A CHARACTERIZATION OF LEXICOGRAPHICALLY ORDERED -SETS

Sums of lexicographically ordered sets

We consider the problem of determining finite integer sets which are knapsack-solvable in linear time (that is, it is possible to determine in linear time, for any integer b, whether b can be expressed as a sum of distinct elements of that set) and where the largest element is as small as possible. We study the condition that the k-subsets (for fixed k) when lexicographically ordered have incre...

Games with lexicographically ordered $ω$-regular objectives

In recent years, two-player zero-sum games with multidimensional objectives have received a lot of interest as a model for intricate systems that are required to satisfy several properties. In this framework, player 1 wins if he can ensure that all objectives are satisfied against any behavior of player 2. It is however often natural to provide more significance to one objective over another, a...

Games with lexicographically ordered $\omega$-regular objectives

In recent years, two-player zero-sum games with multidimensional objectives have received a lot of interest as a model for the synthesis of complex reactive systems. In this framework, player 1 wins if he can ensure that all objectives are satisfied against any behavior of player 2. It is however often natural to provide more significance to one objective over another, a situation that can be m...

Tripled partially ordered sets

In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

General Algorithms for the Address Calculation of Lexicographically Ordered Tuples