Inhaltsangabe
Excerpt from Groups With Solvable Word Problems
Equating truth in G with derivability from a set of axioms suggests the possibility of formulating the word problem for G as the derivability problem for some type of formal system. The first part of the paper is concerned with this. Once this is done, we can consider the questions usually asked about formal systems, such as consistency, decid ability, and completeness, and use results about particular formal systems to obtain results about groups and semigroups corresponding to these systems. In this analogy, nontrivial groups correspond to consistent systems, groups with solvable word problem to decidable systems, and simple groups to complete systems. The last analogy is particularly striking, for, strangely enough, although it has been known for a long time that complete recursively axiomatized theories are decidable, it was only recently noted that recursively presented simple groups have solvable word problems.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
Weitere beliebte Ausgaben desselben Titels
Suchergebnisse für Groups with Solvable Word Problems (Classic Reprint)
Foto des Verkäufers
Groups With Solvable Word Problems (Classic Reprint)
Print-on-DemandAnbieter: Forgotten Books, London, Vereinigtes Königreich
Verkäuferbewertung 4 von 5 Sternen
Paperback. Zustand: 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. Bestandsnummer des Verkäufers 9781330197349_0
Neu kaufen
EUR 16,04
Versand gratis
Versand von Vereinigtes Königreich nach USA
Versand von Vereinigtes Königreich nach USA
Anzahl: Mehr als 20 verfügbar
Beispielbild für diese ISBN
Groups With Solvable Word Problems Classic Reprint
Anbieter: PBShop.store US, Wood Dale, IL, USA
Verkäuferbewertung 5 von 5 Sternen
PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781330197349
Beispielbild für diese ISBN
Groups With Solvable Word Problems Classic Reprint
Anbieter: PBShop.store UK, Fairford, GLOS, Vereinigtes Königreich
Verkäuferbewertung 4 von 5 Sternen
PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781330197349
Neu kaufen
EUR 21,12
EUR 3,77 Versand
Versand von Vereinigtes Königreich nach USA
Versand von Vereinigtes Königreich nach USA
Anzahl: 15 verfügbar