2022/09/06 by Jason P. Bell, Bell, Jason P., Daniel Smertnig +1 · 1 citation
Computer Science · #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Formal Methods in Verification #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2209.02260
openalex publication_date 2022/09/06 · openalex created_date 2022/09/08 · openalex updated_date 2026/07/28
The (left) linear hull of a weighted automaton over a field is a topological invariant. If the automaton is minimal, the linear hull can be used to determine whether or not the automaton is equivalent to a deterministic one. Furthermore, the linear hull can also be used to determine whether the minimal automaton is equivalent to an unambiguous one. We show how to compute the linear hull, and thus prove that it is decidable whether or not a given automaton over a number field is equivalent to a deterministic one. In this case we are also able to compute an equivalent deterministic automaton. We also show the analogous decidability and computability result for the unambiguous case. Our results resolve a problem posed in a 2006 survey by Lombardy and Sakarovitch.