title: ÐÐ²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð¿Ð¾Ð¸ÑÐº Ð·Ð°Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð±ÑÐ»ÐµÐ²Ð¾Ð¹ ÑÑ ÐµÐ¼Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Automated search of given Boolean circuit
Creators: name: ÐÐ°Ð¿Ð»Ð¸Ð½, ÐÐ»ÐµÐºÑÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2021
Subjects: ÐÐ»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ
Ð¤ÑÐ½ÐºÑÐ¸Ð¸ (Ð¼Ð°Ñ.) Ð±ÑÐ»ÐµÐ²Ñ

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÑÑÑ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð¿Ð¾Ð¸ÑÐº Ð·Ð°Ð´Ð°Ð½Ð½ÑÑ ÐÑÐ»ÐµÐ²ÑÑ ÑÑÐµÐ¼. ÐÐ°Ð½Ð¾ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ ÐÑÐ»ÐµÐ²Ð¾Ð¹ ÑÑÐµÐ¼Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ðµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹ ÐÑÐ»ÐµÐ²ÑÑ ÑÑÐ½ÐºÑÐ¸Ð¹ ÑÑÐµÐ¼Ð°Ð¼Ð¸. ÐÐ°Ð½Ð¾ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð²ÑÐ¿Ð¾Ð»Ð½Ð¸Ð¼Ð¾ÑÑÐ¸, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¾Ð±Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð° ÐµÐµ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ°Ñ Ð·Ð½Ð°ÑÐ¸Ð¼Ð¾ÑÑÑ. ÐÑÐ¸Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° CDCL, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼Ð¾Ð³Ð¾ Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ SAT, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½ Ð¿Ð¾Ð´ÑÐ¾Ð´, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐ¸Ð¹ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÑ Ð¿ÑÐµÐ¸Ð¼ÑÑÐµÑÑÐ²Ð° Ð¼Ð½Ð¾Ð³Ð¾ÑÐ´ÐµÑÐ½Ð¾Ð¹ Ð°ÑÑÐ¸ÑÐµÐºÑÑÑÑ Ð¿ÑÐ¸ ÑÐµÑÐµÐ½Ð¸Ð¸ Ð·Ð°Ð´Ð°ÑÐ¸ SAT. ÐÐ°Ð½Ð¾ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ ÑÐ¾ÑÐ¼Ð°ÑÐ° DIMACS CNF. ÐÐ¿Ð¸ÑÐ°Ð½ ÑÐ¿Ð¾ÑÐ¾Ð± ÑÐ²ÐµÐ´ÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°Ñ Ð¾ ÑÑÑÐµÑÑÐ²Ð¾Ð²Ð°Ð½Ð¸Ð¸ ÐºÐ¾Ð¼Ð±Ð¸Ð½Ð°ÑÐ¾ÑÐ½ÑÑ Ð¾Ð±ÑÐµÐºÑÐ¾Ð² Ðº Ð·Ð°Ð´Ð°ÑÐµ Ð²ÑÐ¿Ð¾Ð»Ð½Ð¸Ð¼Ð¾ÑÑÐ¸ Ð¸ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½ Ð¿ÑÐ¸Ð¼ÐµÑ ÑÐ°ÐºÐ¾Ð³Ð¾ ÑÐ²ÐµÐ´ÐµÐ½Ð¸Ñ Ð´Ð»Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¿Ð¾Ð¸ÑÐºÐ° ÑÐµÑÐµÐ½Ð¸Ñ Ð¨Ð¸Ð´Ð¾ÐºÑ. ÐÐ¿Ð¸ÑÐ°Ð½Ð¾ ÑÐ²ÐµÐ´ÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¿Ð¾Ð¸ÑÐºÐ° Ð·Ð°Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð±ÑÐ»ÐµÐ²Ð¾Ð¹ ÑÑÐµÐ¼Ñ, Ð²ÑÑÐ¸ÑÐ»ÑÑÑÐµÐ¹ Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÑ Ð±ÑÐ»ÐµÐ²Ñ ÑÑÐ½ÐºÑÐ¸Ñ, Ðº Ð·Ð°Ð´Ð°ÑÐµ Ð²ÑÐ¿Ð¾Ð»Ð½Ð¸Ð¼Ð¾ÑÑÐ¸. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð°, Ð²ÑÐ¿Ð¾Ð»Ð½ÑÑÑÐ°Ñ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ ÐÐÐ¤, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð²ÑÐ¿Ð¾Ð»Ð½Ð¸Ð¼Ð° ÑÐ¾Ð³Ð´Ð° Ð¸ ÑÐ¾Ð»ÑÐºÐ¾ ÑÐ¾Ð³Ð´Ð°, ÐºÐ¾Ð³Ð´Ð°: ÑÑÑÐµÑÑÐ²ÑÐµÑ ÑÐµÑÐµÐ½Ð¸Ðµ Ð´Ð»Ñ Ð·Ð°Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ ÑÐºÐ·ÐµÐ¼Ð¿Ð»ÑÑÐ° Ð¨Ð¸Ð´Ð¾ÐºÑ, ÑÑÑÐµÑÑÐ²ÑÐµÑ Ð·Ð°Ð´Ð°Ð½Ð½Ð°Ñ ÐÑÐ»ÐµÐ²Ð° ÑÑÐµÐ¼Ð°. ÐÑÐ¸Ð²ÐµÐ´ÐµÐ½Ñ Ð¿ÑÐ¸Ð¼ÐµÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð´Ð»Ñ Ð¿Ð¾Ð¸ÑÐºÐ° ÑÐµÑÐµÐ½Ð¸Ñ Ð¨Ð¸Ð´Ð¾ÐºÑ Ð¸ Ð´Ð»Ñ Ð¿Ð¾Ð¸ÑÐºÐ° Ð·Ð°Ð´Ð°Ð½Ð½Ð¾Ð¹ ÐÑÐ»ÐµÐ²Ð¾Ð¹ ÑÑÐµÐ¼Ñ.
description: In the given work, an automatic search for given Boolean circuits is considered.The definition of a Boolean scheme is given, and the calculation of the values of Booleanfunctions is also shown. The definition of the satisfiability problem is given, and itspractical significance is substantiated. A description of the CDCL algorithm used to solvethe SAT problem is given, and an approach is shown that allows using the advantagesof the multicore architecture when solving the SAT problem. The description of theDIMACS CNF format is given. A method of reducing the problem of the existence ofcombinatorial objects to the problem of satisfiability is described, and an example ofsuch reduction for the problem of finding a solution to Shidoku is given. The reductionof the problem of searching for a given Boolean circuit that computes a certain Boolean function to the problem of satisfiability is described. A program has been developed thatconstructs the CNF, which is executable if and only if: there is a solution for a giveninstance of Shidoku, there is a given Boolean scheme. Examples of using the programfor finding a solution to Shidoku and for finding a given Boolean scheme are given.