相关论文: The complexity of the Structure and Classification…

We investigate the descriptional complexity of limited propagating Lindenmayer systems and their deterministic and tabled variants with respect to the number of rules and the number of symbols. We determine the decrease of complexity when…

A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains…

It is argued that the occurrence of disproportionately ("un-natural") large (or small) numbers, as well as deep cancellations, are comparatively natural traits of the way Nature is geared to operate in most complex systems. The idea is…

We consider classification problems for manifolds and discrete subgroups of Lie groups from a descriptive set-theoretic point of view. This work is largely foundational in conception and character, recording both a framework for general…

The relational complexity, introduced by G. Cherlin, G. Martin, and D. Saracino, is a measure of ultrahomogeneity of a relational structure. It provides an information on minimal arity of additional invariant relations needed to turn given…

We answer two questions on the complexities of decision problems of groups, each related to a classical result. First, C. Miller characterized the complexity of the isomorphism problem for finitely presented groups in 1971. We do the same…

This is the English version of the paper: "Complejidad de los n\'umeros naturales", Gaceta de la Real Sociedad Matem\'atica Espa\~nola 3 (2000) 230--250. In this paper, several conjectures about the complexity of natural numbers are…

We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…

The monadic theory of $(\mathbb R,\le)$ with quantification restricted to Borel sets is decidable. The Boolean combinations of $F_\sigma$ sets form an elementary substructure of the Borel sets. Under determinacy hypotheses, the proof…

We formulate a division problem for a class of overdetermined systems introduced by L. H{\"o}rmander, and establish an effective divisibility criterion. In addition, we prove a coherence theorem which extends Nadel's coherence theorem from…

A difference equation based method of determining two factors of a composite is presented. The feasibility of P-complexity is shown. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non…

Topological complexity for spaces was introduced by M. Farber as a minimal number of continuity domains for motion planning algorithms. It turns out that this notion can be extended to the case of not necessarily commutative C*-algebras.…

We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in references [1], [6] and [5] e.g. to the projective levels.

The term complexity derives etymologically from the Latin plexus, which means interwoven. Intuitively, this implies that something complex is composed by elements that are difficult to separate. This difficulty arises from the relevant…

We study two complexity notions of groups - a computable Scott sentence and the index set of a group. Finding the exact complexity of one of them usually involves finding the complexity of the other, but this is not the case sometimes. J.…

In this note we provide a concise report on the complexity of the causal ordering problem, originally introduced by Simon to reason about causal dependencies implicit in systems of mathematical equations. We show that Simon's classical…

We give an introduction to some of the recent ideas that go under the name "geometric complexity theory". We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent. We then introduce the…

We prove in this paper that there exists some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [Automates et Th\'eorie Descriptive, Ph. D. Thesis, Universit\'e Paris 7, March…

Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…

Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…