor associated with
searching for models that also satisfy the parity constraints quickly gets out
of hand. In this work we prove that one can work with much shorter parity
constraints and still get rigorous mathematical guarantees, especially when the
number of models is large so that many constraints need to be added. Our work
is based on the realization that the essential feature for random systems of
parity constraints to be useful in probabilistic model counting is that the
geometry of their set of solutions resembles an error-correcting code.Comment: To appear in SAT 1
Precise Complexity of the Core in Dichotomous and Additive Hedonic Games
Hedonic games provide a general model of coalition formation, in which a set
of agents is partitioned into coalitions, with each agent having preferences
over which other players are in her coalition. We prove that with additively
separable preferences, it is -complete to decide whether a core- or
strict-core-stable partition exists, extending a result of Woeginger (2013).
Our result holds even if valuations are symmetric and non-zero only for a
constant number of other agents. We also establish -completeness of
deciding non-emptiness of the strict core for hedonic games with dichotomous
preferences. Such results establish that the core is much less tractable than
solution concepts such as individual stability.Comment: ADT-2017, 15 pages in LNCS styl
Descriptive Complexity of Deterministic Polylogarithmic Time and Space
We propose logical characterizations of problems solvable in deterministic
polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We
introduce a novel two-sorted logic that separates the elements of the input
domain from the bit positions needed to address these elements. We prove that
the inflationary and partial fixed point vartiants of this logic capture
PolylogTime and PolylogSpace, respectively. In the course of proving that our
logic indeed captures PolylogTime on finite ordered structures, we introduce a
variant of random-access Turing machines that can access the relations and
functions of a structure directly. We investigate whether an explicit predicate
for the ordering of the domain is needed in our PolylogTime logic. Finally, we
present the open problem of finding an exact characterization of
order-invariant queries in PolylogTime.Comment: Submitted to the Journal of Computer and System Science
Improving Strategies via SMT Solving
We consider the problem of computing numerical invariants of programs by
abstract interpretation. Our method eschews two traditional sources of
imprecision: (i) the use of widening operators for enforcing convergence within
a finite number of iterations (ii) the use of merge operations (often, convex
hulls) at the merge points of the control flow graph. It instead computes the
least inductive invariant expressible in the domain at a restricted set of
program points, and analyzes the rest of the code en bloc. We emphasize that we
compute this inductive invariant precisely. For that we extend the strategy
improvement algorithm of [Gawlitza and Seidl, 2007]. If we applied their method
directly, we would have to solve an exponentially sized system of abstract
semantic equations, resulting in memory exhaustion. Instead, we keep the system
implicit and discover strategy improvements using SAT modulo real linear
arithmetic (SMT). For evaluating strategies we use linear programming. Our
algorithm has low polynomial space complexity and performs for contrived
examples in the worst case exponentially many strategy improvement steps; this
is unsurprising, since we show that the associated abstract reachability
problem is Pi-p-2-complete
Удаление сернистых соединений из дизельных топлив с использованием металлосодержащих ионных жидкостей
Данная статья посвящена проблеме удаления сернистых соединений из дизельных топлив. Представлены характеристики полученных экстракционных систем на основе ионных жидкостей и солей металлов (СuBr[2], CoBr[2], NiBr[2]). Показана возможность использования комплексов ионных жидкостей с солями металлов в качестве экстрагентов для удаления серы из дизельного топлива
An operator representation for Matsubara sums
In the context of the imaginary-time formalism for a scalar thermal field
theory, it is shown that the result of performing the sums over Matsubara
frequencies associated with loop Feynman diagrams can be written, for some
classes of diagrams, in terms of the action of a simple linear operator on the
corresponding energy integrals of the Euclidean theory at T=0. In its simplest
form the referred operator depends only on the number of internal propagators
of the graph.
More precisely, it is shown explicitly that this \emph{thermal operator
representation} holds for two generic classes of diagrams, namely, the
two-vertex diagram with an arbitrary number of internal propagators, and the
one-loop diagram with an arbitrary number of vertices.
The validity of the thermal operator representation for diagrams of more
complicated topologies remains an open problem. Its correctness is shown to be
equivalent to the correctness of some diagrammatic rules proposed a few years
ago.Comment: 4 figures; references added, minor changes in notation, final version
accepted for publicatio
Randomisation and Derandomisation in Descriptive Complexity Theory
We study probabilistic complexity classes and questions of derandomisation
from a logical point of view. For each logic L we introduce a new logic BPL,
bounded error probabilistic L, which is defined from L in a similar way as the
complexity class BPP, bounded error probabilistic polynomial time, is defined
from PTIME. Our main focus lies on questions of derandomisation, and we prove
that there is a query which is definable in BPFO, the probabilistic version of
first-order logic, but not in Cinf, finite variable infinitary logic with
counting. This implies that many of the standard logics of finite model theory,
like transitive closure logic and fixed-point logic, both with and without
counting, cannot be derandomised. Similarly, we present a query on ordered
structures which is definable in BPFO but not in monadic second-order logic,
and a query on additive structures which is definable in BPFO but not in FO.
The latter of these queries shows that certain uniform variants of AC0
(bounded-depth polynomial sized circuits) cannot be derandomised. These results
are in contrast to the general belief that most standard complexity classes can
be derandomised. Finally, we note that BPIFP+C, the probabilistic version of
fixed-point logic with counting, captures the complexity class BPP, even on
unordered structures
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
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