Anisotropic diffusion affords an efficient, adaptive signal smoothing technique that can be used for signal enhancement, signal segmentation, and signal scale-space creation. This paper introduces a novel partial differential equation (PDE)-based diffusion method for generating locally monotonic signals. Unlike previous diffusion techniques that diverge or converge to trivial signals, locally m...

In a monotonic sequence game, two players alternately choose elements of a sequence from some fixed ordered set. The game ends when the resulting sequence contains either an ascending subsequence of length a or a descending one of length d. We investigate the behaviour of this game when played on finite linear orders or Q and provide some general observations for play on arbitrary ordered sets.

We characterize which scoring rules are Maskin-monotonic for each social choice problem as a function of the number of agents and the number of alternatives. We show that a scoring rule is Maskin-monotonic if and only if it satisfies a certain unanimity condition. Since scoring rules are neutral, Maskin-monotonicity turns out to be equivalent to Nash-implementability within the class of scoring...

Boolean satisfiability (SAT) solvers have been successfully applied to a wide variety of difficult combinatorial problems. Many further problems can be solved by SAT Modulo Theory (SMT) solvers, which extend SAT solvers to handle additional types of constraints. However, building efficient SMT solvers is often very difficult. In this paper, we define the concept of a Boolean monotonic theory an...

We consider verification of safety properties for parameterized distributed protocols. Such a protocol consists of an arbitrary number of (infinite-state) processes that communicate asynchronously over FIFO channels. The aim is to perform parameterized verification, i.e., showing correctness regardless of the number of processes inside the system. We consider two non-trivial case studies: the d...

Following up our previous work [9], we distinguish the monotonic properties and the non-monotonic ones in our inference system based on the framework of compositional logic, and give the way to include some non-monotonic properties. As an example, we present a correctness proof of Challenge Response protocol, and explain how such properties can be used in more powerful derivations. We also give...

1. f (x, s) f (x, s + 1) for all x and s; 2. sups f (x, s) < ∞ for every x ; 3. F(x) = sups f (x, s). A set A ⊆ N is limitwise monotonic if A equals to the range of some limitwise monotonic function. If we replace here the computable functions f by X -computable functions for some Turing oracle X then we get the notions of X -limitwise monotonic functions and sets, respectively. Note that a sim...

Non-monotonicity enhances the expressivity of a representation framework allowing high-level representations of (inherently non-monotonic) problems close to their natural specification. This gain in expressivity should not though compromise (severely) the computational effectiveness of the solutions based on non-monotonic representations. In this paper we argue that for abduction and consequent...