The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed submonotone on a residual subset. For example, it is shown that this property need not be valid on the whole space. We prove, under certain hy...

Inferring inductive invariants is one of the main challenges formal verification. The theory abstract interpretation provides a rich framework to devise invariant inference algorithms. One latest breakthroughs in property-directed reachability (PDR), but research community views PDR and as mostly unrelated techniques. This paper shows that, surprisingly, propositional can be formulated an algor...

Let Q be a monotone decreasing property of graphs G on n vertices. Erdős, Suen and Winkler [5] introduced the following natural way of choosing a random maximal graph in Q: start with G the empty graph on n vertices. Add edges to G one at a time, each time choosing uniformly from all e ∈ G such that G + e ∈ Q. Stop when there are no such edges, so the graph G∞ reached is maximal in Q. Erdős, Su...

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state.

We introduce and study a new system of nonlinear variational-like inclusions involving sG, η maximal monotone operators, strongly monotone operators, η-strongly monotone operators, relaxed monotone operators, cocoercive operators, λ, ξ -relaxed cocoercive operators, ζ, φ, g-relaxed cocoercive operators and relaxed Lipschitz operators in Hilbert spaces. By using the resolvent operator technique ...

Cores are, besides connectivity components, one among few concepts that provides us with efficient decompositions of large graphs and networks. In the paper a generalization of the notion of core of a graph based on vertex property function is presented. It is shown that for the local monotone vertex property functions the corresponding cores can be determined in time.