Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata
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Mikołaj Bojańczyk, Bartek Klin, Joshua Moerman
2021
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.
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