Abstract
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.
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Mráz, F., Otto, F. (2013). Lambda-Confluence Is Undecidable for Clearing Restarting Automata. In: Konstantinidis, S. (eds) Implementation and Application of Automata. CIAA 2013. Lecture Notes in Computer Science, vol 7982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39274-0_23
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