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Register a new userMixed Nondeterministic-Probabilistic Interfaces
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Added by
Albert Benveniste
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Authors
Albert Benveniste
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Interface theories are powerful frameworks supporting incremental and compositional design of systems through refinements and constructs for conjunction, and parallel composition. In this report we present a first Interface Theor -- |Modal Mixed Interfaces -- for systems exhibiting both non-determinism and randomness in their behaviour. The associated component model -- Mixed Markov Decision Processes -- is also novel and subsumes both ordinary Markov Decision Processes and Probabilistic Automata.
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The combination of nondeterminism and probability in concurrent systems lead to the development of several interpretations of process behavior. If we restrict our attention to linear properties only, we can identify three main approaches to trace and testing semantics: the trace distributions, the trace-by-trace and the extremal probabilities approaches. In this paper, we propose novel notions of behavioral metrics that are based on the three classic approaches above, and that can be used to measure the disparities in the linear behavior of processes wrt trace and testing semantics. We study the properties of these metrics, like non-expansiveness, and we compare their expressive powers.
Two of the most studied extensions of trace and testing equivalences to nondeterministic and probabilistic processes induce distinctions that have been questioned and lack properties that are desirable. Probabilistic trace-distribution equivalence differentiates systems that can perform the same set of traces with the same probabilities, and is not a congruence for parallel composition. Probabilistic testing equivalence, which relies only on extremal success probabilities, is backward compatible with testing equivalences for restricted classes of processes, such as fully nondeterministic processes or generative/reactive probabilistic processes, only if specific sets of tests are admitted. In this paper, n
We present a spectrum of trace-based, testing, and bisimulation equivalences for nondeterministic and probabilistic processes whose activities are all observable. For every equivalence under study, we examine the discriminating power of three variants stemming from three approaches that differ for the way probabilities of events are compared when nondeterministic choices are resolved via deterministic schedulers. We show that the first approach - which compares two resolutions relatively to the probability distributions of all considered events - results in a fragment of the spectrum compatible with the spectrum of behavioral equivalences for fully probabilistic processes. In contrast, the second approach - which compares the probabilities of the events of a resolution with the probabilities of the same events in possibly different resolutions - gives rise to another fragment composed of coarser equivalences that exhibits several analogies with the spectrum of behavioral equivalences for fully nondeterministic processes. Finally, the third approach - which only compares the extremal probabilities of each event stemming from the different resolutions - yields even coarser equivalences that, however, give rise to a hierarchy similar to that stemming from the second approach.
The original Hegselmann-Krause (HK) model is composed of a finite number of agents characterized by their opinion, a number in $[0,1]$. An agent updates its opinion via taking the average opinion of its neighbors whose opinion differs by at most $epsilon$ for $epsilon>0$ a confidence bound. An agent is absolutely stubborn if it does not change its opinion while update, and absolutely open-minded if its update is the average opinion of its neighbors. There are two types of HK models--the synchronous HK model and the asynchronous HK model. The paper is about a variant of the HK dynamics, called the mixed model, where each agent can choose its degree of stubbornness and mix its opinion with the average opinion of its neighbors at all times. The mixed model reduces to the synchronous HK model if all agents are absolutely open-minded all the time, and the asynchronous HK model if only one uniformly randomly selected agent is absolutely open-minded and the others are absolutely stubborn at all times. In cite{mhk}, we discuss the mixed model deterministically. Point out some properties of the synchronous HK model, such as finite-time convergence, do not hold for the mixed model. In this topic, we study the mixed model nondeterministically. List some properties of the asynchronous model which do not hold for the mixed model. Then, study circumstances under which the asymptotic stability holds.
We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category, which can be used to compose probabilistic games in parallel and sequentially. We also consider morphisms between games, and show that intuitive constructions give rise to functors and adjunctions between pure and probabilistic open games.
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