具有ALOGTIME硬词问题和PSPACE完全压缩词问题的组

IF 0.8 Q3 COMPUTER SCIENCE, THEORY & METHODS

ACM Transactions on Computation Theory Pub Date : 2019-09-30 DOI:10.1145/3569708

L. Bartholdi, Michael Figelius, Markus Lohrey, A. Weiss

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引用次数: 8

摘要

我们给出了一大类不可解无限群的字问题复杂性的下界，我们称之为强有效不可解群。该类包括自由组、格里高丘克组和汤普森组。我们证明了这些群有一个NC1硬字问题，并且对于其中的一些群（包括Grigorchuk群和Thompson群），压缩字问题（相当于电路评估问题）是PSPACE完全的。

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Groups with ALOGTIME-hard Word Problems and PSPACE-complete Compressed Word Problems

We give lower bounds on the complexity of the word problem for a large class of non-solvable infinite groups that we call strongly efficiently non-solvable groups. This class includes free groups, Grigorchuk’s group, and Thompson’s groups. We prove that these groups have an NC1-hard word problem and that for some of them (including Grigorchuk’s group and Thompson’s groups) the compressed word problem (which is equivalent to the circuit evaluation problem) is PSPACE-complete.

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来源期刊

ACM Transactions on Computation Theory COMPUTER SCIENCE, THEORY & METHODS-

CiteScore

2.30

自引率

0.00%

发文量