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Variants of spiking neural P systems and their operational semantics in Haskell

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Abstract

This article presents the Haskell implementations of spiking neural P systems and of two variants subsequently introduced in the literature, namely the spiking neural P systems with inhibitory rules and spiking neural P systems with structural plasticity. These implementations are obtained using their operational semantics in which the involved configurations use continuations. For each variant, the formal syntax is presented, together with the semantics given accurately by the Haskell implementation.

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Notes

  1. \([a]\) is the multiset containing only (one occurrence of) the spike a.

  2. The neuron name \(N_0\) is reserved (as name of the first neuron in any valid \(D\in NDs\)).

  3. In [8], both an operational semantics and a denotational semantics for \(\textsf{SNP}\) calculus are presented; it is used the term resumption as an operational counterpart of the term continuation; in this article we use (only) the term continuation.

  4. vartheta decreases by 1 with each clock tick, and becomes 0 when the neuron moves to the open status.

  5. The constructs (Snd xi1 a) and (Init xi1) implement elementary statements of the form \(\,{\textsf{snd}}\,\xi _1\,a\,\) and \(\,{\textsf{init}}\,\xi _1\,\) given in Definition 2.

  6. A spiking neural P system with inhibitory rules can be represented as a graph with inhibitory arcs [22]. For each \(j=1,\ldots ,m\), there is an arc between neurons \(N_j\) and N corresponding to an inhibitory synapse.

  7. \(\lnot \) is the logical negation operator; the notations were presented in Remark 1.

  8. \(\xi {\setminus }pres(N)\) is the set theoretic difference between sets \(\xi \) and \(pres(N)\); we use the same symbol \(\setminus \) to represent the multiset difference operator, because it is always clear from the context whether the arguments of this operator \(\setminus \) are sets or multisets.

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Authors and Affiliations

  1. Institute of Computer Science, Romanian Academy, Iasi, Romania

    Gabriel Ciobanu

  2. Technical University, Cluj-Napoca, Romania

    Eneia Nicolae Todoran

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  1. Gabriel Ciobanu
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  2. Eneia Nicolae Todoran
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Correspondence to Eneia Nicolae Todoran.

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Ciobanu, G., Todoran, E.N. Variants of spiking neural P systems and their operational semantics in Haskell. J Membr Comput 5, 81–99 (2023). https://doi.org/10.1007/s41965-023-00122-z

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