Specifying Graph Languages with Type Graphs

We investigate three formalisms to specify graph languages, i.e. sets of graphs, based on type graphs. First, we are interested in (pure) type graphs, where the corresponding language consists of all graphs that can be mapped homomorphically to a given type graph. In this context, we also study languages specified by restriction graphs and their relation to type graphs. Second, we extend this basic approach to a type graph logic and, third, to type graphs with annotations. We present decidability results and closure properties for each of the formalisms.Comment: (v2): -Fixed some typos -Added more reference

Towards Translating Graph Transformation Approaches by Model Transformations

Recently, many researchers are working on semantics preserving model transformation. In the field of graph transformation one can think of translating graph grammars written in one approach to a behaviourally equivalent graph grammar in another approach. In this paper we translate graph grammars developed with the GROOVE tool to AGG graph grammars by first investigating the set of core graph transformation concepts supported by both tools. Then, we define what it means for two graph grammars to be behaviourally equivalent, and for the regarded approaches we actually show how to handle different definitions of both - application conditions and graph structures. The translation itself is explained by means of intuitive examples

Action planning for graph transition systems

Graphs are suitable modeling formalisms for software and hardware systems involving aspects such as communication, object orientation, concurrency, mobility and distribution. State spaces of such systems can be represented by graph transition systems, which are basically transition systems whose states and transitions represent graphs and graph morphisms. In this paper, we propose the modeling of graph transition systems in PDDL and the application of heuristic search planning for their analysis. We consider different heuristics and present experimental results

Homotopy Theoretic Models of Type Theory

We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it. On the other hand, those conditions are easy to check and provide a wide class of models some of which are listed in the paper.Comment: Corrected version of the published articl

Model checking usage policies

We study usage automata, a formal model for specifying policies on the usage of resources. Usage automata extend finite state automata with some additional features, parameters and guards, that improve their expressivity. We show that usage automata are expressive enough to model policies of real-world applications. We discuss their expressive power, and we prove that the problem of telling whether a computation complies with a usage policy is decidable. The main contribution of this paper is a model checking technique for usage automata. The model is that of usages, i.e. basic processes that describe the possible patterns of resource access and creation. In spite of the model having infinite states, because of recursion and resource creation, we devise a polynomial-time model checking technique for deciding when a usage complies with a usage policy

A Logic for Constraint-based Security Protocol Analysis

We propose PS-LTL, a pure-past security linear temporal logic that allows the specification of a variety of authentication, secrecy and data freshness properties. Furthermore, we present a sound and complete decision procedure to establish the validity of security properties for symbolic execution traces, and show the integration with constraint-based analysis techniques

The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape