Real functions computable by finite automata using affine representations

AbstractThis paper tries to classify the functions of type In→I (for some interval I⊆R) that can be exactly realized by a finite transducer. Such a class of functions strongly depends on the choice of real number representation. This paper considers only the so-called affine representations where numbers are represented by infinite compositions of affine contracting functions on I. Affine representations include the radix (e.g. decimal, signed binary) representations. The first result is that all piecewise affine functions of n variables with rational coefficients are computable by a finite transducer which uses the signed binary representation. The second and main result is that any function computable by a finite transducer using an affine representation is affine on any open connected subset of In on which it is continuously differentiable. This limitation theorem shows that the set of finitely computable functions is very restricted

Analysis and Visualization of NC Code

Tato práce se zabývá problematikou vizualizace NC obrábění a analýzou NC kódu. V práci jsou uvedena implementační řešení jednotlivých obráběcích technik a nástrojů. Je zde popsán způsob vizualizace samotného obráběcího procesu implementovaného za pomocí OpenGL knihovny a jsou zde rozebrány problémy, na které se během této práce narazilo.This project deals with NC tooling visualization and NC code analysis problems. Implementation`s solutions for tooling`s techniques and tools are described in the project . Here visualization`s solution of the tooling`s proces are described, for this OpenGL library si used. In this work problems, we encoutered during work on this project, are analyzed.

Scan matching by cross-correlation and differential evolution

Scan matching is an important task, solved in the context of many high-level problems including pose estimation, indoor localization, simultaneous localization and mapping and others. Methods that are accurate and adaptive and at the same time computationally efficient are required to enable location-based services in autonomous mobile devices. Such devices usually have a wide range of high-resolution sensors but only a limited processing power and constrained energy supply. This work introduces a novel high-level scan matching strategy that uses a combination of two advanced algorithms recently used in this field: cross-correlation and differential evolution. The cross-correlation between two laser range scans is used as an efficient measure of scan alignment and the differential evolution algorithm is used to search for the parameters of a transformation that aligns the scans. The proposed method was experimentally validated and showed good ability to match laser range scans taken shortly after each other and an excellent ability to match laser range scans taken with longer time intervals between them.Web of Science88art. no. 85

Representations and evaluation strategies for feasibly approximable functions

A famous result due to Ko and Friedman (Theoretical Computer Science 20 (1982) 323–352) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sense. Yet, both functionals are routinely computed at great speed in practice. We aim to resolve this apparent paradox by studying classes of functions which can be feasibly integrated and maximised, together with representations for these classes of functions which encode the information which is necessary to uniformly compute integral and maximum in polynomial time. The theoretical framework for this is the second-order complexity theory for operators in analysis which was introduced by Kawamura and Cook (ACM Transactions on Computation Theory 4(2) (2012) 5). The representations we study are based on approximation by polynomials, piecewise polynomials, and rational functions. We compare these representations with respect to polytime reducibility. We show that the representation based on approximation by piecewise polynomials is polytime equivalent to the representation based on approximation by rational functions. With this representation, all terms in a certain language, which is expressive enough to contain the maximum and integral of most functions of practical interest, can be evaluated in polynomial time. By contrast, both the representation based on polynomial approximation and the standard representation based on function evaluation, which implicitly underlies the Ko-Friedman result, require exponential time to evaluate certain terms in this language. We confirm our theoretical results by an implementation in Haskell, which provides some evidence that second-order polynomial time computability is similarly closely tied with practical feasibility as its first-order counterpart

Semantics of query-driven communication of exact values

We address the question of how to communicate among distributed processes valuessuch as real numbers, continuous functions and geometrical solids with arbitrary precision, yet efficiently. We extend the established concept of lazy communication using streams of approximants by introducing explicit queries. We formalise this approach using protocols of a query-answer nature. Such protocols enable processes to provide valid approximations with certain accuracy and focusing on certain locality as demanded by the receiving processes through queries. A lattice-theoretic denotational semantics of channel and process behaviour is developed. Thequery space is modelled as a continuous lattice in which the top element denotes the query demanding all the information, whereas other elements denote queries demanding partial and/or local information. Answers are interpreted as elements of lattices constructed over suitable domains of approximations to the exact objects. An unanswered query is treated as an error anddenoted using the top element. The major novel characteristic of our semantic model is that it reflects the dependency of answerson queries. This enables the definition and analysis of an appropriate concept of convergence rate, by assigning an effort indicator to each query and a measure of information content to eachanswer. Thus we capture not only what function a process computes, but also how a process transforms the convergence rates from its inputs to its outputs. In future work these indicatorscan be used to capture further computational complexity measures. A robust prototype implementation of our model is available

Detailed Development of the Packing Line Module - Effector for Manipulation with Sets of Objects

Bakalářská práce se zabývá detailním rozpracováním koncového efektoru, který je součástí balicí linky jejíž koncepci navrhoval ve své diplomové práci Ing. David Kubovský. V úvodu práce je rešerše a souhrn veškerých informací o pracovním prostředí efektoru. Na základě zjištěných informací a konkrétních dat byl vytvořen požadavkový list. Pro zachování původní koncepce byly využity původní komponenty a byla provedena náhrada za nevyrobitelné díly. Celková sestava byla doplněna o spojovací materiál, byly provedeny kontrolní výpočty a vypočet uchopovací síly pro zadané objekty manipulace. V příloze je kompletní 3D model efektoru a výkresová dokumentace v daném rozsahu.Bachelor thesis deals with detailed elaboration of the end effector, which is part of the packaging line whose conception designed Ing. David Kubovský in his Master thesis. At the beginning of thesis there is a summary of all information about the working environment of effector. Request sheet was created according to collected information and the specific data. To preserve the original concept was using original components, but the non-manufacturable parts replacement. The overall assembly has been supplemented with fasteners, check calculations have been performed and gripping forces for the specified manipulation objects have been calculated. In the appendix there is a complete 3D model of the effector and a drawing documentation within the specified range.354 - Katedra robotikyvelmi dobř

Static Solution of Reinforced Concrete Structures

Práce se zabývá statickým řešením křížem vyztužené spojité monolitické železobetonové desky ubytovacího objektu. Konstrukce je navržena a posouzena v souladu s ČSN EN 1992-1-1: Navrhování betonových konstrukcí – Část 1-1: Obecná pravidla a pravidla pro pozemní stavby.The thesis deals with structural solution of continuous reinforced concrete slab of accommodation building. The constructure is designed assessed for ultimate limit state according with ČSN EN 1992-1-1: Design of concrete structures – Part 1-1: General rules and rules for buildings.