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

Structural and Computational Existence Results for Multidimensional Subshifts

Symbolic dynamics is a branch of mathematics that studies the structure of infinite sequences of symbols, or in the multidimensional case, infinite grids of symbols. Classes of such sequences and grids defined by collections of forbidden patterns are called subshifts, and subshifts of finite type are defined by finitely many forbidden patterns. The simplest examples of multidimensional subshifts are sets of Wang tilings, infinite arrangements of square tiles with colored edges, where adjacent edges must have the same color. Multidimensional symbolic dynamics has strong connections to computability theory, since most of the basic properties of subshifts cannot be recognized by computer programs, but are instead characterized by some higher-level notion of computability. This dissertation focuses on the structure of multidimensional subshifts, and the ways in which it relates to their computational properties. In the first part, we study the subpattern posets and Cantor-Bendixson ranks of countable subshifts of finite type, which can be seen as measures of their structural complexity. We show, by explicitly constructing subshifts with the desired properties, that both notions are essentially restricted only by computability conditions. In the second part of the dissertation, we study different methods of defining (classes of ) multidimensional subshifts, and how they relate to each other and existing methods. We present definitions that use monadic second-order logic, a more restricted kind of logical quantification called quantifier extension, and multi-headed finite state machines. Two of the definitions give rise to hierarchies of subshift classes, which are a priori infinite, but which we show to collapse into finitely many levels. The quantifier extension provides insight to the somewhat mysterious class of multidimensional sofic subshifts, since we prove a characterization for the class of subshifts that can extend a sofic subshift into a nonsofic one.Symbolidynamiikka on matematiikan ala, joka tutkii äärettömän pituisten symbolijonojen ominaisuuksia, tai moniulotteisessa tapauksessa äärettömän laajoja symbolihiloja. Siirtoavaruudet ovat tällaisten jonojen tai hilojen kokoelmia, jotka on määritelty kieltämällä jokin joukko äärellisen kokoisia kuvioita, ja äärellisen tyypin siirtoavaruudet saadaan kieltämällä vain äärellisen monta kuviota. Wangin tiilitykset ovat yksinkertaisin esimerkki moniulotteisista siirtoavaruuksista. Ne ovat värillisistä neliöistä muodostettuja tiilityksiä, joissa kaikkien vierekkäisten sivujen on oltava samanvärisiä. Moniulotteinen symbolidynamiikka on vahvasti yhteydessä laskettavuuden teoriaan, sillä monia siirtoavaruuksien perusominaisuuksia ei ole mahdollista tunnistaa tietokoneohjelmilla, vaan korkeamman tason laskennallisilla malleilla. Väitöskirjassani tutkin moniulotteisten siirtoavaruuksien rakennetta ja sen suhdetta niiden laskennallisiin ominaisuuksiin. Ensimmäisessä osassa keskityn tiettyihin äärellisen tyypin siirtoavaruuksien rakenteellisiin ominaisuuksiin: äärellisten kuvioiden muodostamaan järjestykseen ja Cantor-Bendixsonin astelukuun. Halutunlaisia siirtoavaruuksia rakentamalla osoitan, että molemmat ominaisuudet ovat olennaisesti laskennallisten ehtojen rajoittamia. Väitöskirjan toisessa osassa tutkin erilaisia tapoja määritellä moniulotteisia siirtoavaruuksia, sekä sitä, miten nämä tavat vertautuvat toisiinsa ja tunnettuihin siirtoavaruuksien luokkiin. Käsittelen määritelmiä, jotka perustuvat toisen kertaluvun logiikkaan, kvanttorilaajennukseksi kutsuttuun rajoitettuun loogiseen kvantifiointiin, sekä monipäisiin äärellisiin automaatteihin. Näistä kolmesta määritelmästä kahteen liittyy erilliset siirtoavaruuksien hierarkiat, joiden todistan romahtavan äärellisen korkuisiksi. Kvanttorilaajennuksen tutkimus valottaa myös niin kutsuttujen sofisten siirtoavaruuksien rakennetta, jota ei vielä tunneta hyvin: kyseisessä luvussa selvitän tarkasti, mitkä siirtoavaruudet voivat laajentaa sofisen avaruuden ei-sofiseksi.Siirretty Doriast

Frontiers of Membrane Computing: Open Problems and Research Topics

This is a list of open problems and research topics collected after the Twelfth Conference on Membrane Computing, CMC 2012 (Fontainebleau, France (23 - 26 August 2011), meant initially to be a working material for Tenth Brainstorming Week on Membrane Computing, Sevilla, Spain (January 30 - February 3, 2012). The result was circulated in several versions before the brainstorming and then modified according to the discussions held in Sevilla and according to the progresses made during the meeting. In the present form, the list gives an image about key research directions currently active in membrane computing

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast

Explorations in machine learning for interacting many-body systems.

Most interacting many-body systems in physics are not analytically solvable. Instead, numerical methods are needed for the study of these complex and high-dimensional problems. At present, there are many interesting problems in strongly correlated systems that remain unsolved with current methods. At the heart of this problem is finding an efficient representation that incorporates symmetries, correlations and general features. In the context of computer science, machine learning techniques have had astonishing success at reducing the dimensionality of data. The leading method is through the use of artificial neural networks. These networks have been enormously successful at sifting through vast amounts of data to find patterns and regularities. In a sense, neural networks are themselves a statistical system whose properties are adjusted to mimic the features of the data. By finding an effective low-dimensional representation of the data, machine learning has greatly subdued the curse of dimensionality found in many real-world problems. In this Thesis, we apply several machine learning techniques to the study of interacting many-body systems in classical and quantum statistical physics. We explore supervised classification of phases of matter with an emphasis on physical interpretation of the net- work. In doing so, we design a custom network architecture that possesses rotational symmetry as an inductive bias. We further investigate connections between the renormalization group and deep learning through applying a super-resolving neural network to the classical Ising model. Towards experimental efforts, we also repurpose generative machine learning to quantum state tomography for the calibration and testing of quantum devices. We conclude with a latent variable model inspired by near-term quantum algorithms. This maps to a variational Monte Carlo ansatz that produces samples efficiently for interacting quantum systems

Pixel-level semantic understanding of ophthalmic images and beyond

Computer-assisted semantic image understanding constitutes the substrate of applications that range from biomarker detection to intraoperative guidance or street scene understanding for self-driving systems. This PhD thesis is on the development of deep learning-based, pixel-level, semantic segmentation methods for medical and natural images. For vessel segmentation in OCT-A, a method comprising iterative refinement of the extracted vessel maps and an auxiliary loss function that penalizes structural inaccuracies, is proposed and tested on data captured from real clinical conditions comprising various pathological cases. Ultimately, the presented method enables the extraction of a detailed vessel map of the retina with potential applications to diagnostics or intraoperative localization. Furthermore, for scene segmentation in cataract surgery, the major challenge of class imbalance is identified among several factors. Subsequently, a method addressing it is proposed, achieving state-of-the-art performance on a challenging public dataset. Accurate semantic segmentation in this domain can be used to monitor interactions between tools and anatomical parts for intraoperative guidance and safety. Finally, this thesis proposes a novel contrastive learning framework for supervised semantic segmentation, that aims to improve the discriminative power of features in deep neural networks. The proposed approach leverages contrastive loss function applied both at multiple model layers and across them. Importantly, the proposed framework is easy to combine with various model architectures and is experimentally shown to significantly improve performance on both natural and medical domain

From specialists to generalists : inductive biases of deep learning for higher level cognition

Les réseaux de neurones actuels obtiennent des résultats de pointe dans une gamme de domaines problématiques difficiles. Avec suffisamment de données et de calculs, les réseaux de neurones actuels peuvent obtenir des résultats de niveau humain sur presque toutes les tâches. En ce sens, nous avons pu former des spécialistes capables d'effectuer très bien une tâche particulière, que ce soit le jeu de Go, jouer à des jeux Atari, manipuler le cube Rubik, mettre des légendes sur des images ou dessiner des images avec des légendes. Le prochain défi pour l'IA est de concevoir des méthodes pour former des généralistes qui, lorsqu'ils sont exposés à plusieurs tâches pendant l'entraînement, peuvent s'adapter rapidement à de nouvelles tâches inconnues. Sans aucune hypothèse sur la distribution génératrice de données, il peut ne pas être possible d'obtenir une meilleure généralisation et une meilleure adaptation à de nouvelles tâches (inconnues). Les réseaux de neurones actuels obtiennent des résultats de pointe dans une gamme de domaines problématiques difficiles. Une possibilité fascinante est que l'intelligence humaine et animale puisse être expliquée par quelques principes, plutôt qu'une encyclopédie de faits. Si tel était le cas, nous pourrions plus facilement à la fois comprendre notre propre intelligence et construire des machines intelligentes. Tout comme en physique, les principes eux-mêmes ne suffiraient pas à prédire le comportement de systèmes complexes comme le cerveau, et des calculs importants pourraient être nécessaires pour simuler l'intelligence humaine. De plus, nous savons que les vrais cerveaux intègrent des connaissances a priori détaillées spécifiques à une tâche qui ne pourraient pas tenir dans une courte liste de principes simples. Nous pensons donc que cette courte liste explique plutôt la capacité des cerveaux à apprendre et à s'adapter efficacement à de nouveaux environnements, ce qui est une grande partie de ce dont nous avons besoin pour l'IA. Si cette hypothèse de simplicité des principes était correcte, cela suggérerait que l'étude du type de biais inductifs (une autre façon de penser aux principes de conception et aux a priori, dans le cas des systèmes d'apprentissage) que les humains et les animaux exploitent pourrait aider à la fois à clarifier ces principes et à fournir source d'inspiration pour la recherche en IA. L'apprentissage en profondeur exploite déjà plusieurs biais inductifs clés, et mon travail envisage une liste plus large, en se concentrant sur ceux qui concernent principalement le traitement cognitif de niveau supérieur. Mon travail se concentre sur la conception de tels modèles en y incorporant des hypothèses fortes mais générales (biais inductifs) qui permettent un raisonnement de haut niveau sur la structure du monde. Ce programme de recherche est à la fois ambitieux et pratique, produisant des algorithmes concrets ainsi qu'une vision cohérente pour une recherche à long terme vers la généralisation dans un monde complexe et changeant.Current neural networks achieve state-of-the-art results across a range of challenging problem domains. Given enough data, and computation, current neural networks can achieve human-level results on mostly any task. In the sense, that we have been able to train \textit{specialists} that can perform a particular task really well whether it's the game of GO, playing Atari games, Rubik's cube manipulation, image caption or drawing images given captions. The next challenge for AI is to devise methods to train \textit{generalists} that when exposed to multiple tasks during training can quickly adapt to new unknown tasks. Without any assumptions about the data generating distribution it may not be possible to achieve better generalization and adaption to new (unknown) tasks. A fascinating possibility is that human and animal intelligence could be explained by a few principles (rather than an encyclopedia). If that was the case, we could more easily both understand our own intelligence and build intelligent machines. Just like in physics, the principles themselves would not be sufficient to predict the behavior of complex systems like brains, and substantial computation might be needed to simulate human intelligence. In addition, we know that real brains incorporate some detailed task-specific a priori knowledge which could not fit in a short list of simple principles. So we think of that short list rather as explaining the ability of brains to learn and adapt efficiently to new environments, which is a great part of what we need for AI. If that simplicity of principles hypothesis was correct it would suggest that studying the kind of inductive biases (another way to think about principles of design and priors, in the case of learning systems) that humans and animals exploit could help both clarify these principles and provide inspiration for AI research. Deep learning already exploits several key inductive biases, and my work considers a larger list, focusing on those which concern mostly higher-level cognitive processing. My work focuses on designing such models by incorporating in them strong but general assumptions (inductive biases) that enable high-level reasoning about the structure of the world. This research program is both ambitious and practical, yielding concrete algorithms as well as a cohesive vision for long-term research towards generalization in a complex and changing world