Deciding Unambiguity and Sequentiality starting from 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.

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 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...

Ambiguity and structural ambiguity of symmetric difference NFAs

Okhotin showed an exponential trade-off in the conversion from nondeterministic unary automata to unambiguous nondeterministic unary automata. We show that the trade-off in the case of unary symmetric difference automata to finitely (structurally) ambiguous unary symmetric difference automata is linear with constant 1 in the number of states. In particular, for every n-state unary nondeterminis...