Automata with Nested Pebbles Capture First-Order Logic with Transitive Closure

String languages recognizable in (deterministic) log-space are characterized either by two-way (deterministic) multi-head automata, or following Immerman, by first-order logic with (deterministic) transitive closure. Here we elaborate this result, and match the number of heads to the arity of the transitive closure. More precisely, first-order logic with k-ary deterministic transitive closure has the same power as deterministic automata walking on their input with k heads, additionally using a finite set of nested pebbles. This result is valid for strings, ordered trees, and in general for families of graphs having a fixed automaton that can be used to traverse the nodes of each of the graphs in the family. Other examples of such families are grids, toruses, and rectangular mazes. For nondeterministic automata, the logic is restricted to positive occurrences of transitive closure. The special case of k=1 for trees, shows that single-head deterministic tree-walking automata with nested pebbles are characterized by first-order logic with unary deterministic transitive closure. This refines our earlier result that placed these automata between first-order and monadic second-order logic on trees.Comment: Paper for Logical Methods in Computer Science, 27 pages, 1 figur

Local movement: agent-based models of pedestrian flows

Modelling movement within the built environment has hitherto been focused on rather coarse spatial scales where the emphasis has been upon simulating flows of traffic between origins and destinations. Models of pedestrian movement have been sporadic, based largely on finding statistical relationships between volumes and the accessibility of streets, with no sustained efforts at improving such theories. The development of object-orientated computing and agent-based models which have followed in this wake, promise to change this picture radically. It is now possible to develop models simulating the geometric motion of individual agents in small-scale environments using theories of traffic flow to underpin their logic. In this paper, we outline such a model which we adapt to simulate flows of pedestrians between fixed points of entry - gateways - into complex environments such as city centres, and points of attraction based on the location of retail and leisure facilities which represent the focus of such movements. The model simulates the movement of each individual in terms of five components; these are based on motion in the direction of the most attractive locations, forward movement, the avoidance of local geometric obstacles, thresholds which constrain congestion, and movement which is influenced by those already moving towards various locations. The model has elements which enable walkers to self-organise as well as learn from their geometric experiences so far. We first outline the structure of the model, present a computable form, and illustrate how it can be programmed as a variant of cellular automata. We illustrate it using three examples: its application to an idealised mall where we show how two key components - local navigation of obstacles and movement towards points of global locational attraction - can be parameterised, an application to the more complex town centre of Wolverhampton (in the UK West Midlands) where the paths of individual walkers are used to explore the veracity of the model, and finally it application to the Tate Gallery complex in central London where the focus is on calibrating the model by letting individual agents learn from their experience of walking within the environment

Pedestrian Flow Simulation Validation and Verification Techniques

For the verification and validation of microscopic simulation models of pedestrian flow, we have performed experiments for different kind of facilities and sites where most conflicts and congestion happens e.g. corridors, narrow passages, and crosswalks. The validity of the model should compare the experimental conditions and simulation results with video recording carried out in the same condition like in real life e.g. pedestrian flux and density distributions. The strategy in this technique is to achieve a certain amount of accuracy required in the simulation model. This method is good at detecting the critical points in the pedestrians walking areas. For the calibration of suitable models we use the results obtained from analyzing the video recordings in Hajj 2009 and these results can be used to check the design sections of pedestrian facilities and exits. As practical examples, we present the simulation of pilgrim streams on the Jamarat bridge. The objectives of this study are twofold: first, to show through verification and validation that simulation tools can be used to reproduce realistic scenarios, and second, gather data for accurate predictions for designers and decision makers.Comment: 19 pages, 10 figure

Sanakielet ja lokaalisuus

In this master's thesis we study the generalization of word languages into multi-dimensional arrays of letters i.e picture languages. Our main interest is the class of recognizable picture languages which has many properties in common with the robust class of regular word languages. After surveying the basic properties of picture languages, we present a logical characterization of recognizable picture languages—a generalization of Büchi's theorem of word languages into pictures, namely that the class of recognizable picture languages is the one recognized by existential monadic second-order logic. The proof presented is a recent one that makes the relation between tilings and logic clear in the proof. By way of the proof we also study the locality of the model theory of picture structures through logical locality obtained by normalization of EMSO on those structures. A continuing theme in the work is also to compare automata and recognizability between word and picture languages. In the fourth section we briefly look at topics related to computativity and computational complexity of recognizable picture languages

Dignity and the Phenomenology of Recognition-Respect

What is dignity? My starting point is that dignity is one of those philosophical primitives that admit of no informative analysis. Nonetheless, I suggest, dignity might yield to indirect illumination when we consider the kind of experience we have (or rather find it fitting to have) in its presence. This experience, I claim, is what is sometimes known as recognition-respect. Through an examination of a neglected aspect of the phenomenology of recognition-respect, I argue that the possession of inner consciousness is a precondition for the possession of dignity. The reason for this, I suggest, is that the ultimate privacy of the contents of our consciousness grounds a kind of inviolability characteristic of dignity

Simulating city growth by using the cellular automata algorithm

The objective of this thesis is to develop and implement a Cellular Automata (CA) algorithm to simulate urban growth process. It attempts to satisfy the need to predict the future shape of a city, the way land uses sprawl in the surroundings of that city and its population. Salonica city in Greece is selected as a case study to simulate its urban growth. Cellular automaton (CA) based models are increasingly used to investigate cities and urban systems. Sprawling cities may be considered as complex adaptive systems, and this warrants use of methodology that can accommodate the space-time dynamics of many interacting entities. Automata tools are well-suited for representation of such systems. By means of illustrating this point, the development of a model for simulating the sprawl of land uses such as commercial and residential and calculating the population who will reside in the city is discussed

Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions

We describe the implementation of algorithms to construct and maintain three-dimensional dynamic Delaunay triangulations with kinetic vertices using a three-simplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points is triangulated. Time evolution of the triangulation is not only governed by kinetic vertices but also by a changing number of vertices. We use three-dimensional simplex flip algorithms, a stochastic visibility walk algorithm for point location and in addition, we propose a new simple method of deleting vertices from an existing three-dimensional Delaunay triangulation while maintaining the Delaunay property. The dual Dirichlet tessellation can be used to solve differential equations on an irregular grid, to define partitions in cell tissue simulations, for collision detection etc.Comment: 29 pg (preprint), 12 figures, 1 table Title changed (mainly nomenclature), referee suggestions included, typos corrected, bibliography update