相关论文: Mathematical Informatics: Algorithms
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
In the last decades, several objects such as grammars, economical agents, laws of physics... have been defined as algorithms. In particular, after Brouwer, Heyting, and Kolomogorov, mathematical proofs have been defined as algorithms. In…
Macroprogramming refers to the theory and practice of conveniently expressing the macro(scopic) behaviour of a system using a single program. Macroprogramming approaches are motivated by the need of effectively capturing global/system-level…
Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this…
Over the past two decades, Yuri Gurevich and his colleagues have formulated axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in the new generic framework of abstract state…
Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional…
A program is usually represented as a word chain. It is exactly a word chain that appears as the lexical analyzer output and is parsed. The work shows that a program can be syntactically represented as an oriented word tree, that is a…
Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic…
In order to gain a better understanding of the state space of programs, with the aim of making their verification more tractable, models based on directed topological spaces have been introduced, allowing to take in account equivalence…
We consider two classes of stream-based computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. The dataflow architecture is a natural platform for programming with streams.…
This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…
Would it be possible to explain the emergence of new computational ideas using the computation itself? Would it be feasible to describe the discovery process of new algorithmic solutions using only mathematics? This study is the first…
The remarkable growth and significant success of machine learning have expanded its applications into programming languages and program analysis. However, a key challenge in adopting the latest machine learning methods is the representation…
In computability theory and computable analysis, finite programs can compute infinite objects. Presenting a computable object via any program for it, provides at least as much information as presenting the object itself, written on an…
Graphs, and graph transformation systems, are used in many areas within Computer Science: to represent data structures and algorithms, to define computation models, as a general modelling tool to study complex systems, etc. Research in term…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
A formal consideration in this paper is given for the essential notations to characterize the object that is distinguished in a problem domain. The distinct object is represented by another idealized object, which is a schematic element.…