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2025 year, volume 29, issue 4 (PDF)
This article describes the algorithmic language LDS (logical description of situations). It describes the language’s basic operators, the LDS program editor, and demonstrates how to debug LDS programs.
Keywords: mathematical problem solver, logical processes, logical language, logical formalization of problems.
Phase transitions in multicomponent oil solutions are considered. Dependencies for the molar volumes of the gas and liquid phases are proposed. The formulas take into account the behavioral characteristics of solutions, nnamely, changes in concentration during phase transitions. They enable highly accurate approximation of real dependencies and the construction of analytical models with phase transitions over wide ranges of pressures and temperatures.
Keywords: hydrocarbon solutions, phase equilibrium, mathematical modeling, thermodynamics.
The surjective graph homomorphism problem \[Surj-Hom(H)\] is a problem of deciding whether a given graph allows vertex-surjective homomorphism to a fixed graph \[H\]. In this paper we study the \[Surj-Hom\] problem for cyclic graphs which are obtained from undirected cycles by assigning direction to some edges and in which each vertex contains a loop. We explore the \[Surj-Hom\] problem in its conjunction with the surjective constraint satisfaction problem \[SCSP\]. We define a property which allows to obtain the complexity of the SCSP problem for some predicates via reduction. We implement this property to determine the complexity of the \[Surj-Hom\] problem for all desired cycles except for three cycles with \[4\], \[5\] and \[6\] vertices.
Keywords: surjective graph homomorphism, computational complexity, constraint satisfaction, polymorphism.
In linear definite automata, the output signals at each moment depend only on a bounded number of the most recent input values. This paper studies functional completeness with respect to the operator of approximation closure for the class of linear definite automata over the two-element field. For this class of automata, a completeness criterion is obtained, formulated in terms of a system of precomplete classes.
Keywords: approximation closure, linear automata, definite automata.
The class of finite automata is finitely generated by composition operations [1]. An important subclass of this class are classes of automata with linear output functions. A set of operations on automata consisting of variable substitution, automata substitution, and feedback is called bounded composition. The class of unary automata is closed under bounded composition operations. In this paper, we show that the class of unary finite automata with linear output functions and bounded composition operations lacks finite complete sets. However, automata from this class, implemented by circuits with at most one delay, generate this class.
Keywords: finite automata, composition operations for automata, finite automata with linear outputs.