Analysing oscillatory trends of discrete-state stochastic processes through HASL statistical model checking

The application of formal methods to the analysis of stochastic oscillators has been at the focus of several research works in recent times. In this paper we provide insights on the application of an expressive temporal logic formalism, namely the Hybrid Automata Stochastic Logic (HASL), to that issue. We show how one can take advantage of the expressive power of the HASL logic to define and assess relevant characteristics of (stochastic) oscillators

MathMC: A mathematica-based tool for CSL model checking of deterministic and stochastic Petri nets

Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discreteevent systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. CSL (Continuous Stochastic Logic) is a (branching) temporal logic developed to express probabilistic properties in continuous time Markov chains (CTMCs). In this paper we present a Mathematica-based tool that implements recent developments for model checking CSL style properties on DSPNs. Furthermore, as a consequence of the type of process underlying DSPNs (a superset of Markovian processes), we are also able to check CSL properties of Generalized Stochastic Petri Nets (GSPNs) and labeled CTMCs

CSL model checking of Deterministic and Stochastic Petri Nets

Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under certain restrictions, corresponds to a class of Markov Regenerative Stochastic Processes (MRGP). In this paper, we investigate the use of CSL (Continuous Stochastic Logic) to express probabilistic properties, such a time-bounded until and time-bounded next, at the DSPN level. The verication of such properties requires the solution of the steady-state and transient probabilities of the underlying MRGP. We also address a number of semantic issues regarding the application of CSL on MRGP and provide numerical model checking algorithms for this logic. A prototype model checker, based on SPNica, is also described

Statistical Model Checking of Dynamic Networks of Stochastic Hybrid Automata

In this paper we present a modelling formalism for dynamic networksof stochastic hybrid automata. In particular, our formalism is based on primitivesfor the dynamic creation and termination of hybrid automata components duringthe execution of a system. In this way we allow for natural modelling of conceptssuch as multiple threads found in various programming paradigms, as well as thedynamic evolution of biological systems.We provide a natural stochastic semantics of the modelling formalism based on re-peated output races between the dynamic evolving components of a system. Asspecification language we present a quantified extension of the logic Metric Tempo-ral Logic (MTL). As a main contribution of this paper, the statistical model checkingengine of U PPAAL has been extended to the setting of dynamic networks of hybridsystems and quantified MTL. We demonstrate the usefulness of the extended for-malisms in an analysis of a dynamic version of the well-known Train Gate example,as well as in natural monitoring of a MTL formula, where observations may lead todynamic creation of monitors for sub-formulas

Performance queries on Semi-Markov Stochastic Petri nets with an extended continuous Stochastic logic

Semi-Markov Stochastic Petri Nets (SM-SPNs) are a highlevel formalism for defining semi-Markov processes. We present an extended Continuous Stochastic Logic (eCSL) which provides an expressive way to articulate performance queries at the SM-SPN model level. eCSL supports queries involving steady-state, transient and passage time measures. We demonstrate this by formulating and answering eCSL queries on an SM-SPN model of a distributed voting system with up to ¢¤£¦ ¥ states.

Formalisms for agents reasoning with stochastic actions and perceptions.

Ph. D. University of KwaZulu-Natal, Durban 2014.The thesis reports on the development of a sequence of logics (formal languages based on mathematical logic) to deal with a class of uncertainty that agents may encounter. More accurately, the logics are meant to be used for allowing robots or software agents to reason about the uncertainty they have about the effects of their actions and the noisiness of their observations. The approach is to take the well-established formalism called the partially observable Markov decision process (POMDP) as an underlying formalism and then design a modal logic based on POMDP theory to allow an agent to reason with a knowledge-base (including knowledge about the uncertainties). First, three logics are designed, each one adding one or more important features for reasoning in the class of domains of interest (i.e., domains where stochastic action and sensing are considered). The final logic, called the Stochastic Decision Logic (SDL) combines the three logics into a coherent formalism, adding three important notions for reasoning about stochastic decision-theoretic domains: (i) representation of and reasoning about degrees of belief in a statement, given stochastic knowledge, (ii) representation of and reasoning about the expected future rewards of a sequence of actions and (iii) the progression or update of an agent’s epistemic, stochastic knowledge. For all the logics developed in this thesis, entailment is defined, that is, whether a sentence logically follows from a knowledge-base. Decision procedures for determining entailment are developed, and they are all proved sound, complete and terminating. The decision procedures all employ tableau calculi to deal with the traditional logical aspects, and systems of equations and inequalities to deal with the probabilistic aspects. Besides promoting the compact representation of POMDP models, and the power that logic brings to the automation of reasoning, the Stochastic Decision Logic is novel and significant in that it allows the agent to determine whether or not a set of sentences is entailed by an arbitrarily precise specification of a POMDP model, where this is not possible with standard POMDPs. The research conducted for this thesis has resulted in several publications and has been presented at several workshops, symposia and conferences

Stochastic Relational Presheaves and Dynamic Logic for Contextuality

Presheaf models provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in quantum systems. After reviewing what presheaf models represent and what certain operations on them mean in terms of notions such as internal and external choices, composition of systems, and so on, I will show how to extend those models and ideas by combining them with ideas from other category-theoretic approaches to relational models and to stochastic processes. It turns out that my extension yields a transitional formulation of sheaf-theoretic structures that Abramsky and Brandenburger proposed to characterize non-locality and contextuality. An alternative characterization of contextuality will then be given in terms of a dynamic modal logic of the models I put forward.Comment: In Proceedings QPL 2014, arXiv:1412.810