https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:30657 Wed 17 Nov 2021 16:30:05 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:21496 i≤_sF_i, where each F_i is either a free or finite group, or a free monoid with involution. In all cases the result is the same: the set of all solutions in reduced words is EDT0L. This was known only for quadratic word equations by, which is a very restricted case. Our general result became possible due to the recent recompression technique of Jeż. In this paper we use a new method to integrate solutions of linear Diophantine equations into the process and obtain more general results than in the related paper. For example, we improve the complexity from quadratic nondeterministic space in to quasi-linear nondeterministic space here. This implies an improved complexity for deciding the existential theory of non-abelian free groups: NSPACE(n log n). The conjectured complexity is NP, however, we believe that our results are optimal with respect to space complexity, independent of the conjectured NP.]]> Wed 11 Apr 2018 12:43:02 AEST ]]>