Search

It is already known that the 1-Poset and 2-Poset Cover Problems are in 𝑷. In this paper, we extended the previous results and devised an algorithm for the 𝒌-Poset Cover Problem, for any 𝒌 number of posets that cover the input. The algorithm runs in 𝑶(𝒎2k 𝒏2), where 𝒎 and 𝒏 are the input size. With this running time, we can say that the problem belongs to XP (slicewise polynomial). The algorithm runs efficiently for small fixed 𝒌 but runs exponentially for large 𝒌. While the algorithm running time has yet not to be efficient for large 𝒌, we have shown a significant improvement from a brute-force solution, which runs in 2𝒎 𝒏2 + 𝑶(􀷌𝒌 𝒊 􀰸 1 2𝒎𝒊𝒏) - exponential even for small fixed [ABSTRACT FROM AUTHOR]

A spiking neural P system (SN P system) is a model of computation inspired by the mechanism of a network of spiking neurons. A homogeneous SN P system is an SN P system whose neurons have identical rule set. In this work, we introduced an algorithm that, under certain condition, transforms a non-homogeneous SN P system Π to a homogeneous SN P system Π ′ that computes the same set as the system Π. Two transformation operations called neuron translation and neuron scaling are introduced which are then used by the homogenization algorithm. [ABSTRACT FROM AUTHOR]