## DECIDABILITY AND COMPLEXITY IN AUTOMATIC MONOIDS

by
Markus Lohrey

Venue: | INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE |

Citations: | 3 - 1 self |

### BibTeX

@MISC{Lohrey_decidabilityand,

author = {Markus Lohrey},

title = { DECIDABILITY AND COMPLEXITY IN AUTOMATIC MONOIDS },

year = {}

}

### OpenURL

### Abstract

Several complexity and decidability results for automatic monoids are shown: (i) there exists an automatic monoid with a P-complete word problem, (ii) there exists an automatic monoid such that the first-order theory of the corresponding Cayley-graph is not elementary decidable, and (iii) there exists an automatic monoid such that reachability in the corresponding Cayley-graph is undecidable. Moreover, it is shown that for every hyperbolic group the word problem belongs to LOGCFL, which improves a result of Cai [8].