We discuss the connection of additive set functions to dual function spaces by means of integrals. Isometrical isomorphisms are presented between: a) bounded contents and the dual of uniformly approximable functions, b) charges on Baire algebras and the duals of bounded, continuous functions over A-topological spaces, c) Hewitt measures on Baire σ-algebras and the duals of continuous functions ...

We say the sets of nonnegative integers A and B are additive complements if their sum contains all sufficiently large integers. In this paper we prove a conjecture of Chen and Fang about additive complement of a finite set. 2000 AMS Mathematics subject classification number : primary: 11B13, secondary: 11P99.

It is shown that the set of periods of any additive cellular automata F, where the addition is done modulo a prime p, can be determined using some simple conditions on the coefficients in the linear expression of F. In particular, we establish that the set of periods has only four possibilities: {1,m} for some m where 1 m<p, N\{pm : m ∈ N}, N\{2pm : m ∈ N ∪ {0}} or the whole set N = {1, 2, 3, ....

Security agencies have found security games to be useful models to understand how to better protect their assets. The key practical elements in this work are: (i) the attacker can simultaneously attack multiple targets, and (ii) different targets exhibit different types of dependencies based on the assets being protected (e.g., protection of critical infrastructure, network security, etc.). How...

Additive Cost Register Automata (ACRA) map strings to integers using a finite set of registers that are updated using assignments of the form “x := y+ c” at every step. The corresponding class of additive regular functions has multiple equivalent characterizations, appealing closure properties, and a decidable equivalence problem. In this paper, we solve two decision problems for this model. Fi...

We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.

Strategically allocating resources to protect targets against potential threats in an efficient way is a key challenge facing our society. From the classical interdiction game to the recently proposed Stackelberg Security Game, applying computational game models to the security domain has made a real-world impact on numerous fields including military attack and defense, financial system securit...