Processing Succinct Matrices and Vectors

  • Markus Lohrey
  • Manfred Schmidt-Schauß
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8476)

Abstract

We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of a semiring (instead of 0 and 1). A simple example shows that the product of two MTDD-represented matrices cannot be represented by an MTDD of polynomial size. To overcome this deficiency, we extended MTDDs to MTDD +  by allowing componentwise symbolic addition of variables (of the same dimension) in rules. It is shown that accessing an entry, equality checking, matrix multiplication, and other basic matrix operations can be solved in polynomial time for MTDD + -represented matrices. On the other hand, testing whether the determinant of a MTDD-represented matrix vanishes is PSPACE-complete, and the same problem is NP-complete for MTDD + -represented diagonal matrices. Computing a specific entry in a product of MTDD-represented matrices is #P-complete. Complete proofs can be found in the full version [19] of this paper.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Markus Lohrey
    • 1
  • Manfred Schmidt-Schauß
    • 2
  1. 1.Department für Elektrotechnik und InformatikUniversität SiegenGermany
  2. 2.Institut für InformatikGoethe-UniversitätFrankfurtGermany

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