The Power of Convex Algebras

Probabilistic automata (PA) combine probability and nondeterminism. They can be given different semantics, like strong bisimilarity, convex bisimilarity, or (more recently) distribution bisimilarity. The latter is based on the view of PA as transformers of probability distributions, also called belief states, and promotes distributions to first-class citizens. We give a coalgebraic account of the latter semantics, and explain the genesis of the belief-state transformer from a PA. To do so, we make explicit the convex algebraic structure present in PA and identify belief-state transformers as transition systems with state space that carries a convex algebra. As a consequence of our abstract approach, we can give a sound proof technique which we call bisimulation up-to convex hull.Comment: Full (extended) version of a CONCUR 2017 paper, to be submitted to LMC

A new Nested Graph Model for Data Integration

Despite graph data gained increasing interest in several fields, no data model suitable for both querying and integrating differently structured graph and (semi)structured data has been currently conceived. The lack of operators allowing combinations of (multiple) graphs in current graph query languages (graph joins), and on graph data structure allowing neither data integration nor nested multidimensional representations (graph nesting) are a possible motivation. In order to make such data integration possible, this thesis proposes a novel model (General Semistructured data Model) allowing the representation of both graphs and arbitrarily nested contents (e.g., one node can be contained by more than just one parent node), thus allowing the definition of a nested graph model, where both vertices and edges may include (overlapping) graphs. We provide two graph joins algorithms (Graph Conjunctive Equijoin Algorithm and Graph Conjunctive Less-equal Algorithm) and one graph nesting algorithm (Two HOp Separated Patterns). Their evaluation on top of our secondary memory representation showed the inefficiency of existing query languages’ query plan on top of their respective data models (relational, graph and document-oriented). In all three algorithms, the enhancement was possible by using an adjacency list graph representation, thus reducing the cost of joining the vertices with their respective outgoing (or ingoing) edges, and by associating hash values to both vertices and edges. As a secondary outcome of this thesis, a general data integration scenario is provided where both graph data and other semistructured and structured data could be represented and integrated into the General Semistructured data Model. A new query language outlines the feasibility of this approach (General Semistructured Query Language) over the former data model, also allowing to express both graph joins and graph nestings. This language is also capable of representing both traversal and data manipulation operators

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science