Finite Sequentiality of Unambiguous 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...

Structurally Unambiguous Finite Automata

We define a structurally unambiguous finite automaton (SUFA) to be a nondeterministic finite automaton (NFA) with one starting state q0 such that for all input strings w and for any state q, there is at most one path from q0 to q that consumes w. The definition of SUFA differs from the usual definition of an unambiguous finite automaton (UFA) in that the new definition is defined in terms of th...

Multidimensional fuzzy finite tree automata

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for e...

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...