Characterising Space Complexity Classes via Knuth-Bendix Orders
We study three different space complexity classes: LINSPACE, PSPACE, and ESPACE and give complete characterisations for these classes. We employ rewrite systems, whose termination can be shown by Knuth Bendix orders. To capture LINSPACE, we consider positively weighted Knuth Bendix orders. To capture PSPACE, we consider unary rewrite systems, compatible with a Knuth Bendix order, where we allow for padding of the input. And to capture ESPACE, we make use of a non-standard generalisation of the Knuth Bendix order.
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