Abstract
We consider binary relations on words which can be recognized by finite two-tape devices in two different ways: the traditional way where the two tapes are scanned in the same direction and a new one where they are scanned in different directions. The devices of the former type define the family of rational relations, while those of the latter define an a priori really different family. We characterize the partial functions that are in the intersection of the two families. We state a conjecture for the intersection for general, nonfunctional, relations.
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Notes
- 1.
We compose the relations from left to right: \(R\circ S\) denotes the relation \(\left\{ {(u,v)\mid \exists w,\ (u,w)\in R\text { and }(w,v)\in S}\right\} \).
- 2.
The image of a relation R is the subset \(\left\{ {v\in \varDelta ^*\mid \exists u\in \varSigma ^*,\ \left( {u,v}\right) \in R}\right\} \).
- 3.
An \(\epsilon \)-free automaton is trim if each of its state q is accessible (i.e., there exists a path from the initial state to q) and co-accessible (i.e., there exists a path from q to some accepting state). Every finite automaton is equivalent to some trim automaton.
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Choffrut, C., Guillon, B. (2016). Both Ways Rational Functions. In: Brlek, S., Reutenauer, C. (eds) Developments in Language Theory. DLT 2016. Lecture Notes in Computer Science(), vol 9840. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53132-7_10
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DOI: https://doi.org/10.1007/978-3-662-53132-7_10
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