Structural Operational Semantics

Aceto, Luca; Fokkink, Wan; Verhoef, C.

doi:10.1016/b978-044482830-9/50021-7

Cited by 126 publications

(135 citation statements)

References 91 publications

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“…10); (b) we prove that up-to context is compatible for lax models of positive [1] GSOS specifications (Sect. 11); and, (c) as an application, we obtain soundness of up-to context for weak bisimulations of systems specified by the cool rule format from [55] (Sect.…”

Section: Example 92mentioning

confidence: 99%

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A general account of coinduction up-to

et al. 2016

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Bisimulation up-to enhances the coinductive proof method for bisimilarity, providing efficient proof techniques for checking properties of different kinds of systems. We prove the soundness of such techniques in a fibrational setting, building on the seminal work of Hermida and Jacobs. This allows us to systematically obtain up-to techniques not only for bisimilarity but for a large class of coinductive predicates modeled as coalgebras. The fact that bisimulations up to context can be safely used in any language specified by GSOS rules can also be seen as an instance of our framework, using the well-known observation by Turi and Plotkin that such languages form bialgebras. In the second part of the paper, we provide a new categorical treatment of weak bisimilarity on labeled transition systems and we prove the soundness of up-to context for weak bisimulations of systems specified by cool rule formats, as defined by Bloom to ensure congruence of weak bisimilarity. The weak transition systems obtained from such cool rules give rise to lax bialgebras, rather than to bialgebras. Hence, to reach our goal, we extend the categorical framework developed in the first part to an ordered setting. B Daniela Petrişan

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Section: Example 92mentioning

confidence: 99%

“…A minimal requirement for such systems usually is that behavioural equivalence should be a congruence. In the special case of bisimilarity on LTSs, several rule formats have been proposed to ensure such a congruence property [1]. At the categorical level, the main concept to study such systems is that of bialgebras.…”

Section: Bialgebras and Up To Contextmentioning

confidence: 99%

A general account of coinduction up-to

et al. 2016

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“…Every first transition of L 1 and L 2 can be mimicked. interrupt [5] [1] , a, s [2] ) | s ∈ S 1 ∧ (ŝ 2 , a, s ) ∈ Δ 2 }, Δ 1 and Δ 2 are like above, and s =ŝ [1] 1 . That is, L 1 L 2 behaves first like L 1 , but may at any instant of time start behaving like L 2 .…”

Section: Definitionmentioning

confidence: 99%

“…1 We say that an n-ary function f from LTSs to LTSs respects "≈" if and only if "≈" is a congruence with respect to f , that is, for every…”

Section: Labelled Transition Systemsmentioning

confidence: 99%

On constructibility and unconstructibility of LTS operators from other LTS operators

Valmari

2015

Acta Informatica

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An LTS operator can be constructed from a set of LTS operators up to an equivalence if and only if there is an LTS expression that only contains operators from the set and whose result is equivalent to the result of the operator. In this publication this idea is made precise in the context where each LTS has an alphabet of its own and the operators may depend on the alphabets. Then the extent to which LTS operators are constructible is studied. Most, if not all, established LTS operators have the property that each trace of the result arises from the execution of no more than one trace of each of its argument LTSs, and similarly for infinite traces. All LTS operators that have this property and satisfy some other rather weak regularity properties can be constructed from parallel composition and hiding up to the equivalence that compares the alphabets, traces, and infinite traces of the LTSs. Furthermore, a collection of other miscellaneous constructibility and unconstructibility results is presented.

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“…15) is given in a hybrid process algebra ("Pann") which is built from typical concepts in the concurrency literature ( [9,10,11] and especially Hybrid χ [12]). Its behaviour is defined using an operational semantics [13,14,15], using a novel approach for hybrid concepts that builds on earlier work for discrete systems [16,17]. The semantics is used to derive a set of equations for reasoning about processes, which are used to elucidate properties of the model.…”

Section: Introductionmentioning

confidence: 99%

Modelling and analysing neural networks using a hybrid process algebra

Colvin

2016

Theoretical Computer Science

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Please cite this article in press as: R.J. Colvin, Modeling and analysing neural networks using a hybrid process algebra, Theoret. Comput. Sci. (2015), http://dx.doi.org/10.1016/j.tcs. 2015.08.019 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Modeling and analysing neural networks using a hybrid process algebra Robert J. ColvinThe University of Queensland, Queensland Brain Institute, Brisbane, Australia, 4072 AbstractResearch involving artificial neural networks has tended to be driven towards efficient computation, especially in the domain of pattern recognition, or towards elucidating biological processes in the brain. Models have become more detailed as our understanding of the biology of the brain has increased, incorporating real-time behaviour of individual neurons interacting within complex system structures and dynamics. There are few examples of abstract and fully formal models of biologically plausible neural networks: in the neural networks literature models are often presented as a mixture of mathematical equations and natural language, supported by simulation code and associated experimental results. The informality often hides or obscures important aspects of a particular model, and leaves a large conceptual gap between the model descriptions and the usually low-level programming code used to simulate them.The main contribution of this paper is formally modelling and analysing a biologically plausible neural network model from the literature that exhibits complex neuron-level behaviour and network-level structure. To achieve this a modelling language 'Pann' is developed, based on the process algebras CSP and Hybrid χ . It is designed to be convenient for mixing the behaviour of discrete events (such as a neuron spike) with mutable continuous and discrete variables (representing chemical properties of a neuron, for instance). Its behaviour is defined using an operational semantics, from which a set of general properties of the language is proved.The groundwork for the biological model is laid by first formalising some well-known concepts from the artificial neural networks domain, such as feedforward behaviour, backpropagation, and recurrent neural networks. The Pann model of a feedforward network, comprising a set of communicating processes representing individual neurons, is proved equivalent to the standard one-line calculation of feedforward behaviour.

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Structural Operational Semantics

Cited by 126 publications

References 91 publications

A general account of coinduction up-to

A general account of coinduction up-to

On constructibility and unconstructibility of LTS operators from other LTS operators

Modelling and analysing neural networks using a hybrid process algebra

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