Probabilistic Logical Characterization

Hermanns, Holger; Parma, Augusto; Segala, Roberto; Wachter, Björn; Zhang, Lijun

doi:10.1016/j.ic.2010.11.024

Cited by 60 publications

(71 citation statements)

References 45 publications

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“…Formula ⟨a⟩ p φ is satisfied by a state s if action a can be performed by s and lead to a distribution where the states satisfying φ are given probability at least p. For nondeterministic and probabilistic processes, where several outgoing transitions from a state can have the same label, an extension of HML with an operator [.] p was proposed in [21]. The formula [φ] p is satisfied by a distribution if the probability of the set of states that satisfy formula φ is at least p. In [22] a two-sorted logic was considered to characterise probabilistic bisimulation, with nondeterministic formulae interpreted over states and probabilistic formulae interpreted over distributions.…”

Section: Y Deng M Hennessy / Science Of Computer Programming ( ) -mentioning

confidence: 99%

Compositional reasoning for weighted Markov decision processes

Deng

Hennessy

2013

Science of Computer Programming

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h i g h l i g h t s• We develop compositional methods for reasoning about weighted Markov decision processes (MDPs).• A coinductive simulation-based behavioural preorder is proposed for weighted MDPs.• The preorder is preserved by structural operators for constructing weighted MDPs from components.• For finitary convergent processes, the preorder can be characterised by a probabilistic logic and a novel form of testing. a r t i c l e i n f o b s t r a c tWeighted Markov decision processes (MDPs) have long been used to model quantitative aspects of systems in the presence of uncertainty. However, much of the literature on such MDPs takes a monolithic approach, by modelling a system as a particular MDP; properties of the system are then inferred by analysis of that particular MDP. In contrast in this paper we develop compositional methods for reasoning about weighted MDPs, as a possible basis for compositional reasoning about their quantitative behaviour. In particular we approach these systems from a process algebraic point of view. For these we define a coinductive simulation-based behavioural preorder which is compositional in the sense that it is preserved by structural operators for constructing weighted MDPs from components.For finitary convergent processes, which are finite-state and finitely branching systems without divergence, we provide two characterisations of the behavioural preorder. The first uses a novel quantitative probabilistic logic, while the second is in terms of a novel form of testing, in which benefits are accrued during the execution of tests.

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Section: Y Deng M Hennessy / Science Of Computer Programming ( ) -mentioning

confidence: 99%

Compositional reasoning for weighted Markov decision processes

Deng

Hennessy

2013

Science of Computer Programming

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“…They are coalgebras of the form c : X → P(A × DX), mixing probability and non-determinism. In a recent paper [9], with ideas appearing already in [21,10,6,13], it has been recognized that it might be useful for verification purposes to transform them into so-called distribution LTSs, i.e. into LTSs with state space DX of so-called uncertain or belief states.…”

Section: Simple Segala Systems In Em-stylementioning

confidence: 99%

Trace Semantics via Determinization

Jacobs

Silva

Sokolova

2012

Coalgebraic Methods in Computer Science

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Abstract. This paper takes a fresh look at the topic of trace semantics in the theory of coalgebras. The first development of coalgebraic trace semantics used final coalgebras in Kleisli categories, stemming from an initial algebra in the underlying category. This approach requires some non-trivial assumptions, like dcpo enrichment, which do not always hold, even in cases where one can reasonably speak of traces (like for weighted automata). More recently, it has been noticed that trace semantics can also arise by first performing a determinization construction. In this paper, we develop a systematic approach, in which the two approaches correspond to different orders of composing a functor and a monad, and accordingly, to different distributive laws. The relevant final coalgebra that gives rise to trace semantics does not live in a Kleisli category, but more generally, in a category of Eilenberg-Moore algebras. In order to exploit its finality, we identify an extension operation, that changes the state space of a coalgebra into a free algebra, which abstractly captures determinization of automata. Notably, we show that the two different views on trace semantics are equivalent, in the examples where both approaches are applicable.

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“…There are already quite a few variations on the theme of bisimulations for PAs which can be used to establish behavioural equivalences between MAs [24,18,15,6,11]. A characteristic of our formulation is that it allows bisimulations to relate states to distributions rather than simply states, thus differentiating it from most of these.…”

Section: Theorem 4 (Completeness)mentioning

confidence: 99%

On the Semantics of Markov Automata

Deng

Hennessy

2011

Automata, Languages and Programming

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Abstract. Markov automata describe systems in terms of events which may be nondeterministic, may occur probabilistically, or may be subject to time delays. We define a novel notion of weak bisimulation for such systems and prove that this provides both a sound and complete proof methodology for a natural extensional behavioural equivalence between such systems, a generalisation of reduction barbed congruence, the well-known touchstone equivalence for a large variety of process description languages.

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Probabilistic Logical Characterization

Cited by 60 publications

References 45 publications

Compositional reasoning for weighted Markov decision processes

Compositional reasoning for weighted Markov decision processes

Trace Semantics via Determinization

On the Semantics of Markov Automata

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