9781330197349 - Groups With Solvable Word Problems (Classic Reprint) de Semeniuk, Christine (3 resultados)

PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000.

Paperback. Condición: New. Print on Demand. This book explores the fascinating connections between formal systems and the computational complexity of word problems in groups. The author establishes striking analogies between theorems from logic and results about groups, revealing that groups with solvable word problems correspond to decidable systems and simple groups to complete systems. The author investigates the concept of decidability in groups, defining a group as having a word problem in level n of the Grzegorczyk hierarchy if the running time of the algorithm solving the word problem is in 8n. A significant contribution of this book is the construction of finitely presented groups with word problems in 8n (n ⥠2). This is achieved by utilizing a technique for constructing semigroups following J. Robinson's method of functional equations, which provides a concrete representation of the groups. The author demonstrates that if a semigroup has a word problem in 8n (and not lower), then the resulting group also has a word problem in 8n (and not lower). The insights presented in this book not only contribute to the understanding of word problems in groups but also shed light on the relationship between formal systems and decidability, offering valuable perspectives for further research and applications in computer science and mathematics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item.