Related papers: Instruction sequences and non-uniform complexity t…
We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the…
The principles on which can be based computer model of process of training are formulated. Are considered: 1) the unicomponent model, which is recognizing that educational information consists of equal elements; 2) the multicomponent model,…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the…
We develop a unified second-order parameterized complexity theory for spaces of integrable functions. This generalizes the well-established case of second-order parameterized complexity theory for spaces of continuous functions.…
We introduce the notion of universal odd generalized Poisson superalgebra associated to an associative algebra A, by generalizing a construction made in [5]. By making use of this notion we give a complete classification of simple linearly…
A recently introduced measure of Boolean functions complexity--disjunc\-tive complexity (DC)--is compared with other complexity measures: the space complexity of streaming algorithms and the complexity of nondeterministic branching programs…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…
This paper concerns the question to what extent it can be efficiently determined whether an arbitrary program correctly solves a given problem. This question is investigated with programs of a very simple form, namely instruction sequences,…
The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions. This complexity measure is quite relevant to understand general…
The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that…
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
We define counting classes #P_R and #P_C in the Blum-Shub-Smale setting of computations over the real or complex numbers, respectively. The problems of counting the number of solutions of systems of polynomial inequalities over R, or of…
We investigate machine models similar to Turing machines that are augmented by the operations of a first-order structure $\mathcal{R}$, and we show that under weak conditions on $\mathcal{R}$, the complexity class $\text{NP}(\mathcal{R})$…
We introduce the notion of nonuniform coercion, which is the promotion of a value of one type to an enriched value of a different type via a nonuniform procedure. Nonuniform coercions are a generalization of the (uniform) coercions known in…
We consider the arithmetic complexity of index sets of uniformly computably enumerable families learnable under different learning criteria. We determine the exact complexity of these sets for the standard notions of finite learning,…
The P versus NP problem is studied under the relational model of E. F. Codd. I found that the term "complete configuration" is unnecessary and harmful in computational complexity theory because of excessive symbol redundancy. For an input,…
In recent research on non-monotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P union R and Q union R have the same answer sets for any other program R. This…