Abstract
Abstract We introduce the notion of rewriting systems for sets, and consider the complexity of two reachability problems for these systems, showing that these problems are PSPACE-complete. Using such problems as bridge between Turing Machine computations and Binary Systolic Tree Automata (BSTA) we are able to prove that a number of important decision problems concerning these automata are PSPACE-complete. Finally, as a consequence, we show that the emptiness problem and the finiteness problem for E0L systems are PSPACE-complete, solving a long standing open problem.
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