Algorithms for the Join and Auto-Intersection of Multi-Tape Weighted Finite-State Machines.

Abstract : A weighted finite-state machine with n tapes describes a rational relation on n strings. We recall some basic operations on n-ary rational relations, recast the important join operation in terms of "auto-intersection", and propose restricted algorithms for both operations. If two rational relations are joined on more than one tape, it can unfortunately lead to non-rational relations with undecidable properties. As a consequence, there cannot be a fully general algorithm, able to compile any rational join or auto-intersection. We define a class of triples 〈A,i,j〉 for which we are able to compile the auto-intersection of the machine A w.r.t. tapes i and j. We hope that this class is sufficient for many practical applications.
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https://hal.archives-ouvertes.fr/hal-00400775
Contributor : Franck Guingne <>
Submitted on : Wednesday, July 1, 2009 - 4:47:06 PM
Last modification on : Thursday, February 7, 2019 - 5:43:53 PM

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Franck Guingne, Jean-Marc Champarnaud, Florent Nicart, André Kempe. Algorithms for the Join and Auto-Intersection of Multi-Tape Weighted Finite-State Machines.. International Journal of Foundations of Computer Science, World Scientific Publishing, 2008, 19, pp.453 - 476. ⟨10.1142/S0129054108005760⟩. ⟨hal-00400775⟩

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