Stackelberg games have been widely used to model interactions between attackers and defenders in a broad array of security domains. One related approach involves plan interdiction, whereby a defender chooses a subset of actions to block (remove), and the attacker constructs an optimal plan in response. In previous work, this approach has been introduced in the context of Markov decision process...

Recently defined, three-level logic sum of pseudoproducts (SPP) forms are EXOR-AND-OR networks representing Boolean functions, and are much shorter than standard two-level sum of products (SOP) expressions (Luccio and Pagli, 1999). The main disadvantages of SPP networks are their cumbersome theory in the original formulation and their high minimization time. In addition, the current technology ...

Recall that every commutative ring R determines an affine scheme in algebraic geometry. This consists of two components: a topological space Spec(R) (the spectrum) and a sheaf of local rings OR (the structure sheaf). In this way, a scheme encodes both geometric and algebraic data. In this work, we present a construction of “logical schemes,” geometric entities which represent logical theories i...

For a minimal inequality derived from a maximal lattice-free simplicial polytope in R, we investigate the region where minimal liftings are uniquely defined, and we characterize when this region covers R. We then use this characterization to show that a minimal inequality derived from a maximal lattice-free simplex in R with exactly one lattice point in the relative interior of each facet has a...

The Elliptic Curve Discrete Logarithm Problem(ECDLP) is known to be an exponential time problem except the cases of smooth curves, supersingular curves and anomalous curves. Recently, several new methods to solve ECDLP on a prime eld were proposed. All of them try to solve ECDLP on a prime eld by lifting a given elliptic curve to low rank elliptic curves de ned over the rationals. In this exten...

motivated by an arens regularity problem, we introduce the concepts of matrix banach space and matrix banach algebra. the notion of matrix normed space in the sense of ruan is a special case of our matrix normed system. a matrix banach algebra is a matrix banach space with a completely contractive multiplication. we study the structure of matrix banach spaces and matrix banach algebras. then we...

In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense ...