Finite Sequentiality of Finitely Ambiguous Max-Plus Tree Automata

The Equivalence, Unambiguity and Sequentiality Problems of Finitely Ambiguous Max-Plus Tree Automata are Decidable

A max-plus automaton is a finite automaton with transition weights in the real numbers. To each word, it assigns the maximum weight of all accepting paths on the word, where the weight of a path is the sum of the path’s transition weights. Max-plus automata and their min-plus counterparts are weighted automata [19, 18, 13, 2, 4] over the max-plus or min-plus semiring. Under varying names, max-p...

Deciding the Sequentiality of a Finitely Ambiguous Max-Plus Automaton

Deciding unambiguity and sequentiality from a finitely ambiguous max-plus automaton

Finite automata with weights in the max-plus semiring are considered. The main result is: it is decidable in an effective way whether a series that is recognized by a finitely ambiguous max-plus automaton is unambiguous, or is sequential. A collection of examples is given to illustrate the hierarchy of max-plus series with respect to ambiguity.

Deciding Unambiguity and Sequentiality starting from a Finitely Ambiguous Max-Plus Automaton

Finite automata with weights in the max-plus semiring are considered. The main result is: it is decidable in an effective way whether a series that is recognized by a finitely ambiguous max-plus automaton is unambiguous, or is sequential. A collection of examples is given to illustrate the hierarchy of max-plus series with respect to ambiguity.

Deciding Unambiguity and Sequentiality of Polynomially Ambiguous Min-Plus Automata

This paper solves the unambiguity and the sequentiality problem for polynomially ambiguous min-plus automata. This result is proved through a decidable algebraic characterization involving so-called metatransitions and an application of results from the structure theory of finite semigroups. It is noteworthy that the equivalence problem is known to be undecidable for polynomially ambiguous auto...