In graph pebbling games, one considers a distribution of pebbles on the vertices of a graph, and a pebbling move consists of taking two pebbles off one vertex and placing one on an adjacent vertex. The t-pebbling number πt(G) of a graph G is the smallest m such that for every initial distribution of m pebbles on V (G) and every target vertex x there exists a sequence of pebbling moves leading t...

We generalize to eventually regular (or ‘π-regular’) semigroups the study of the lattice of full regular subsemigroups of a regular semigroup, which has its most complete exposition in the case of inverse semigroups. By means of a judicious definition, it is shown that the full eventually regular subsemigroups of such a semigroup form a complete lattice LF , which projects onto the lattices of ...

Background. For X a smooth scheme over ~, K.t(X; 2g/{") is isomorphic to the usual rood(" topological K-theory of X as a complex manifold ([6]). In this case, Theorem 1 essentially answers a question of Fulton, [9], w 5. For many such X the mapp: Ko(X)~K~ot(X) cannot be a surjection, as non-trivial Hodge conditions on the Chern classes prevent some topological bundles from being stably algebrai...

Static analyses make the increasingly tenuous assumption that all source code is available for analysis; for example, large libraries often call into native code that cannot be analyzed. We propose a pointsto analysis that initially makes optimistic assumptions about missing code, and then inserts runtime checks that report counterexamples to these assumptions that occur during execution. Our a...

Large scale distributed data stores rely on optimistic replication to scale and remain highly available in the face of network partitions. Managing data without coordination results in eventually consistent data stores that allow for concurrent data updates. These systems often use anti-entropy mechanisms (like Merkle Trees) to detect and repair divergent data versions across nodes. However, in...

In this paper, we consider the so-called eventually positive systems, that is systems with trajectories originating in a positive orthant becoming positive after some finite transient. We extend this notion to the input-output system case. Our extension is performed in such a manner, that some valuable properties of internally positive input-output systems are preserved. For example, the stable...

Let M be a numerical monoid (i.e., an additive submonoid of N0) with minimal generating set 〈n1, . . . , nt〉. For m ∈ M , if m = Pt i=1 xini, then Pt i=1 xi is called a factorization length of m. We denote by L(m) = {m1, . . . , mk} (where mi < mi+1 for each 1 ≤ i < k) the set of all possible factorization lengths of m. The Delta set of m is defined by ∆(m) = {mi+1 −mi | 1 ≤ i < k } and the Del...

This thesis builds on the work of Fekete et al. [1], who defined an eventually-serializable data service (ESDS) and an abstract algorithm for it. ESDS allows its users to relax consistency requirements in return for improved responsiveness, while providing guarantees of eventual consistency of the replicated data. An important consideration in formulating ESDS was that it could be employed in b...