1. Subset Sum

The Subset Sum problem is known as the following problem: a set of integers and an integer s, does any non-empty subset sum to s?  It is formally stated as follows: Given a finite set A = {a1,...,an}, of n elements, where each element ai has an associated weight, wi, and a constant k ∈ N, it is requested to determine whether or not there exists a subset B ⊆ A such that w(B) = k, where w(B) = ∑ai∈Bwi.

Download the kPLingua model here, and some example properties to be verified here in kP-Query specification. 

2. Pulse Generator

The Pulse Generator is a synthetic biology system. It is composed of two types of bacterial strains: sender and pulsing cells (see the figure below). The sender cells produce a signal (3OC6-HSL) and propagates it through the pulsing cells, which express the green fluorescent protein (GFP) upon sensing the signal. The excess of the signalling molecules are propagated to the neighbouring cells.

 Sender Cell and Pulsing Cell

 

Sender cells synthesize the signalling molecule 3OC6-HSL (AHL) through the enzyme LuxI, expressed under the constitutive expression of the promoter PLtetO1. Pulsing cells express GFP under the regulation of the PluxPR promoter, activated by the LuxR_3OC6_2 complex. The LuxR protein is expressed under the control of the PluxL promoter. The GFP production is repressed by the transcription factor CI, codified under the regulation of the promoter PluxR that is activated upon binding of the transcription factor LuxR_3OC6_2. 

Download the kPLingua model for 1 sender, 3 pulsing cells here.

3. Simulation of Kernel P Systems Using FLAME

In a recent paper, Agent-Based Simulation of Kernel P Systems with Division Rules Using FLAME, the Subset sum problem was considered in a comparative case study between kPWorkbench models simulation and their FLAME counterparts.

For more details, you can download: 

- The paper and conference presentation.  

- The archive with the kP-Lingua models for Subset sum problem.

- The Flame models used for simulation, automatically generated using the kPWorkbench translator module here

- The kPWorkbench tool used for simulation and its user interface kpUI

4. Modelling and validating a cruise control system for an electric bike

In a recently submitted paper, Modelling and Validating an Engineering Application in Kernel P Systems, a kernel P system model was designed and used for modelling and validating a cruise control system for an electric bike. For more details you can download an archive with the kP-Lingua model, kP-Query file, the NuSMV translation and result of the verification.