International Postdoctoral Fellows Program: Rewriting Systems for Groups

国际博士后项目：群体重写系统

• 批准号: 9223826
• 负责人: Susan Hermiller
• 金额: $ 3.96万
• 依托单位: New Mexico State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-08-01 至 1995-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9223826&HistoricalAwards=false
• 关键词: International; Postdoctoral; Fellows; Program; Rewriting

This award is under the International Postdoctoral Fellows Program, which enables U.S. scientists and engineers to conduct three to twelve months of research at foreign centers of proven excellence. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad. This award will support a twelve-month postdoctoral research visit by Dr. Susan Hermiller of New Mexico State University to the University of Melbourne, Victoria, Australia, to work with Dr. John R. J. Groves. A finite complete rewriting system for a group is a presentation which solves the word problem for the group in a way that is particularly easy to implement on a computer, and which provides a regular language of normal forms. The proposed research is a study of the class of groups with such rewriting systems. Several questions will be pursued. The first - Given a group with a finite complete rewriting system, must every finite index subgroup also have one? The second - Does an automatic group necessarily have a finite complete rewriting system? The third - If a finitely presented group has finite derivation type, does it have a finite complete rewriting system? To answer these questions, it would be helpful to construct rewriting systems for more families of groups, especially Artin groups, if possible. They also intend to study a weaker property for a group, given by a subword closed regular language of normal forms. The award recommendation provides funds to cover international travel and a stipend for twelve months.

该奖项属于国际博士后研究员计划，该计划使美国科学家和工程师能够在国外卓越的中心进行三到十二个月的研究。 该项目的奖项提供了联合研究以及使用国外独特或互补的设施、专业知识和实验条件的机会。 该奖项将支持新墨西哥州立大学的 Susan Hermiller 博士前往澳大利亚维多利亚州墨尔本大学进行为期 12 个月的博士后研究访问，与 John R. J. Groves 博士合作。 群的有限完全重写系统是一种以特别容易在计算机上实现的方式解决群的文字问题的表示，并且提供范式的常规语言。 拟议的研究是对具有此类重写系统的群体类别的研究。 将追究几个问题。 第一个 - 给定一个具有有限完全重写系统的群，是否每个有限索引子群也必须有一个？ 第二个——自动群是否一定有一个有限的完全重写系统？ 第三个——如果一个有限呈现群有有限的推导类型，它是否有一个有限的完全重写系统？ 为了回答这些问题，如果可能的话，为更多的群体家族，特别是 Artin 群体构建重写系统将很有帮助。 他们还打算研究一个群的较弱属性，由范式的子词封闭正则语言给出。 该奖项建议提供国际旅行资金和十二个月的津贴。