182,155 research outputs found
Automated reasoning for attributed graph properties
Graphs are ubiquitous in computer science. Moreover, in various application fields, graphs are equipped with attributes to express additional information such as names of entities or weights of relationships. Due to the pervasiveness of attributed graphs, it is highly important to have the means to express properties on attributed graphs to strengthen modeling capabilities and to enable analysis. Firstly, we introduce a new logic of attributed graph properties, where the graph part and attribution part are neatly separated. The graph part is equivalent to first-order logic on graphs as introduced by Courcelle. It employs graph morphisms to allow the specification of complex graph patterns. The attribution part is added to this graph part by reverting to the symbolic approach to graph attribution, where attributes are represented symbolically by variables whose possible values are specified by a set of constraints making use of algebraic specifications. Secondly, we extend our refutationally complete tableau-based reasoning method as well as our symbolic model generation approach for graph properties to attributed graph properties. Due to the new logic mentioned above, neatly separating the graph and attribution parts, and the categorical constructions employed only on a more abstract level, we can leave the graph part of the algorithms seemingly unchanged. For the integration of the attribution part into the algorithms, we use an oracle, allowing for flexible adoption of different available SMT solvers in the actual implementation. Finally, our automated reasoning approach for attributed graph properties is implemented in the tool AutoGraph integrating in particular the SMT solver Z3 for the attribute part of the properties. We motivate and illustrate our work with a particular application scenario on graph database query validation.Peer ReviewedPostprint (author's final draft
A Systematic Approach to Constructing Families of Incremental Topology Control Algorithms Using Graph Transformation
In the communication systems domain, constructing and maintaining network
topologies via topology control (TC) algorithms is an important cross-cutting
research area. Network topologies are usually modeled using attributed graphs
whose nodes and edges represent the network nodes and their interconnecting
links. A key requirement of TC algorithms is to fulfill certain consistency and
optimization properties to ensure a high quality of service. Still, few
attempts have been made to constructively integrate these properties into the
development process of TC algorithms. Furthermore, even though many TC
algorithms share substantial parts (such as structural patterns or tie-breaking
strategies), few works constructively leverage these commonalities and
differences of TC algorithms systematically. In previous work, we addressed the
constructive integration of consistency properties into the development
process. We outlined a constructive, model-driven methodology for designing
individual TC algorithms. Valid and high-quality topologies are characterized
using declarative graph constraints; TC algorithms are specified using
programmed graph transformation. We applied a well-known static analysis
technique to refine a given TC algorithm in a way that the resulting algorithm
preserves the specified graph constraints.
In this paper, we extend our constructive methodology by generalizing it to
support the specification of families of TC algorithms. To show the feasibility
of our approach, we reneging six existing TC algorithms and develop e-kTC, a
novel energy-efficient variant of the TC algorithm kTC. Finally, we evaluate a
subset of the specified TC algorithms using a new tool integration of the graph
transformation tool eMoflon and the Simonstrator network simulation framework.Comment: Corresponds to the accepted manuscrip
Query Processing on Attributed Graphs
An attributed graph is a powerful tool for modeling a variety of information networks. It is not only able to represent relationships between objects easily, but it also allows every vertex and edge to have its attributes. Hence, a lot of data, such as the web, sensor networks, biological networks, economic graphs, and social networks, are modeled as attributed graphs. Due to the popularity of attributed graphs, the study of attributed graphs has caught attentions of researchers. For example, there are studies of attributed graph OLAP, query engine, clustering, summary, constrained pattern matching query, and graph visualization, etc. However, to the best of our knowledge, the studies of topological and attribute relationships between vertices on attributed graphs have not drawn much attentions of researchers. Given the high expressive power and popularity of attributed graph, in this thesis, we define and study the processing of three new attributed graph queries, which would help users to understand the topological and attribute relationships between entities in attributed graphs. For example, a reachability query on a social network can tell whether two persons can be connected given certain attribute constraints; a reachability query on a biological network can tell whether a compound can be transformed to another compound under given chemical reaction conditions; a How-to-Reach query can tell why the answers of the above two reachability query are negative; a visualizable path summary query can offer an overall picture of topological and attribute relationship between any two vertices in attributed graphs. Except for the proposed query types in this thesis, we believe that there is still penalty of meaningful attributed graph query types that have not been proposed and studied by the database and data mining community since an attributed graph is a very rich source of information. Through this thesis, we hope to draw people's attentions on attributed graph query processing so that more hidden information contained in attributed graphs can be queried and discovered
Weisfeiler--Lehman goes Dynamic: An Analysis of the Expressive Power of Graph Neural Networks for Attributed and Dynamic Graphs
Graph Neural Networks (GNNs) are a large class of relational models for graph
processing. Recent theoretical studies on the expressive power of GNNs have
focused on two issues. On the one hand, it has been proven that GNNs are as
powerful as the Weisfeiler-Lehman test (1-WL) in their ability to distinguish
graphs. Moreover, it has been shown that the equivalence enforced by 1-WL
equals unfolding equivalence. On the other hand, GNNs turned out to be
universal approximators on graphs modulo the constraints enforced by
1-WL/unfolding equivalence. However, these results only apply to Static
Undirected Homogeneous Graphs with node attributes. In contrast, real-life
applications often involve a variety of graph properties, such as, e.g.,
dynamics or node and edge attributes. In this paper, we conduct a theoretical
analysis of the expressive power of GNNs for these two graph types that are
particularly of interest. Dynamic graphs are widely used in modern
applications, and its theoretical analysis requires new approaches. The
attributed type acts as a standard form for all graph types since it has been
shown that all graph types can be transformed without loss to Static Undirected
Homogeneous Graphs with attributes on nodes and edges (SAUHG). The study
considers generic GNN models and proposes appropriate 1-WL tests for those
domains. Then, the results on the expressive power of GNNs are extended by
proving that GNNs have the same capability as the 1-WL test in distinguishing
dynamic and attributed graphs, the 1-WL equivalence equals unfolding
equivalence and that GNNs are universal approximators modulo 1-WL/unfolding
equivalence. Moreover, the proof of the approximation capability holds for
SAUHGs, which include most of those used in practical applications, and it is
constructive in nature allowing to deduce hints on the architecture of GNNs
that can achieve the desired accuracy
Checking bisimilarity for attributed graph transformation
Borrowed context graph transformation is a technique developed by Ehrig and Koenig to define bisimilarity congruences from reduction semantics defined by graph transformation. This means that, for instance, this technique can be used for defining bisimilarity congruences for process calculi whose operational semantics can be defined by graph transformation. Moreover, given a set of graph transformation rules, the technique can be used for checking bisimilarity of two given graphs. Unfortunately, we can not use this ideas to check if attributed graphs are bisimilar, i.e. graphs whose nodes or edges are labelled with values from some given data algebra and where graph transformation involves computation on that algebra. The problem is that, in the case of attributed graphs, borrowed context transformation may be infinitely branching. In this paper, based on borrowed context transformation of what we call symbolic graphs, we present a sound and relatively complete inference system for checking bisimilarity of attributed graphs. In particular, this means that, if using our inference system we are able to prove that two graphs are bisimilar then they are indeed bisimilar. Conversely, two graphs are not bisimilar if and only if we can find a proof saying so, provided that we are able to prove some formulas over the given data algebra. Moreover, since the proof system is complex to use, we also present a tableau method based on the inference system that is also sound and relatively complete.Postprint (published version
Conflict Detection for Edits on Extended Feature Models using Symbolic Graph Transformation
Feature models are used to specify variability of user-configurable systems
as appearing, e.g., in software product lines. Software product lines are
supposed to be long-living and, therefore, have to continuously evolve over
time to meet ever-changing requirements. Evolution imposes changes to feature
models in terms of edit operations. Ensuring consistency of concurrent edits
requires appropriate conflict detection techniques. However, recent approaches
fail to handle crucial subtleties of extended feature models, namely
constraints mixing feature-tree patterns with first-order logic formulas over
non-Boolean feature attributes with potentially infinite value domains. In this
paper, we propose a novel conflict detection approach based on symbolic graph
transformation to facilitate concurrent edits on extended feature models. We
describe extended feature models formally with symbolic graphs and edit
operations with symbolic graph transformation rules combining graph patterns
with first-order logic formulas. The approach is implemented by combining
eMoflon with an SMT solver, and evaluated with respect to applicability.Comment: In Proceedings FMSPLE 2016, arXiv:1603.0857
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