Skip to Main content Skip to Navigation
New interface
Reports (Research report)

Reachability problems for products of matrices in semirings

Abstract : We consider the following matrix reachability problem: given r square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix? We define similarly the vector (resp. scalar) reachability problem, by requiring that the matrix product, acting by right multiplication on a prescribed row vector, gives another prescribed row vector (resp. when multiplied at left and right by prescribed row and column vectors, gives a prescribed scalar). We show that over any semiring, scalar reachability reduces to vector reachability which is equivalent to matrix reachability, and that for any of these problems, the specialization to any r >= 2 is equivalent to the specialization to r=2. As an application of this result and of a theorem of Krob, we show that when r=2, the vector and matrix reachability problems are undecidable over the max-plus semiring (Z U {-infinity},max,+). We also show that the matrix, vector, and scalar reachability problems are decidable over semirings whose elements are «positive», like the tropical semiring (N U {+infinity},min,+).
Document type :
Reports (Research report)
Complete list of metadata
Contributor : Rapport De Recherche Inria Connect in order to contact the contributor
Submitted on : Tuesday, May 23, 2006 - 6:22:23 PM
Last modification on : Wednesday, October 26, 2022 - 8:16:17 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:30:22 PM


  • HAL Id : inria-00071635, version 1



Stéphane Gaubert, Ricardo David Katz. Reachability problems for products of matrices in semirings. [Research Report] RR-4944, INRIA. 2003. ⟨inria-00071635⟩



Record views


Files downloads