We descrive some theoretical and practical aspects we had to solve while developing of a toolset to prototype (symbolically execute) algebraic specifications of concurrent, systems and languages. The methodology used in writing such specifications has allowed us to develop efficient specialized algorithms and strategies which we have implemented. The resulting prototype is being used as a research tool and its use, especially in conjunction with other existing verification tools, seems very promising.

We address the problem of building valid representations of non-manifold d-dimensional objects through an approach based on decomposing a non-manifold d-dimensional object into an assembly of more regular components. We first define a standard decomposition of d-dimensional non-manifold objects described by abstract simplicial complexes. This decomposition splits a non-manifold object into components that belong to a well-understood class of objects, that we call initial quasi-manifold. Initial quasi-manifolds cannot be decomposed without cutting them along manifold faces. They form a decidable superset of d-manifolds for d⩾3, and coincide with manifolds for d⩽2. We then present an algorithm that computes the standard decomposition of a general non-manifold complex. This decomposition is unique, and removes all singularities which can be removed without cutting the complex along its manifold faces.

Abstract simplicial complexes are used in many application contexts to represent multi-dimensional, possibly non-manifold and non-uniformly dimensional, geometric objects. In this paper we introduce a new general yet compact data structure for representing simplicial complexes, which is based on a decomposition approach that we have presented in our previous work [3]. We compare our data structure with the existing ones and we discuss in which respect it performs better than others.

We consider the problem of transmitting huge triangle meshes in the context of a Web-like client–server architecture. Approximations of the original mesh are transmitted by applying selective refinement. A multiresolution geometric model is maintained by the server. A client may query the server for a mesh at an arbitrary, continuously variable, level of detail. The client makes repeated queries over time with different query parameters. The server answers to queries by traversing the multiresolution model and transmitting updates to the client, which uses them to progressively modify a current mesh. We study this problem in the context of a vertex-based multiresolution model, which is a special instance of the Multi-Triangulation (a model that was developed in an earlier work), based on vertex insertion and removal. We define a compact data structure for such a model that exploits the specific update rule. We propose a dynamic algorithm for selective refinement and we discuss in detail its implementation as a client–server application. In order to reduce memory requirements and channel traffic, we develop a compressed representation which allows us to express mesh updates with a code of small size. We also address client caching to further limit bandwidth occupancy. Experimental results show that the Multi-Triangulation can be a key Web technology for triangle mesh manipulation.