Abstract
We present a metric denotational semantics for an experimental concurrent language inspired by the spiking neural P systems. At syntactic level, the language provides constructions for specifying the neurons, synapses and rules with time delays defining a spiking neural P system. The denotational semantics presented in this paper is designed by using continuations. We employ metric spaces, including a metric powerdomain to describe the nondeterministic behaviour. Our denotational semantics describes accurately the time delays between firings and spikings, the nondeterministic behaviour and the synchronized functioning that are specific of a spiking neural P system. An implementation in the functional language Haskell is also provided; it can be tested and evaluated, being available for software experiments.
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- 1.
We will see later that in \({\mathcal {L}}_{SNP}\) the parallel composition operator \(\parallel \) is commutative and associative; see Proposition 14. Hence the parentheses in the expression \((a\parallel (\cdots \parallel (a\parallel {}a)\cdots ))\) are actually not needed.
- 2.
More precisely, we can say that the destination of the objects contained in \(ms_Y(y)\) is given by \(\xi _N\).
- 3.
The size of a term is given by the number of nodes in its abstract syntax tree [21].
- 4.
\(\oplus \) is defined based on the set union operator \(\cup \).
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Ciobanu, G., Todoran, E.N. (2019). A Semantic Investigation of Spiking Neural P Systems. In: Hinze, T., Rozenberg, G., Salomaa, A., Zandron, C. (eds) Membrane Computing. CMC 2018. Lecture Notes in Computer Science(), vol 11399. Springer, Cham. https://doi.org/10.1007/978-3-030-12797-8_9
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