674,059 research outputs found
Fragments of first-order logic over infinite words
We give topological and algebraic characterizations as well as language
theoretic descriptions of the following subclasses of first-order logic FO[<]
for omega-languages: Sigma_2, FO^2, the intersection of FO^2 and Sigma_2, and
Delta_2 (and by duality Pi_2 and the intersection of FO^2 and Pi_2). These
descriptions extend the respective results for finite words. In particular, we
relate the above fragments to language classes of certain (unambiguous)
polynomials. An immediate consequence is the decidability of the membership
problem of these classes, but this was shown before by Wilke and Bojanczyk and
is therefore not our main focus. The paper is about the interplay of algebraic,
topological, and language theoretic properties.Comment: Conference version presented at 26th International Symposium on
Theoretical Aspects of Computer Science, STACS 200
Improving files availability for BitTorrent using a diffusion model
The BitTorrent mechanism effectively spreads file fragments by copying the
rarest fragments first. We propose to apply a mathematical model for the
diffusion of fragments on a P2P in order to take into account both the effects
of peer distances and the changing availability of peers while time goes on.
Moreover, we manage to provide a forecast on the availability of a torrent
thanks to a neural network that models the behaviour of peers on the P2P
system. The combination of the mathematical model and the neural network
provides a solution for choosing file fragments that need to be copied first,
in order to ensure their continuous availability, counteracting possible
disconnections by some peers
Inexpressiveness of First-Order Fragments
It is well-known that first-order logic is semi-decidable. Therefore, first-order logic is less than ideal for computational purposes (computer science, knowledge engineering). Certain fragments of first-order logic are of interest because they are decidable. But decidability is gained at the cost of expressiveness. The objective of this paper is to investigate inexpressiveness of fragments that have received much attention
Adding modular predicates to first-order fragments
We investigate the decidability of the definability problem for fragments of
first order logic over finite words enriched with modular predicates. Our
approach aims toward the most generic statements that we could achieve, which
successfully covers the quantifier alternation hierarchy of first order logic
and some of its fragments. We obtain that deciding this problem for each level
of the alternation hierarchy of both first order logic and its two-variable
fragment when equipped with all regular numerical predicates is not harder than
deciding it for the corresponding level equipped with only the linear order and
the successor. For two-variable fragments we also treat the case of the
signature containing only the order and modular predicates.Relying on some
recent results, this proves the decidability for each level of the alternation
hierarchy of the two-variable first order fragmentwhile in the case of the
first order logic the question remains open for levels greater than two.The
main ingredients of the proofs are syntactic transformations of first order
formulas as well as the algebraic framework of finite categories
Complete Axiomatizations of Fragments of Monadic Second-Order Logic on Finite Trees
We consider a specific class of tree structures that can represent basic
structures in linguistics and computer science such as XML documents, parse
trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We
present axiomatizations of the monadic second-order logic (MSO), monadic
transitive closure logic (FO(TC1)) and monadic least fixed-point logic
(FO(LFP1)) theories of this class of structures. These logics can express
important properties such as reachability. Using model-theoretic techniques, we
show by a uniform argument that these axiomatizations are complete, i.e., each
formula that is valid on all finite trees is provable using our axioms. As a
backdrop to our positive results, on arbitrary structures, the logics that we
study are known to be non-recursively axiomatizable
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