Properties and Complexity of Some Superposition Choice Procedures
In this paper, the application of two-stage superposition choice procedures to the choice problem when the number of alternatives is too large is studied. Two-stage superposition choice procedures consist in sequential application of two choice procedures where the result of the first choice procedure is the input for the second choice procedures. We focus on the study of properties of such choice procedures and evaluate its computational complexity in order to determine which of two-stage superposition choice procedures can be applied in the case of large amount of alternatives.
This book constitutes the proceedings of the 13th International Computer Science Symposium in Russia, CSR 2018, held in Moscow, Russia, in May 2018.
The 24 full papers presented together with 7 invited lectures were carefully reviewed and selected from 42 submissions. The papers cover a wide range of topics such as algorithms and data structures; combinatorial optimization; constraint solving; computational complexity; cryptography; combinatorics in computer science; formal languages and automata; algorithms for concurrent and distributed systems; networks; and proof theory and applications of logic to computer science.
The invention relates to a method for selecting and ranking valid variants in search and recommendation systems. The claimed method makes it possible to select and rank variants with a high degree of accuracy and speed, especially in the case of a large number of variants which can be characterized by a large set of indicators. In the claimed method (variant), criteria for evaluating the relevance of a variant to the search request are first generated and a set of procedures for the selection and ranking of variants and a sequence for performing said procedures for the selection of variants evaluated as the most valid are established, and an evaluation of each of the variants is made on the basis of the relevance to search request criteria and, on the basis of this evaluation, the variants are ranked by means of assigning a rank to each of said variants based on the condition of correspondence to the greatest number of criteria in decreasing order, and then the variants are selected and ranked in at least two stages using the superposition method, and the variants are selected, ranked and excluded until all of the established selection procedures have been used and the selected group of variants is evaluated as being the most valid.
M. Rabin's principle asserts that the depth of any algebraic decision tree, recognizing a closed orthant in scRn, is no less than n. Using the techniques of Newton polyhedra, we give the shortest possible proof of this fact, extending it to arbitrary collections of open or closed orthants, and apply it to trees distinguishing real polynomials having at least l real roots.
We investigate regular realizability (RR) problems, which are the prob- lems of verifying whether intersection of a regular language – the input of the problem – and fixed language called filter is non-empty. In this pa- per we focus on the case of context-free filters. Algorithmic complexity of the RR problem is a very coarse measure of context-free languages com- plexity. This characteristic is compatible with rational dominance. We present examples of P-complete RR problems as well as examples of RR problems in the class NL. Also we discuss RR problems with context- free filters that might have intermediate complexity. Possible candidates are the languages with polynomially bounded rational indices.
This book constitutes the refereed proceedings of the 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012, held in Helsinki, Finalnd, in July 2012. The 33 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 60 submissions. The papers address issues of searching and matching strings and more complicated patterns such as trees, regular expressions, graphs, point sets, and arrays. The goal is to derive non-trivial combinatorial properties of such structures and to exploit these properties in order to either achieve superior performance for the corresponding computational problems or pinpoint conditions under which searches cannot be performed efficiently. The meeting also deals with problems in computational biology, data compression and data mining, coding, information retrieval, natural language processing, and pattern recognition.
We study the following computational problem: for which values of k, the majority of n bits MAJn can be computed with a depth two formula whose each gate computes a majority function of at most k bits? The corresponding computational model is denoted by MAJk o MAJk. We observe that the minimum value of k for which there exists a MAJk o MAJk circuit that has high correlation with the majority of n bits is equal to Θ(n1/2). We then show that for a randomized MAJk o MAJk circuit computing the majority of n input bits with high probability for every input, the minimum value of k is equal to n2/3+o(1). We show a worst case lower bound: if a MAJk o MAJk circuit computes the majority of n bits correctly on all inputs, then k ≥ n13/19+o(1). This lower bound exceeds the optimal value for randomized circuits and thus is unreachable for pure randomized techniques. For depth 3 circuits we show that a circuit with k = O(n2/3) can compute MAJn correctly on all inputs.
This book constitutes the refereed proceedings of the 44th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2018, held in Krems, Austria, in January/February 2018. The 48 papers presented in this volume were carefully reviewed and selected from 97 submissions. They were organized in topical sections named: foundations of computer science; software engineering: advances methods, applications, and tools; data, information and knowledge engineering; network science and parameterized complexity; model-based software engineering; computational models and complexity; software quality assurance and transformation; graph structure and computation; business processes, protocols, and mobile networks; mobile robots and server systems; automata, complexity, completeness; recognition and generation; optimization, probabilistic analysis, and sorting; filters, configurations, and picture encoding; machine learning; text searching algorithms; and data model engineering.
The Arctic region is one of the most sensitive and vulnerable to climate change. The dramatic melting of Arctic ice has several negative consequences for the whole ecosystem as well as for a way of life of native people but it also creates new opportunities for the region. First, it opens up potential for exploitation of large deposits of natural resources such oil and gas. Second, it shrinks Arctic shipping routes which offer significant economic savings for many countries. These benefits has already attracted many countries, both Arctic and non-Arctic, thus resulting in potential conflict of interests. Unclear borders and existing territorial claims made the problem even more complicated. In our paper we made an attempt to evaluate the level of interest of countries in the Arctic region with respect to main resources – oil, gas, fish and maritime routes. As a result, we identified conflict of zones and presented a model of conflict resolution based on the idea of superposition which allocates each zone to a particular country.