This book discusses the semantic foundations of concurrent systems with nondeterministic and probabilistic behaviour. Particular attention is given to clarifying the relationship between testing and simulation semantics and characterising bisimulations from metric, logical, and algorithmic perspectives. Besides presenting recent research outcomes in probabilistic concurrency theory, the book exemplifies the use of many mathematical techniques to solve problems in computer science, which is intended to be accessible to postgraduate students in Computer Science and Mathematics. It can also be used by researchers and practitioners either for advanced study or for technical reference.

This book provides an overview of the theoretical underpinnings of modern probabilistic programming and presents applications in e.g., machine learning, security, and approximate computing. Comprehensive survey chapters make the material accessible to graduate students and non-experts. This title is also available as Open Access on Cambridge Core.

Probabilistic Logic Programming extends Logic Programming by enabling the representation of uncertain information by means of probability theory. Probabilistic Logic Programming is at the intersection of two wider research fields: the integration of logic and probability and Probabilistic Programming.Logic enables the representation of complex relations among entities while probability theory is useful for model uncertainty over attributes and relations. Combining the two is a very active field of study.Probabilistic Programming extends programming languages with probabilistic primitives that can be used to write complex probabilistic models. Algorithms for the inference and learning tasks are then provided automatically by the system.Probabilistic Logic programming is at the same time a logic language, with its knowledge representation capabilities, and a Turing complete language, with its computation capabilities, thus providing the best of both worlds.Since its birth, the field of Probabilistic Logic Programming has seen a steady increase of activity, with many proposals for languages and algorithms for inference and learning. Foundations of Probabilistic Logic Programming aims at providing an overview of the field with a special emphasis on languages under the Distribution Semantics, one of the most influential approaches. The book presents the main ideas for semantics, inference, and learning and highlights connections between the methods.Many examples of the book include a link to a page of the web application http://cplint.eu where the code can be run online.

This volume contains the proceedings of the second joint PAPM-PROBMIV Workshop, held at the University of Copenhagen, Denmark, July 25–26, 2002 as part of the Federated Logic Conference (FLoC 2002). The PAPM-PROBMIV workshop results from the combination of two wo- shops: PAPM (Process Algebras and Performance Modeling) and PROBMIV (Probabilistic Methods in Veri?cation). The aim of the joint workshop is to bring together the researchers working across the whole spectrum of techniques for the modeling, speci?cation, analysis, and veri?cation of probabilistic systems. Probability is widely used in the design and analysis of software and hardware systems, as a means to derive e?cient algorithms (e.g. randomization), as a model for unreliable or unpredictable behavior (as in the study of fault-tolerant systems and computer networks), and as a tool to study performance and - pendability properties. The topics of the workshop include speci?cation, m- els, and semantics of probabilistic systems, analysis and veri?cation techniques, probabilistic methods for the veri?cation of non-probabilistic systems, and tools and case studies. The ?rst PAPM workshop was held in Edinburgh in 1993; the following ones were held in Regensberg (1994), Edinburgh (1995), Turin (1996), Enschede (1997), Nice (1998), Zaragoza (1999), and Geneva (2000). The ?rst PROBMIV workshop was held in Indianapolis, Indiana (1998); the next one took place in Eindhoven (1999). In 2000, PROBMIV was replaced by a Dagstuhl seminar on Probabilistic Methods in Veri?cation.

Abstract: "In this thesis, we develop a mathematical formalism for the specification and proof of correctness of probabilistic communicating processes. This formalism combines a notion of probabilistic correctness with the theory of concurrency provided by the language of Communicating Sequential Processes (CSP). We first present the semantics of a model in which processes are defined as probability measures on the space of infinite traces. The model contains definitions for prefixing, probabilistic choice, hiding, simple parallel composition, sequential composition, interleaving, relabelling and recursion. These operators are defined as functions (mostly transformations) of probability measures.