Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems

The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem for the system of probabilistic ITL with respect to an abstract semantics and a relative completeness theorem for the system of probabilistic DC with respect to real-time semantics. The proposed systems subsume probabilistic real-time DC as known from the literature. A correspondence between the proposed systems and a system of probabilistic interval temporal logic with finite intervals and expanding modalities is established too.Comment: 43 page

Categories of Timed Stochastic Relations

AbstractStochastic behavior—the probabilistic evolution of a system in time—is essential to modeling the complexity of real-world systems. It enables realistic performance modeling, quality-of-service guarantees, and especially simulations for biological systems. Languages like the stochastic pi calculus have emerged as effective tools to describe and reason about systems exhibiting stochastic behavior. These languages essentially denote continuous-time stochastic processes, obtained through an operational semantics in a probabilistic transition system. In this paper we seek a more descriptive foundation for the semantics of stochastic behavior using categories and monads. We model a first-order imperative language with stochastic delay by identifying probabilistic choice and delay as separate effects, modeling each with a monad, and combining the monads to build a model for the stochastic language

On formal and automatic security verification of WSN transport protocols

In this paper, we address the problem of formal and automated security verification of WSN transport protocols that may perform cryptographic operations. The verification of this class of protocols is difficult because they typically consist of complex behavioral characteristics, such as real-time, probabilistic, and cryptographic operations. To solve this problem, we propose a probabilistic timed calculus for cryptographic protocols, and demonstrate how to use this formal language for proving security or vulnerability of protocols. The main advantage of the proposed language is that it supports an expressive syntax and semantics, including bisimilarities that supports real-time, probabilistic, and cryptographic issues at the same time. Hence, it can be used to verify the systems that involve these three property in a more convenient way. In addition, we propose an automatic verification method, based on the well-known PAT process analysis toolkit, for this class of protocols. For demonstration purposes, we apply the proposed manual and automatic proof methods for verifying the security of DTSN and SDTP, which are two of the recently proposed WSN tranport protocols

Real-time and Probabilistic Temporal Logics: An Overview

Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

Model checking probabilistic and stochastic extensions of the pi-calculus

We present an implementation of model checking for probabilistic and stochastic extensions of the pi-calculus, a process algebra which supports modelling of concurrency and mobility. Formal verification techniques for such extensions have clear applications in several domains, including mobile ad-hoc network protocols, probabilistic security protocols and biological pathways. Despite this, no implementation of automated verification exists. Building upon the pi-calculus model checker MMC, we first show an automated procedure for constructing the underlying semantic model of a probabilistic or stochastic pi-calculus process. This can then be verified using existing probabilistic model checkers such as PRISM. Secondly, we demonstrate how for processes of a specific structure a more efficient, compositional approach is applicable, which uses our extension of MMC on each parallel component of the system and then translates the results into a high-level modular description for the PRISM tool. The feasibility of our techniques is demonstrated through a number of case studies from the pi-calculus literature