269 research outputs found
Loader and Urzyczyn Are Logically Related
International audienceIn simply typed \lam-calculus with one ground type the following theorem due to Loader holds. Given the full model \cF over a finite set, %with at least seven elements, the question whether some element f\in\cF is \lam-definable is undecidable. In the \lam-calculus with intersection types based on countably many atoms, the following is proved by Urzyczyn. It is undecidable whether a type is inhabited. Both statements are major results presented in \cite{Bare2}. We show that and follow from each other in a natural way, by interpreting intersection types as continuous functions logically related to elements of \cF. From this, and a result by Joly on \lam-definability, we get that \Urz's theorem already holds for intersection types with at most two atoms
Busy beaver machines and the observant otter heuristic
The busy beaver problem is to find the maximum number of non-zero characters that can be printed by an n-state Turing machine of a particular type. A critical step in the solution of this problem is to determine whether or not a given n-state Turing machine halts on a blank input. Given the enormous output sizes that can be produced by some small machines, it becomes critical to have appropriate methods for dealing with the exponential behaviour of both terminating and nonterminating machines. In this paper, we investigate a heuristic which can be used to greatly accelerateexecution of this class of machines. This heuristic, which we call the observant otter, is based on the detection of patterns earlier in the execution trace. We describe our implementation of this method and report various experimental results based on it, including showing how it can be used to evaluate all known 'monster' machines, including some whose naive execution would take around 10^36,534 steps
Classical, quantum and biological randomness as relative unpredictability
International audienceWe propose the thesis that randomness is unpredictability with respect to an intended theory and measurement. From this point view we briefly discuss various forms of randomness that physics, mathematics and computing science have proposed. Computing science allows to discuss unpredictability in an abstract, yet very expressive way, which yields useful hierarchies of randomness and may help to relate its various forms in natural sciences. Finally we discuss biological randomness â its peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness in biology has a positive character as it contributes to the organisms' and populations' structural stability by adaptation and diversity. Abstract We propose the thesis that randomness is unpredictability with respect to an intended theory and measurement. From this point view we briefly discuss various forms of randomness that physics, mathematics and computing science have proposed. Computing science allows to discuss unpredictability in an abstract, yet very expressive way, which yields useful hierarchies of randomness and may help to relate its various forms in natural sciences. Finally we discuss biological randomnessâits peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness in biology has a positive character as it contributes to the organisms' and populations' structural stability by adaptation and diversity
East-West Paths to Unconventional Computing
Unconventional computing is about breaking boundaries in thinking, acting and computing. Typical topics of this non-typical field include, but are not limited to physics of computation, non-classical logics, new complexity measures, novel hardware, mechanical, chemical and quantum computing. Unconventional computing encourages a new style of thinking while practical applications are obtained from uncovering and exploiting principles and mechanisms of information processing in and functional properties of, physical, chemical and living systems; in particular, efficient algorithms are developed, (almost) optimal architectures are designed and working prototypes of future computing devices are manufactured. This article includes idiosyncratic accounts of âunconventional computingâ scientists reflecting on their personal experiences, what attracted them to the field, their inspirations and discoveries.info:eu-repo/semantics/publishedVersio
Regular Matching and Inclusion on Compressed Tree Patterns with Context Variables
International audienceWe study the complexity of regular matching and inclusion for compressed tree patterns extended by context variables. The addition of context variables to tree patterns permits us to properly capture compressed string patterns but also compressed patterns for unranked trees with tree and hedge variables. Regular inclusion for the latter is relevant to certain query answering on Xml streams with references
Towards a Self-Replicating Turing Machine
We provide partial implementations of von Neumann's universal constructor and
universal copier, starting out with three types of simple building blocks using
minimal assumptions. Using the same principles, we also construct Turing
machines. Combining both, we arrive at a proposal for a self-replicating Turing
machine. Our construction allows for mutations if desired, and we give a simple
description language
Game Fiction
âGame Fictionâ provides a framework for understanding the relationship between narrative and computer games and is defined as a genre of game that draws upon and uses narrative strategies to create, maintain, and lead a user through a fictional environment. Competitive, ergodic, progressive (and often episodic), game fictionsâ primary goal must include the actualization of predetermined events. Building on existing game and new media scholarship and drawing from theories of narrative, cinema, and literature, my project details the formal materiality that undergirds game fiction and shapes its themes. In doing so, I challenge the critiques of narrativism levied at those scholars who see a relationship between computer games and narrative forms, while also detailing the ways that computational media alter and reform narratological preconceptions. My study proposes a methodology for discussing game fiction through a series of âclose playings,â and while not intended to be chronological or comprehensive, provides a model for understanding narrative and genre in this growing field
Quantum exploration algorithms for multi-armed bandits
Identifying the best arm of a multi-armed bandit is a central problem in
bandit optimization. We study a quantum computational version of this problem
with coherent oracle access to states encoding the reward probabilities of each
arm as quantum amplitudes. Specifically, we show that we can find the best arm
with fixed confidence using
quantum
queries, where represents the difference between the mean reward
of the best arm and the -best arm. This algorithm, based on
variable-time amplitude amplification and estimation, gives a quadratic speedup
compared to the best possible classical result. We also prove a matching
quantum lower bound (up to poly-logarithmic factors).Comment: 18 pages, 1 figure. To appear in the Thirty-Fifth AAAI Conference on
Artificial Intelligence (AAAI 2021
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