Communication Complexity Method for Measuring Nondeterminism in Finite Automata

A Burnside Approach to the Termination of Mohri's Algorithm for Polynomially Ambiguous Min-Plus-Automata

“…Polynomially ambiguous (unweighted) automata have been studied by various authors, e.g., [14,15,25]. The following characterization is shown implicitly in [14,15] (cf.…”

“…The following characterization is shown implicitly in [14,15] (cf. Proof of Theorem 3.1 in [15] or Lemma 4.3 in [14]).…”

“…Proof of Theorem 3.1 in [15] or Lemma 4.3 in [14]). Although [14,15] deal with unweighted automata, the construction carries over to WFA over Z in a straightforward way. 2.…”

“…Let us mention that it was shown implicitly in [15,13,14] in an automata theoretic framework that every subsemigroup of B n×n which satisfies condition (2) Assume that S is polynomially ambiguous and let e ∈ E(T ). By Lemma 4.2(1), ≤ e is antisymmetric.…”

Ambiguity, Nondeterminism and State Complexity of Finite Automata

“…The celebrated separation result of Leung [30] establishes that there exist (exponentially ambiguous) n-state NFAs such that any equivalent polynomially ambiguous NFA needs 2 n − 1 states. Hromkovič et al [19,20] have used powerful techniques from communications complexity for state complexity separations for NFAs with different degree of ambiguity.…”