GROUPS THAT DO AND DO NOT HAVE GROWING CONTEXT-SENSITIVE WORD PROBLEM

DEREK F. HOLT, SARAH REES, MICHAEL SHAPIRO
2008 International journal of algebra and computation  
We prove that a group has word problem that is a growing contextsensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and Shapiro in [6]). We generalise results of [6] to find many examples of groups not admitting non-deterministic Cannon's algorithms. This adds to the examples of Kambites and Otto in [7] of groups separating context-sensitive and growing contextsensitive word problems,
more » ... nd provides a new language-theoretic separation result.
doi:10.1142/s0218196708004834 pmid:19997524 pmcid:PMC2789434 fatcat:epgfqrvulfexfbtua4fldbkp5i