title: Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÑÐ½Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð Ð¾Ð±Ð¸Ð½ÑÐ¾Ð½Ð° Ð¸ ÐÐ°ÑÐµÑÑÐ¾Ð½Ð°-ÐÐµÐ³Ð¼Ð°Ð½Ð° Ð½Ð° ÑÐ·ÑÐºÐµ Java
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: Implementation of the Robinson and PatersonâWegman unification algorithms in Java
Creators: name: ÐÐ»ÐµÐºÑÐµÐµÐ², ÐÐ¸ÐºÐ¾Ð»Ð°Ð¹
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: 2024
Subjects: ÑÐ½Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ
Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÐÐ°ÑÐµÑÑÐ¾Ð½Ð°âÐÐµÐ³Ð¼Ð°Ð½Ð°
Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð Ð¾Ð±Ð¸Ð½ÑÐ¾Ð½Ð°
unification
PatersonâWegman algorithm
Robinson algorithm

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸ Ð½Ð° ÑÐ·ÑÐºÐµ Java, Ð¿ÑÐµÐ´Ð¾ÑÑÐ°Ð²Ð»ÑÑÑÐµÐ¹ API, Ð² ÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ñ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ ÑÐ½Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸: Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð Ð¾Ð±Ð¸Ð½ÑÐ¾Ð½Ð° Ð´Ð»Ñ ÑÐ½Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¿Ð°ÑÑ ÑÐµÑÐ¼Ð¾Ð², Ð¿Ð¾Ð»Ð¸Ð½Ð¾Ð¼Ð¸Ð°Ð»ÑÐ½ÑÐ¹ Ð²Ð°ÑÐ¸Ð°Ð½Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð Ð¾Ð±Ð¸Ð½ÑÐ¾Ð½Ð°, Ð° ÑÐ°ÐºÐ¶Ðµ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¹ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÐÐ°ÑÐµÑÑÐ¾Ð½Ð°âÐÐµÐ³Ð¼Ð°Ð½Ð° Ð´Ð»Ñ ÑÐ½Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¿Ð°ÑÑ ÑÐµÑÐ¼Ð¾Ð². ÐÐ°Ð´Ð°ÑÐ¸, ÑÐµÑÐ°ÐµÐ¼ÑÐµ Ð² ÑÐ°Ð¼ÐºÐ°Ñ Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: 1. ÐÐµÑÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ñ Ð²ÑÐµÑ Ð²ÑÑÐµÑÐ¿Ð¾Ð¼ÑÐ½ÑÑÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÑÐ½Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð² Ð²Ð¸Ð´Ðµ Ð¿ÑÐµÐ²Ð´Ð¾ÐºÐ¾Ð´Ð°; 2. Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ ÑÐµÑÐ¼Ð° Ð² Ð²Ð¸Ð´Ðµ Ð¾ÑÐ¸ÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð°ÑÐ¸ÐºÐ»Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð³ÑÐ°ÑÐ°; 3. Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ ÑÐ¸Ð½ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°ÑÐ¾ÑÐ°; 4. Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÑÐ½Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸; 5. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð½ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÑÐ½Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸ Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¸Ñ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸ Ð¼ÐµÐ¶Ð´Ñ ÑÐ¾Ð±Ð¾Ð¹. Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½ Ð¾Ð±Ð·Ð¾Ñ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÑ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¹ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² ÑÐ½Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¸. ÐÑÐ»Ð¾ Ð¾ÑÐ¼ÐµÑÐµÐ½Ð¾, ÑÑÐ¾ Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð½Ðµ Ð¿ÑÐµÐ´Ð¾ÑÑÐ°Ð²Ð»ÑÑÑ API; Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÐµ Ð¸Ð· Ð½Ð¸Ñ Ð¿Ð»Ð¾ÑÐ¾ Ð·Ð°Ð´Ð¾ÐºÑÐ¼ÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ñ; Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÐµ Ð¸Ð· Ð½Ð¸Ñ Ð½Ðµ Ð²ÑÐ»Ð¾Ð¶ÐµÐ½Ñ Ð² Ð¾ÑÐºÑÑÑÑÐ¹ Ð´Ð¾ÑÑÑÐ¿. Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¿Ð¾Ð´ÑÐ¾Ð±Ð½Ð¾Ðµ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ðµ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð½Ð¾Ð¹ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸, Ð¾Ð¿Ð¸ÑÐ°Ð½ Ð¿ÑÐ¸Ð¼ÐµÑ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ñ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¾Ð¹. ÐÑÐ»Ð¾ Ð¾ÑÑÑÐµÑÑÐ²Ð»ÐµÐ½Ð¾ ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð±Ð¸Ð±Ð»Ð¸Ð¾ÑÐµÐºÐ¸, ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð½ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð¼ÐµÐ¶Ð´Ñ ÑÐ¾Ð±Ð¾Ð¹. Ð¢Ð°ÐºÐ¶Ðµ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° ÐÐ°ÑÐµÑÑÐ¾Ð½Ð°âÐÐµÐ³Ð¼Ð°Ð½Ð° Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸ÐµÐ¹ ÑÑÐ¾Ð³Ð¾ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð² ÑÐ°Ð±Ð¾ÑÐµ de Champeaux.
description: This work is devoted to the development of a library in the Java language, providing an API, which implements the following unification algorithms: the Robinson algorithm, a polynomial version of the Robinson algorithm and the Paterson-Wegman linear algorithm. The goals of this work are: 1. Detailed description of all the above-mentioned unification algorithms in the form of a pseudocode; 2. Implementation of the representation of the term as a directed acyclic graph; 3. Implementation of a syntax analyzer; 4. Implementation of unification algorithms; 5. Testing the implemented unification algorithms and comparison of their efficiency. In this work the overview of existing software implementations of unification algorithms is given. It was noted that some implementations do not provide APIs; some are poorly documented; some are not publicly available. This work provides a detailed description of the implemented library, provides an example of interaction with the library. The library was tested, the implemented algorithms were compared among themselves. The comparison results of this implementation of the Paterson-Wegman algorithm with the de Champeaux implementation are also given.