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Axiomatizing Rectangular Grids with no Extra Non-unary Relations

Kopczyński Eryk

Fundamenta Informaticae

2020

Vol. 176, nr 2

129--138

We construct a first-order formula φ such that all finite models of φ are non-narrow rectangular grids without using any binary relations other than the grid neighborship relations. As a corollary, we prove that a set A ⊆ ℕ is a spectrum of a formula which has only planar models if numbers n ∈ A can be recognized by a non-deterministic Turing machine (or a one-dimensional cellular automaton) in time t (n) and space s (n), where t (n)s (n) ≤ n and t (n), s (n) = Ω(log(n)).

Sevilla Carpets Revisited : Enriching the Membrane Computing Toolbox

Orellana-Martín D., Graciani C., Macías-Ramos L.-F., Martínez-del-Amor M. A., Riscos-Núñez A., Romero-Jiménez A., Valencia-Cabrera L.

Fundamenta Informaticae

2014

Vol. 134, nr 1/2

153--166

Sevilla carpets have already been used to compare different solutions of the Subset Sum problem: either designed in the framework of P systems with active membranes (both in the case of membrane division and membrane creation), and in the framework of tissue-like P systems with cell division. Recently, the degree of parallelism and other descriptive complexity details have been found to be relevant when designing parallel simulators running on GPUs. We present here a new way to use the information provided by Sevilla carpets in this context, and a script that allows to generate them automatically from P-Lingua files.