Showing papers in "Bulletin of The European Association for Theoretical Computer Science in 2007"

An Introduction to Population Protocols.

Abstract: Population protocols are used as a theoretical model for a collection (or population) of tiny mobile agents that interact with one another to carry out a computation. The agents are identically programmed finite state machines. Input values are initially distributed to the agents, and pairs of agents can exchange state information with other agents when they are close together. The movement pattern of the agents is unpredictable, but subject to some fairness constraints, and computations must eventually converge to the correct output value in any schedule that results from that movement. This framework can be used to model mobile ad hoc networks of tiny devices or collections of molecules undergoing chemical reactions. This chapter surveys results that describe what can be computed in various versions of the population protocol model.

Spiking Neural P Systems: A Tutorial.

Abstract: We brie y present (basic ideas, some examples, classes of spiking neural P systems, some results concerning their power, research topics) a recently initiated branch of membrane computing with motivation from neural computing. Further details can be found at the web page of membrane computing, from http://psystems.disco.unimib.it. 1 The General Framework The most intuitive way to introduce spiking neural P systems (in short, SN P systems) is by watching the movie available at http://www.igi.tugraz. at/tnatschl/spike_trains_eng.html, in the web page of Wofgang Maass, Graz, Austria: neurons are sending to each others spikes, electrical impulses of identical shape (duration, voltage, etc.), with the information encoded in the frequency of these impulses, hence in the time passes between consecutive spikes. For neurologists, this is nothing new, related drawings already appears in papers by Ramon y Cajal, a pioneer of neuroscience at the beginning of the last century, but in the recent years computing by spiking is a vivid research area, with the hope to lead to a neural computing of the third generation see [12], [21], etc. For membrane computing it is somehow natural to incorporate the idea of spiking neurons (already neural-like P systems exist, based on di erent ingredients see [23], e orts to compute with a small number of objects were recently made in several papers see, e.g., [2], using the time as a support of information, for instance, taking the time between two events as the result of a computation, was also considered see [3]), but still important di erences exist between the general way of working with multisets of objects in the compartments of a cell-like membrane structure as in membrane computing and the way the neurons communicate by spikes. A way to answer this challenge was proposed in [18]: neurons as single membranes, placed in the nodes of a graph corresponding to synapses, only one type of objects present

Background of Computation.

Abstract: In a computational process, certain entities (for example sets or arrays) and operations on them may be automatically available, for example by being provided by the programming language. We define background classes to formalize this idea, and we study some of their basic properties. The present notion of background class is more general than the one we introduced in an earlier paper 143, and it thereby corrects one of the examples in that paper. The greater generality requires a non-trivial notion of equivalence of background classes, which we explain and use. Roughly speaking, a background class assigns to each set (of atoms) a structure (for example of sets or arrays or combinations of these and similar entities), and it assigns to each embedding of one set of atoms into another a standard embedding between the associated background structures. We discuss several, frequently useful, properties that background classes may have, for example that each element of a background structure depends (in some sense) on only finitely many atoms, or that there are explicit operations by which all elements of background structures can be produced from atoms.

Formal Modeling and Analysis of Flexible Processes in Mobile Ad-Hoc Networks.

Abstract: GOAL Adequate specification technique for multilevel modeling of workflows in MANETs Emergency Scenario: Archaeological Site after an Earthquake Network of mobile devices Team members communicate with one another via wireless links without relying on an underlying infrastructure Team members execute sets of activities modeled as workflows MANETs topology both influences and is influenced by the workflow Modeling workflow modifications as required by topology transformations

Zero-One Laws: Thesauri and Parametric Conditions.

Abstract: Quisani: I’ve been thinking about zero-one laws for first-order logic. I know it’s a rather old topic, but I noticed something in the literature that I’d like to understand better. The first proof [6] established that, for any first-order sentence σ in a finite relational vocabulary ϒ, the proportion of models of σ among all ϒ-structures with base set {1,2,…,n} approaches 0 or 1 as n tends to infinity. Fagin [5] rediscovered the result (with a simpler proof) and added, near the end of his paper, some remarks about what happens if, instead of considering all ϒ-structures, we consider only those satisfying some specified sentence τ. He pointed out that for some but not all choices of τ, there is still a 0-1 law: The proportion of models of σ among models of τ with base set {1,2,…,n} approaches 0 or 1 as n tends to infinity. He gave two examples of such τ, both in the language with just a single binary relation symbol E, the language of digraphs. One example was the sentence saying that τ is symmetric and irreflexive, so the models are undirected loopless graphs. The other example defined the class of tournaments. The case of undirected graphs was rediscovered in [3], where another example was added, pure d-dimensional simplicial complexes, formulated using a completely symmetric and completely irreflexive (d + 1)-ary relation.

Characteristic Formulae: From Automata to Logic.

Abstract: This paper discusses the classic notion of characteristic formulae for processes using variations on Hennessy-Milner logic as the underlying logical specification language. It is shown how to characterize logically (states of) finite labelled transition systems modulo bisimilarity using a single formula in Hennessy-Milner logic with recursion. Moreover, characteristic formulae for timed automata with respect to timed bisimilarity and the faster-than preorder of Moller and Tofts are offered in terms of the logic L_nu of Laroussinie, Larsen and Weise.

Algorithmic aspects of cartogram computation

Abstract: In this note we describe some recent algorithms for the computation of rectangular and rectilinear cartograms.

The Domino Problem of the Hyperbolic Plane is Undecidable.

Abstract: In this paper, we prove that the general tiling problem of the hyperbolic plane is undecidable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles. The problem was raised by a paper of Raphael Robinson in 1971, in his famous simplified proof that the general tiling problem is undecidable for the Euclidean plane, initially proved by Robert Berger in 1966.

Quantum Computing and the Hunt for Hidden Symmetry.

Abstract: In 1994, Peter Shor gave e cient quantum algorithms for factoring integers and extracting discrete logarithms [20] If we believe that nature will permit us to faithfully implement our current model of quantum computation, then these algorithms dramatically contradict the Strong Church-Turing thesis The e ect is heightened by the fact that these algorithms solve computational problems with long histories of attention by the computational and mathematical communities alike In this article we discuss the branch of quantum algorithms research arising from attempts to generalize the core quantum algorithmic aspects of Shor's algorithms Roughly, this can be viewed as the problem of generalizing algorithms of Simon [21] and Shor [20], which work over abelian groups, to general nonabelian groups The article is meant to be self-contained, assuming no knowledge of quantum computing or the representation theory of nite groups We begin in earnest in Section 2, describing the problem of symmetry nding : given a function f : G → S on a group G, this is the problem of determining {g ∈ G | ∀x, f(x) = f(gx)}, the set of symmetries of f We switch gears in Section 3, giving a short introduction to the circuit model of quantum computation The connection between these two sections is eventually established in Section 4, where we discuss the representation theory of nite groups and the quantum Fourier transform a unitary transformation speci cally tuned to the symmetries of the underlying group Section 42 is devoted to Fourier