Abstract. We present an encoding of the semantics of the probabilistic guarded command language (pGCL) in the Unifying Theories of Programming (UTP) framework. Our contribution is a UTP encoding that captures pGCL programs as predicate-transformers, on predicates over probability distributions on before-and after-states: these predicates capture the same information as the models traditionally used to give semantics to pGCL; in addition our formulation allows us to define a generic choice construct, that covers conditional, probabilistic and non-deterministic choice. As an example we study the Monty Hall game in this framework.

Abstract. We present a theory of designs based on functions from the state space to real numbers, which we term distributions. This theory uses predicates, in the style of UTP, based on homogeneous relations between distributions, and is richer than the standard UTP theory of designs as it allows us to reason about probabilistic programs; the healthiness conditions H1-H4 of the standard theory are implicitly accounted for in the distributional theory we present. In addition we propose a Galois connection linkage between our distribution-based model of probabilistic designs, and the standard UTP model of (non-probabilistic) designs.

When some agents want to communicate through a media stream (for example voice or video), the Real Time Protocol (RTP) is used. This protocol does not provide encryption, so it is necessary to use Secure RTP (SRTP) to secure the communication. In order for this to work, the agents need to agree on key material and ZRTP provides them with a procedure to perform this task: it is a key agreement protocol, which relies on a Diffie-Hellman exchange to generate SRTP session parameters, providing confidentiality and protecting against Man-in-the-Middle attacks even without a public key infrastructure or endpoint certificates. This is an analysis of the protocol performed with ProVerif, which tests security properties of ZRTP; in order to perform the analysis, the protocol has been modeled in the applied π-calculus 1 .

When some agents want to communicate through a media stream (for example voice or video), the Real Time Protocol (RTP) is used. This protocol does not provide encryption, so it is necessary to use Secure RTP (SRTP) to secure the communication. In order for this to work, the agents need to agree on key material and ZRTP provides them with a procedure to perform this task: it is a key agreement protocol, which relies on a Diffie-Hellman exchange to generate SRTP session parameters, providing confidentiality and protecting against Man-in-the-Middle attacks even without a public key infrastructure or endpoint certificates. This is an analysis of the ZRTP protocol performed with ProVerif, which tests security properties; in order to perform the analysis, the protocol has been modeled in the applied π-calculus.

Abstract. We have introduced probability in the UTP framework by using functions from the state space to real numbers, which we term distributions, that are embedded in the predicates describing the different program constructs. This has allowed us to derive a probabilistic theory of designs starting from a probabilistic version of the relational theory, and continuing further down this road we can get to a theory of probabilistic reactive programs. This paper presents the route that connects these steps, and discusses the challenges lying ahead in view of a probabilistic CSP based on distributions.