A new algorithm is presented for the D0L sequence equivalence problem which, when the alphabets are fixed, works in time polynomial in the rest of the input data. The algorithm uses a polynomial encoding of words and certain well-known properties of -rational sequences.
A new algorithm is presented for the D0L sequence equivalence problem which, when the alphabets are fixed, works in time polynomial in the rest of the input data. The algorithm uses a polynomial encoding of words and certain well-known properties of -rational sequences.
The paper contains short description of -algorithm for the approximation of the function with two independent variables by the sum of products of one-dimensional functions. Some realizations of this algorithm based on the continuous and discrete splines are presented here. Few examples concerning with compression in the solving of approximation problems and colour image processing are described and discussed.
The quality of digital mathematical library depends on the formats and quality of data it offers. We show several enhancements of (meta)data of the Czech Digital Mathematics Library DML-CZ. We discuss possible minimalist modification of regular LaTeX documents that would simplify generating basic metadata that describes the article in an XML/MathML format. We also show a proof of concept of a method that enables us to include LaTeX source code of mathematical expressions into pdfTeX-generated PDFs...
With the availability of very large data storage today, redundant data structures are no longer a big issue. However, an intelligent way of managing materialised projection and selection views that can lead to fast access of data is the central issue dealt with in this paper. A set of implementation steps for the data warehouse administrators or decision makers to improve the response time of queries is also defined. The study concludes that both attributes and tuples, are important factors to be...
In this paper we introduce a method of classification based on data probes. Data points are considered as point masses in space and a probe is simply a particle that is launched into the space. As the probe passes by data clusters, its trajectory will be influenced by the point masses. We use this information to help us to find vertical trajectories. These are trajectories in the input space that are mapped onto the same value in the output space and correspond to the data classes.
Kernel Principal Component Analysis (KPCA), an example of machine learning, can be considered a non-linear extension of the PCA method. While various applications of KPCA are known, this paper explores the possibility to use it for building a data-driven model of a non-linear system-the water distribution system of the Chojnice town (Poland). This model is utilised for fault detection with the emphasis on water leakage detection. A systematic description of the system's framework is followed by...
On June 11, 2024, OpenAI announced a collaboration with Apple to deeply integrate the ChatGPT generative language model into Apple's product lineup. With support from various generative AI models, devices like smartphones will become more intelligent. The text-to-image diffusion model, known for its stable and superior generative capabilities, has gained wide recognition in image generation and will undoubtedly play a crucial role on mobile devices. However, the large size and complex architecture...
We explore the borderline between decidability and undecidability of the following question: “Let C be a class of codes. Given a machine of type X, is it decidable whether the language lies in C or not?” for codes in general, ω-codes, codes of finite and bounded deciphering delay, prefix, suffix and bi(pre)fix codes, and for finite automata equipped with different versions of push-down stores and counters.
In this paper we prove the decidability of the HD0L ultimate periodicity problem.
Various static analyses of functional programming languages that permit infinite data structures make use of set constants like Top, Inf, and Bot, denoting all terms, all lists not eventually ending in Nil, and all non-terminating programs, respectively. We use a set language that permits union, constructors and recursive definition of set constants with a greatest fixpoint semantics in the set of all, also infinite, computable trees, where all term constructors are non-strict. This...
In the last decade, formal methods have proved their interest when analyzing security protocols. Security protocols require in particular to reason about the attacker knowledge. Two standard notions are often considered in formal approaches: deducibility and indistinguishability relations. The first notion states whether an attacker can learn the value of a secret, while the latter states whether an attacker can notice some difference between protocol runs with different values of the secret. Several...