for each a ∈ A. We denote the top and bottom elements of a σ-frame A respectively by 1A and 0A. σ-Frame homomorphisms preserve countable joins and finite meets. The resulting category is denoted σFrm. Extending the above notions by allowing arbitrary subsets and arbitrary joins in the definitions leads to the notions of a frame and a frame homomorphism, and the corresponding category Frm of fra...

Provenance Graphs: Anticipating and Exploiting Schema-Level Data Provenance Daniel Zinn Bertram Ludäscher {dzinn,ludaesch}@ucdavis.edu Abstract. Provenance graphs capture flow and dependency information recorded during scientific workflow runs, which can be used subsequently to interpret, validate, and debug workflow results. In this paper, we propose a new concept, called abstract provenance g...

Extremal problems for graph homomorphisms have recently become a topic of much research. Let hom(G,H) denote the number of homomorphisms from G to H. A natural set of problems arises when we fix an image graph H and determine which graph(s) G on n vertices and m edges maximize hom(G,H). We prove that if H is loop-threshold, then, for every n and m, there is a threshold graph G with n vertices a...

Infinite presentations are given for all of the higher Torelli groups of once-punctured surfaces. In the case of the classical Torelli group, a finite presentation of the corresponding groupoid is also given. Furthermore, the first Johnson homomorphism, which is defined from the classical Torelli group to the third exterior power of the homology of the surface, is shown to lift to an explicit c...

We present an equational framework for term graph rewriting with cycles. The usual notion of homomorphism is phrased in terms of the notion of bisimulation, which is well-known in process algebra and concurrency theory. Speciically, a homomorphism is a functional bisimulation. We prove that the bisimilarity class of a term graph, partially ordered by functional bisimulation, is a complete latti...

Canonical extensions of (bounded) lattices have been extensively studied, and the basic existence and uniqueness theorems for these have been extended to general posets. This paper focuses on the intermediate class S∧ of (unital) meet semilattices. Any S ∈ S∧ embeds into the algebraic closure system Filt(Filt(S)). This iterated filter completion, denoted Filt(S), is a compact and ∨∧ -dense exte...

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

Because of the associativity of fusion products ⊠, the above hypothesis is equivalent to the condition that for each irreducible module W , there is an irreducible module W̃ such that HomV (W̃ ⊠ W,V ) 6= 0. In the previous paper [6], we have introduced a concept of ”Semi-Rigidity” and then proved that if W is semi-rigid, then W is flat for the fusion products ⊠, that is, 0 → W ⊠ A → W ⊠ B → W ⊠ C...

The rst systematic treatment of weighted extended tree transducers (wxtt) over countably complete semirings is provided. It is proved that the extension in the left-hand sides of a wxtt can be simulated by the inverse of a linear and nondeleting tree homomorphism. In addition, a characterization of weighted tree transformations computed by bottomup wxtt in terms of bimorphisms is provided. Back...