On the complexity of some extended word problems defined by cancellation rules
Information Processing Letters
Limitedness theorem on finite automata with distance functions: an algebraic proof
Theoretical Computer Science
On the degree of ambiguity of finite automata
Theoretical Computer Science
New upper bounds to the limitedness of distance automata
Theoretical Computer Science
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Introduction to Formal Language Theory
Introduction to Formal Language Theory
The Product of Rational Languages
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
The finite power property in free groups
Theoretical Computer Science
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In this paper the following problem is studied. Let Σ = Σ ∪ Σ be a finite alphabet where Σ and Σ, are disjoint and equipotent sets. Let L be a rational language over Σ and let SL be the Simon distance automaton of L. Let C be the square matrix with entries in the extended set of natural numbers given by the formula: for every pair (p, q) of states of SL, Cpq is the minimum weight of a computation in SL from p to q labelled by a Dyck word if such a computation exists, otherwise it is ∞. We exhibit a polynomial time algorithm which allows us to compute the matrix C in the case Σ is the unary alphabet. This result partially solves an open question raised in [4].