Finite Sequentiality of Finitely Ambiguous Max-Plus Tree Automata

We show that the finite sequentiality problem is decidable for finitely ambiguous max-plus tree automata. A max-plus tree automaton is a weighted tree automaton over the max-plus semiring. A max-plus tree automaton is called finitely ambiguous if the number of accepting runs on every tree is bounded by a global constant. The finite sequentiality problem asks whether for a given max-plus tree automaton, there exist finitely many deterministic max-plus tree automata whose pointwise maximum is equivalent to the given automaton.

Finite Sequentiality of Unambiguous Max-Plus Tree Automata

We show the decidability of the finite sequentiality problem for unambiguous max-plus tree automata. A max-plus tree automaton is called unambiguous if there is at most one accepting run on every tree. The finite sequentiality problem asks whether for a given max-plus tree automaton, there exist finitely many deterministic max-plus tree automata whose pointwise maximum is equivalent to the given automaton.

The extremal index and clustering of high values for derived stationary sequences

Given a sequence of independent identically distributed random variables, we derive a moving-maximum sequence (with random translations). The extremal index of the derived sequence is computed and the limiting behaviour of clusters of high values is studied. We are then given two or more independent stationary sequences whose extremal indices are known. We derive a new stationary sequence by taking either a pointwise maximum or by a mixture of the original sequences. In each case, we compute the extremal index of the derived sequence.