Study of the word problem for algebraic systems by means of rewriting

用改写系统的方法研究了有限表示代数的词问题和其他决策问题。在语言理论意义上，我们发现了有限表示一元群的词问题的可解性与具有良好性质的完备重写系统的存在性之间的某种关系。我们还研究了与上述性质有关的单群的截面。要解决单词问题，上下文敏感的横截面就足够了，而上下文无关的横截面则不行（参见[2]和[9]）。我们在一篇调查文章b[5]中报道了这些结果。研究了改写系统本身的合流性和终止性等重要性质。在b[6]中，我们给出了合流单规则系统终止的结果。我们证明了改写技术在与一元表示相关的导数图的同伦理论中也是有用的。如果一个单群具有完全同伦约简系统，则它满足同伦有限性FP4。我们总是有左正则化约简系统，如果表示是非特殊的，它就是完备的。这些结果已在b[8]中报道。提出了用大秩修正Neron法构造g <大于等于>2的代数曲线族的方法

We studied the word problem and other decision problems for finitely presented algebras by means of rewriting systems.We found some relationship between the solvability of the word problem and the existence of complete rewriting systems with good properties in a language- theoretical sense for finitely presented monoids. We also studied cross-sections of monoids related to the above properties. For the word problem to be solvable, context-sensitive cross-sections suffice but context-free cross-sections do not (see [2] and [9]). We reported these results in a survey article [5].We studied some important properties such as confluence and termination of rewriting systems themselves. In [6] we gave a result on the termination for confluent one-rule systems.We showed that the rewriting techniques are useful too in the homotopy theory of the derivation graphs associated with monoid presentations. If a monoid has a complete homotopy reduction system, then it satisfies the homological finiteness property FP4. We always have the left canonical reduction system and it is complete if the presentation is nonspecial. These results are reported in [8].We developed the method to construct a family of algebraic curves of genus g <greater than or equal> 2 with large rank modifying Neron's method