Skip to Main content Skip to Navigation
Journal articles

Grammatical compression: compressed equivalence and other problems

Abstract : In this work, we focus our attention to algorithmic solutions for problems where the instances are presented as straight-line programs on a given algebra. In our exposition, we try to survey general results by presenting some meaningful examples; moreover, where possible, we outline the proofs in order to give an insight of the methods and the techniques. We recall some recent results for the problem PosSLP, consisting of deciding if the integer defined by a straight-line program on the ring Z is greater than zero; we discuss some implications in the areas of numerical analysis and strategic games. Furthermore, we propose some methods for reducing Compressed Word Problem from an algebra to another; reductions from trace monoids to the semiring of nonnegative integers are exhibited and polynomial time algorithms for compressed equivalence in monoids related to Dyck reductions are shown. Finally, we consider inclusion problems for context-free languages, proving how in some cases efficient algorithms for these problems benefit from the ability to work with compressed data.
Document type :
Journal articles
Complete list of metadata

Cited literature [40 references]  Display  Hide  Download
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s Connect in order to contact the contributor
Submitted on : Tuesday, May 13, 2014 - 3:37:35 PM
Last modification on : Wednesday, December 8, 2021 - 9:22:03 AM
Long-term archiving on: : Monday, April 10, 2017 - 10:24:59 PM


Files produced by the author(s)




Alberto Bertoni, Roberto Radicioni. Grammatical compression: compressed equivalence and other problems. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, Vol. 12 no. 4 (4), pp.109-126. ⟨10.46298/dmtcs.526⟩. ⟨hal-00990458⟩



Record views


Files downloads