OrbitFiniteDimensional Vector Spaces and Weighted Register Automata
Abstract
We develop a theory of vector spaces spanned by orbitfinite 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 DOI:
 10.48550/arXiv.2104.02438
 arXiv:
 arXiv:2104.02438
 Bibcode:
 2021arXiv210402438B
 Keywords:

 Computer Science  Formal Languages and Automata Theory;
 F.1.1;
 F.4.3
 EPrint:
 Journal Version for TheoretiCS