On deciding the confluence of a finite string-rewriting system on a given congruence class
Journal of Computer and System Sciences
String-rewriting systems
On monotonic automata with a restart operation
Journal of Automata, Languages and Combinatorics
FCT '95 Proceedings of the 10th International Symposium on Fundamentals of Computation Theory
On the Complexity of 2-Monotone Restarting Automata
Theory of Computing Systems
Fundamenta Informaticae - Non-Classical Models of Automata and Applications
Learning analysis by reduction from positive data
ICGI'06 Proceedings of the 8th international conference on Grammatical Inference: algorithms and applications
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Clearing restarting automata are based on contextual rewriting. A word w is accepted by an automaton of this type if there is a computation that reduces the word w to the empty word λ by a finite sequence of rewritings. Accordingly, the word problem for a clearing restarting automaton can be solved nondeterministically in quadratic time. If, however, the contextual rewritings happen to be λ-confluent, that is, confluent on the congruence class of the empty word, then the word problem can be solved deterministically in linear time. Here we show that, unfortunately, λ-confluence is not even recursively enumerable for clearing restarting automata. This follows from the fact that λ-confluence is not recursively enumerable for finite factor-erasing string-rewriting systems.