A Bio-inspired Software for Homology Groups of 2D Digital Images Bisan Alsalibi, Ibrahim Venkat, K.G. Subramanian School of Computer Sciences Universiti Sains Malaysia 11800 penang, Malaysia besansalipi@gmail.com, ibrahim@cs.usm.my, kgs@cs.usm.my Hepzibah A. Christinal Department of Mathematics Karunya University Coimbatore, Tamilnadu, India hepzia@yahoo.com Abstract—Computational topology within the context of digi- tal imagery has gained a considerable role in several applications like structural pattern recognition and digital image processing. Membrane computing, which is a new computational model inspired from the structure and functioning of biological cells, has been adapted as a rich framework for handling many problems. In this paper, we present a membrane computing software for automatically computing homology groups of 2D digital images in a logarithmic number of steps. Keywords—Homology, P systems, P-lingua, Membrane comput- ing. I. I NTRODUCTION Membrane Computing (MC) is a fascinating and fast growing area of research. MC takes its inspiration from the subdivisions of biological cells into compartments delimited by membranes. The computational models in MC are known as P systems in honor of their initiator Paun [?]. The distinguishing hallmarks of P systems are the intrinsic parallelism, the locality of interactions and the capacity of generating new cells in linear time. Basically, the basic ingredients of a membrane system consist of: (1) the membrane structure, delimiting compartments, which either corresponds to a tree like hier- archical arrangement of membranes like in the cell, or a net of membranes represented by a directed graph like in a tissue. In each membrane, (2) multi-sets of objects are placed in the compartments which evolve according to specific (3) evolution rules. Typically, the external membrane is called the skin membrane which contains several internal membranes, where elementary membrane is the one without any other membranes inside it. Several variants of P systems have been proposed [?], [?], [?], [?]. Tissue-like P systems, one of the most investigated P systems [?], are inspired by the intercellular communica- tion and cooperation between neurons. Its basic mathematical model is a network of processors dealing with objects and communicating these objects through communication channels specified in advance. From the computational point of view, the essential feature of this P system is that membranes do not have electrical charges as in the cell like P systems [?]. Spiking neural P systems consists of a set of neurons placed in the nodes of a directed graph and sending spikes along synapses (arcs of the graph), under the control of firing rules. Hence, the structure is that of a tissue-like P system, with only one kind of objects present in the cells. Within the context of algebraic topology, homology theory is the mathematics that arises in the attempt to describe spaces by constructing algebraic invariants so as to identify the connectivity properties of the space [?]. Homology groups are invariants from algebraic topology which are frequently used in applications of digital image processing [?] and structural pattern recognition [?]. In some way, they reflect the topological nature of the object in terms of the number and characteristics of its holes. In a binary 2D image, the computation of homology groups can be reduced to a process of black and white connected components labeling. The differ- ent black connected components are the generators of the 0- dimensional homology group of the “black” part of the image whereas the closed “black” curves surrounding the different white connected components of the image are the generators of its 1-dimensional homology group. Interestingly, a new research line has been recently launched in which MC has been adapted to solve several problems related to digital imagery. For example, obtaining homology groups of 2D and 3D images has been investigated in [?]. However, in the work of Christinal et al. [?], the image has been manually codified in the tissue simulator. In this paper, we present a dynamic software for obtaining homology groups of 2D digital images based on the work presented in [?]. II. TISSUE- LIKE PSYSTEMS Basically, a tissue-like P system [?] is a tuple of degree q ≥ 1 Π = (Γ, Σ, ε, μ, M 1 ,..., M q , (R 1 ,p 1 ) ,..., (R q ,p q ) ,i Π ,o Π ) where : 1) Γ is a finite alphabet of objects including two distin- guished objects yes and no, occurring in at least one copy in some initial multi-sets M i but not in ε; 2) Σ ⊂ Γ is the input alphabet; 3) ε ⊆ Γ is the list of objects in the environment, each one available in arbitrarily infinite copies; 4) μ is the membrane structure; 5) M i is a set of strings over Γ representing the multi- sets of objects associated with the membrane i, 1 ≤ i ≤ q at the initial configuration; 6) R i is a finite set of evolution rules of the following form:(i, u/v, j ) , for i, j ∈{0, 1, 2,...,q} ,i = j, u, v ∈ Γ * 7) P i is a strict partial ordering to indicate priority relations between rules over R i ; 8) o Π ∈{0, 1, 2,...,q} indicates the output membrane; 2014 Asian Conference on Membrane Computing [ACMC' 14] 2014 Asian Conference on Membrane Computing [ACMC' 14] 978-1-4799-8011-6/14/© 2014 IEEE 1