Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata

Abstract

We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automata for infinite alphabets. The algorithm runs in exponential time, and in polynomial time for a fixed number of registers. As a special case, we can decide, with the same complexity, language equivalence for unambiguous register automata, which improves previous results in three ways: (a) we allow for order comparisons on atoms, and not just equality; (b) the complexity is exponentially better; and (c) we allow automata with guessing.

Authors 3

1. Mikołaj Bojańczyk

   University of Warsaw

   Affiliation as printed

   University of Warsaw

2. Bartek Klin

   University of Warsaw

   Affiliation as printed

   University of Warsaw

3. Joshua Moerman Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen