41,722 research outputs found
The model-theoretic complexity of automatic linear orders
Automatic structures are—possibly infinite—structures which are finitely presentable by means of finite automata on strings or trees. Largely motivated by the fact that their first-order theories are uniformly decidable, automatic structures gained a lot of attention in the "logic in computer science" community during the last fifteen years. This thesis studies the model-theoretic complexity of automatic linear orders in terms of two complexity measures: the finite-condensation rank and the Ramsey degree. The former is an ordinal which indicates how far a linear order is away from being dense. The corresponding main results establish optimal upper bounds on this rank with respect to several notions of automaticity. The Ramsey degree measures the model-theoretic complexity of well-orders by means of the partition relations studied in combinatorial set theory. This concept is investigated in a purely set-theoretic setting as well as in the context of automatic structures.Auch im Buchhandel erhältlich:
The model-theoretic complexity of automatic linear orders / Martin Huschenbett
Ilmenau : Univ.-Verl. Ilmenau, 2016. - xiii, 228 Seiten
ISBN 978-3-86360-127-0
Preis (Druckausgabe): 16,50
Towards a complexity theory for the congested clique
The congested clique model of distributed computing has been receiving
attention as a model for densely connected distributed systems. While there has
been significant progress on the side of upper bounds, we have very little in
terms of lower bounds for the congested clique; indeed, it is now know that
proving explicit congested clique lower bounds is as difficult as proving
circuit lower bounds.
In this work, we use various more traditional complexity-theoretic tools to
build a clearer picture of the complexity landscape of the congested clique:
-- Nondeterminism and beyond: We introduce the nondeterministic congested
clique model (analogous to NP) and show that there is a natural canonical
problem family that captures all problems solvable in constant time with
nondeterministic algorithms. We further generalise these notions by introducing
the constant-round decision hierarchy (analogous to the polynomial hierarchy).
-- Non-constructive lower bounds: We lift the prior non-uniform counting
arguments to a general technique for proving non-constructive uniform lower
bounds for the congested clique. In particular, we prove a time hierarchy
theorem for the congested clique, showing that there are decision problems of
essentially all complexities, both in the deterministic and nondeterministic
settings.
-- Fine-grained complexity: We map out relationships between various natural
problems in the congested clique model, arguing that a reduction-based
complexity theory currently gives us a fairly good picture of the complexity
landscape of the congested clique
Edge distribution and density in the characteristic sequence
The characteristic sequence of hypergraphs associated to a
formula , introduced in [arXiv:0908.4111], is defined by
. This paper
continues the study of characteristic sequences, showing that graph-theoretic
techniques, notably Szemer\'edi's celebrated regularity lemma, can be naturally
applied to the study of model-theoretic complexity via the characteristic
sequence. Specifically, we relate classification-theoretic properties of
and of the (considered as formulas) to density between components in
Szemer\'edi-regular decompositions of graphs in the characteristic sequence. In
addition, we use Szemer\'edi regularity to calibrate model-theoretic notions of
independence by describing the depth of independence of a constellation of sets
and showing that certain failures of depth imply Shelah's strong order property
; this sheds light on the interplay of independence and order in
unstable theories
The prospects for mathematical logic in the twenty-first century
The four authors present their speculations about the future developments of
mathematical logic in the twenty-first century. The areas of recursion theory,
proof theory and logic for computer science, model theory, and set theory are
discussed independently.Comment: Association for Symbolic Logi
The tractability frontier of graph-like first-order query sets
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this problem is tractable, in the sense of parameterized complexity theory. To this end, we define the notion of a graph-like sentence set, which definition is inspired by previous work on first-order model checking wherein the permitted connectives and quantifiers were restricted. Our main theorem is the complete tractability classification of such graphlike sentence sets, which is (to our knowledge) the first complexity classification theorem concerning a class of sentences that has no restriction on the connectives and quantifiers. To present and prove our classification, we introduce and develop a novel complexity-theoretic framework which is built on parameterized complexity and includes new notions of reduction
A Game Theoretic Approach to Computer Science: Survey and Research Directions
Theoretical Computer Science classically aimed to develop a mathematical understanding of capabilities and limits of traditional computing architecture (Boole, von Neuman, Turing, Church, Godel), investigating in computability, complexity theory and algorithmics. Now it seems more natural to revisit classical computer science notions under a new game- theoretic model. The purpose of this work is to investigate some themes at the intersection of algorithmics and game theory, emphasizing both mathematical and technological issues.computer science, game theory, network, protocol
Models of Bounded Arithmetic Theories and Some Related Complexity Questions
In this paper, we study bounded versions of some model-theoretic notions and results. We apply these results to the context of models of bounded arithmetic theories as well as some related complexity questions. As an example, we show that if the theory has bounded model companion then . We also study bounded versions of some other related notions such as Stone topology
Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence
Recently, it has been shown that probabilistic entailment under coherence is
weaker than model-theoretic probabilistic entailment. Moreover, probabilistic
entailment under coherence is a generalization of default entailment in System
P. In this paper, we continue this line of research by presenting probabilistic
generalizations of more sophisticated notions of classical default entailment
that lie between model-theoretic probabilistic entailment and probabilistic
entailment under coherence. That is, the new formalisms properly generalize
their counterparts in classical default reasoning, they are weaker than
model-theoretic probabilistic entailment, and they are stronger than
probabilistic entailment under coherence. The new formalisms are useful
especially for handling probabilistic inconsistencies related to conditioning
on zero events. They can also be applied for probabilistic belief revision.
More generally, in the same spirit as a similar previous paper, this paper
sheds light on exciting new formalisms for probabilistic reasoning beyond the
well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on
Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks
in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200
- …