(Hybrid) automata and (stochastic) programs * The hybrid automata lattice of a stochastic program

Bortolussi, Luca; Policriti, Alberto

doi:10.1093/logcom/exr045

Cited by 15 publications

(36 citation statements)

References 31 publications

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“…These may arise e.g. as approximations to CTMCs where some of the populations have large numbers (which can be well approximated as continuous variables) while others have sufficiently small numbers to require a discrete treatment [14,12,32]. The models so obtained are known as stochastic hybrid systems (SHS) [16], and their dynamics can be seen as a sequence of discrete jumps, instantaneously modifying population variables, interleaved by periods of continuous evolution along a trajectory of the SDE.…”

Section: Stochastic Processesmentioning

confidence: 99%

Learning and Designing Stochastic Processes from Logical Constraints

Bortolussi

Sanguinetti²

2015

Logical Methods in Computer Science

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Abstract. Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics must be known exactly. As this is seldom the case, many methods have been devised over the last decade to infer (learn) such parameters from observations of the state of the system. In this paper, we depart from this approach by assuming that our observations are qualitative properties encoded as satisfaction of linear temporal logic formulae, as opposed to quantitative observations of the state of the system. An important feature of this approach is that it unifies naturally the system identification and the system design problems, where the properties, instead of observations, represent requirements to be satisfied. We develop a principled statistical estimation procedure based on maximising the likelihood of the system's parameters, using recent ideas from statistical machine learning. We demonstrate the efficacy and broad applicability of our method on a range of simple but non-trivial examples, including rumour spreading in social networks and hybrid models of gene regulation.

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Section: Stochastic Processesmentioning

confidence: 99%

Learning and Designing Stochastic Processes from Logical Constraints

Bortolussi

Sanguinetti²

2015

Logical Methods in Computer Science

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“…If all transitions of a sCCP program are stochastic and have constant increment updates, they can be interpreted as flows, and a fluid semantics can be defined [21]. However, to properly deal with random resets and instantaneous transitions, it is more convenient to consider a more general semantics for sCCP, in terms of stochastic hybrid automata [17,18,19]. This approach will also allow us to partition variables and transitions into discrete and continuous, so that only a portion of the state space will be approximated as fluid.…”

Section: Stochastic Concurrent Constraint Programmingmentioning

confidence: 99%

“…We will assume to work with flat sCCP models, so that we can ignore the structure of agents and focus our attention on system variables. In this respect, this approach differs from the one of [18], but it provides a more homogeneous treatment.…”

Section: From Sccp To Tdshamentioning

confidence: 99%

Hybrid behaviour of Markov population models

Bortolussi

2016

Information and Computation

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We investigate the behaviour of population models written in Stochastic Concurrent Constraint Programming (sCCP), a stochastic extension of Concurrent Constraint Programming. In particular, we focus on models from which we can define a semantics of sCCP both in terms of Continuous Time Markov Chains (CTMC) and in terms of Stochastic Hybrid Systems, in which some populations are approximated continuously, while others are kept discrete. We will prove the correctness of the hybrid semantics from the point of view of the limiting behaviour of a sequence of models for increasing population size. More specifically, we prove that, under suitable regularity conditions, the sequence of CTMC constructed from sCCP programs for increasing population size converges to the hybrid system constructed by means of the hybrid semantics. We investigate in particular what happens for sCCP models in which some transitions are guarded by boolean predicates or in the presence of instantaneous transitions.

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“…The behaviour of a stochastic HYPE model is determined by mapping the model to a mathematical formalism, namely a transition-driven stochastic hybrid automaton (TDSHA) [13,14]. In choosing a mapping for Bio-PEPA to a stochastic hybrid formalism, the choice is between a language-based formalism such as stochastic HYPE and a mathematical formalism such as TDSHA.…”

Section: Stochastic Hypementioning

confidence: 99%

“…This information is then used to describe the continuous behaviour of the model, while the structure of the multitransition system describes the discrete behaviour, both instantaneous and stochastic. For reasons of space, details of TDSHA are omitted from this article and the reader is referred to [13,14].…”

Section: Semanticsmentioning

confidence: 99%

Hybrid semantics for Bio-PEPA

Galpin

2014

Information and Computation

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This paper investigates the stochastic, continuous and instantaneous (hybrid) modelling of systems defined in Bio-PEPA, a quantitative process algebra for biological modelling. This is achieved by mapping a Bio-PEPA model to a model in stochastic HYPE, a process algebra that models these three behaviour types in a compositional and structured manner. The novel mapping between process algebras provides another method of analysis for Bio-PEPA models and presents the modeller with a well-structured stochastic HYPE model which can itself be easily modified and is only a small constant larger in size than the Bio-PEPA model. The structure of the stochastic HYPE model generated has desirable properties and also gives a general framework for modelling biochemical systems where the advantages of both stochastic and deterministic simulation are required. Thresholds are introduced for each reaction, and when all values are above these thresholds, the reaction is treated deterministically. However, if a relevant value is below a threshold, the reaction is treated stochastically (as are the changes in species quantities as a result of that reaction). It is proved that in the purely deterministic case and in the purely stochastic case, the stochastic HYPE model has the same behaviour as the Bio-PEPA model when considered purely deterministically and purely stochastically, respectively. Furthermore, addition of instantaneous events in the style of Bio-PEPA with events is illustrated, and a proposal for mapping Bio-PEPA with delays (Bio-PEPAd) to stochastic HYPE is presented.

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(Hybrid) automata and (stochastic) programs * The hybrid automata lattice of a stochastic program

Cited by 15 publications

References 31 publications

Learning and Designing Stochastic Processes from Logical Constraints

Learning and Designing Stochastic Processes from Logical Constraints

Hybrid behaviour of Markov population models

Hybrid semantics for Bio-PEPA

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