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A variety of two-dimensional array grammar models generating picture array languages have been introduced and investigated, utilizing and extending the well-established notions and techniques of formal string language theory. On the other hand the versatile computing model with a generic name of P system in the area of membrane computing, has turne...
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Context 1
... Σ ++ = Σ * * − {λ}. An empty unit square in the plane is indicated by the blank symbol # / ∈ Σ. A pictorial way of representing a picture array is done by showing the labels of the non-blank unit squares that constitute the picture array. For example, a picture array representing the digitized Chinese character "center" [52, p. 228] is shown in Fig. 1. Sometimes, if needed, the blank symbol is shown in some empty square but in general, we assume that the empty unit square in the plane contains this symbol even if the blank symbol is not shown. A picture array can be given in a formal manner by listing the coordinates of the non-blank unit squares of the picture array along with the ...
Context 2
... corresponding labels of the unit squares. Note that a translation of the picture array in the two-dimensional plane changes only the coordinates of the unit squares of a picture array and hence only relative positions of the symbols in the non-blank unit squares are essential for describing a picture array. For example, for the picture array in Fig. 1, taking the origin (0, 0) at the lowermost non-blank unit square of the leftmost vertical line of x s, the coordinates of the non-blank unit squares of the picture array can be specified as follows: ...
Context 3
... alphabet Σ is a finite set of symbols. A word or a string α over Σ is a finite sequence of symbols taken from Σ. The empty word with no symbols is denoted by λ. The set of all words over Σ including λ, is denoted by Σ * . For any word α = a 1 a 2 . . . a n , we denote by t α the word α written vertically, so that t α = t (α). Interpreting the two-dimensional digital plane as a set of unit squares, a picture array in the two-dimensional plane (also called, simply as an array) over Σ, is composed of a finite number of labelled unit squares (also called pixels), with the labels taken from the alphabet Σ. The set of all picture arrays over Σ will be denoted by Σ * * . The empty picture array is also denoted by λ and Σ ++ = Σ * * − {λ}. An empty unit square in the plane is indicated by the blank symbol # / ∈ Σ. A pictorial way of representing a picture array is done by showing the labels of the non-blank unit squares that constitute the picture array. For example, a picture array representing the digitized Chinese character "center" [52, p. 228] is shown in Fig. 1. Sometimes, if needed, the blank symbol is shown in some empty square but in general, we assume that the empty unit square in the plane contains this symbol even if the blank symbol is not shown. A picture array can be given in a formal manner by listing the coordinates of the non-blank unit squares of the picture array along with the corresponding labels of the unit squares. Note that a translation of the picture array in the two-dimensional plane changes only the coordinates of the unit squares of a picture array and hence only relative positions of the symbols in the non-blank unit squares are essential for describing a picture array. For example, for the picture array in Fig. 1, taking the origin (0, 0) at the lowermost non-blank unit square of the leftmost vertical line of x s, the coordinates of the non-blank unit squares of the picture array can be specified as follows: ...
Context 4
... alphabet Σ is a finite set of symbols. A word or a string α over Σ is a finite sequence of symbols taken from Σ. The empty word with no symbols is denoted by λ. The set of all words over Σ including λ, is denoted by Σ * . For any word α = a 1 a 2 . . . a n , we denote by t α the word α written vertically, so that t α = t (α). Interpreting the two-dimensional digital plane as a set of unit squares, a picture array in the two-dimensional plane (also called, simply as an array) over Σ, is composed of a finite number of labelled unit squares (also called pixels), with the labels taken from the alphabet Σ. The set of all picture arrays over Σ will be denoted by Σ * * . The empty picture array is also denoted by λ and Σ ++ = Σ * * − {λ}. An empty unit square in the plane is indicated by the blank symbol # / ∈ Σ. A pictorial way of representing a picture array is done by showing the labels of the non-blank unit squares that constitute the picture array. For example, a picture array representing the digitized Chinese character "center" [52, p. 228] is shown in Fig. 1. Sometimes, if needed, the blank symbol is shown in some empty square but in general, we assume that the empty unit square in the plane contains this symbol even if the blank symbol is not shown. A picture array can be given in a formal manner by listing the coordinates of the non-blank unit squares of the picture array along with the corresponding labels of the unit squares. Note that a translation of the picture array in the two-dimensional plane changes only the coordinates of the unit squares of a picture array and hence only relative positions of the symbols in the non-blank unit squares are essential for describing a picture array. For example, for the picture array in Fig. 1, taking the origin (0, 0) at the lowermost non-blank unit square of the leftmost vertical line of x s, the coordinates of the non-blank unit squares of the picture array can be specified as follows: ...
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In the bio-inspired area of membrane computing, a novel computing model with a generic name of P system was introduced around the year 2000. Among its several variants, string or array language generating P systems involving rewriting rules have been considered. A new picture array model of array generating P system with a restricted type of pictur...
Citations
... language theory [7, 13, 14,22] were linked in [4], by defining a cell-like array P 5 system with array-objects in the compartments of a membrane structure and array-rewriting rules of the isometric variety to evolve the arrays. Several kinds of array P systems were subsequently introduced and investigated involving rectangular or non-rectangular array-objects and isometric or non-isometric kind of rewriting rules (See, for example, [18,21] and references therein). 10 Unlike the non-isometric array rewriting rules, the isometric array rewriting rules preserve the geometric shape of the rewritten subarray. ...
... One such area of application of P systems is formal language theory with different models of P systems having been developed [29][30][31][32] for handling the problem of generation of classes of languages, starting with the seminal work of Pȃun [4]. In the extension of language theory to two dimensions, P systems have also played a significant role with different kinds of P systems with array objects and array evolving rules having been introduced (see, for example, [33][34][35]). ...
... Linking the two areas, namely, membrane computing and picture languages, an array P system with array-rewriting rules, was introduced in [33], which is one of the earliest models in this topic. This model motivated extensive research with several variants of array P systems being introduced based on different considerations (See, for example, [35] and references therein). We now introduce a new kind of array P system with picture arrays as objects and with restricted picture insertion rules in the regions. ...
... A computation in APRPIS is defined in the same way as in an array-rewriting P system [34,35] with the successful computations being the halting ones: each array, from each region of Π, which can be obtained by applying the restricted picture insertion rules to the arrays associated with that region, should be obtained but rules of only one table is applied; the array obtained in a region is placed in the region indicated by the target associated with the table of rules used; the target here indicates that the array remains in the same region, out indicates that the array is sent to the immediate outer region except for the outermost skin membrane in which case the array sent out is "lost" in the environment; and in indicates that the array is sent to the immediately inner membrane, nondeterministically chosen (but if no innner membrane exists, then the table of rules with the target indication in cannot be used). A computation is successful only if it stops and a configuration is reached where no table of rules can be applied to the existing arrays. ...
In the bio-inspired area of membrane computing, a novel computing model with a generic name of P system was introduced around the year 2000. Among its several variants, string or array language generating P systems involving rewriting rules have been considered. A new picture array model of array generating P system with a restricted type of picture insertion rules and picture array objects in its regions, is introduced here. The generative power of such a system is investigated by comparing with the generative power of certain related picture array grammar models introduced and studied in two-dimensional picture language theory. It is shown that this new model of array P system can generate picture array languages which cannot be generated by many other array grammar models. The theoretical model developed is for handling the application problem of generation of patterns encoded as picture arrays over a finite set of symbols. As an application, certain floor-design patterns are generated using such an array P system.
... Clustering based on membrane systems has shown good convergence, robustness, and parallelism [25]- [29]. In image processing applications, membranes can operate in parallel in different local areas independently of the image size [30]. In particular, the tissuelike membrane system (TMS) is a particularly flexible network membrane structure that is adaptable to various network topologies [31], [32]. ...
Accurate segmentation of choroidal neovascularization (CNV) patterns is vital for precise lesion size quantification in age-related macular degeneration. In this paper, we develop a method for unsupervised and parallel segmentation of CNV in optical coherence tomography based on a grid tissuelike membrane (GTM) system. A GTM system incorporates a modified Clustering In QUEst (CLIQUE) algorithm into tissue-like membrane systems. Exploiting CLIQUE’s aptitude for unsupervised clustering, GTM systems can detect CNV of different shapes, positions and density without the need of a training stage. The average dice ratio is 0.84±0.04, outperforms both baseline and the state-of-the-art methods. Besides, being a parallel computational paradigm, GTM systems can handle all scans under analysis simultaneously and therefore they are less time consuming, completing CNV detection on 48 scans in 0.56 seconds.
... 2 Some of these applications were collected in the volume [34]. 3 An overview of 2D picture array generating models based on membrane computing can be found in [164]. 4 Adapted from the Example 1 in [22]. ...
Membrane computing is a well-known research area in computer science inspired by the organization and behavior of live cells and tissues. Their computational devices, called P systems, work in parallel and distributed mode and the information is encoded by multisets in a localized manner. All these features make P systems appropriate for dealing with digital images. In this paper, some of the open research lines in the area are presented, focusing on segmentation problems, skeletonization and algebraic-topological aspects of the images. An extensive bibliography about the application of membrane computing to the study of digital images is also provided.
Asynchronous spiking neural P systems with rules on synapses (ARSSN P systems) are a class of computation models, where spiking rules are placed on synapses. In this work, we investigate the computation power of ARSSN P systems working in the rule synchronization mode, where a family of rule sets are specified, and all the rules in a such set should be synchronously used or not. We prove that ARSSN P systems working in the rule synchronization mode are universal as number generating, number accepting, and function computing devices, respectively. Additionally, two universal ARSSN P systems working in the rule synchronization mode are constructed. The results indicate that rule synchronization is a powerful ingredient for resource-saving, as the constructed universal ARSSN P systems working in rule synchronization mode use less neurons than the counterpart universal systems without rule synchronization.
The study of two-dimensional picture languages has a wide application in image analysis and pattern recognition [5, 7, 13, 17]. There are various models such as grammars, automata, P systems and Petri Nets to generate different picture languages available in the literature [1, 2, 3, 4, 6, 8, 10, 11, 12, 14, 15, 18]. In this paper we consider Petri Nets generating tetrahedral picture languages. The patterns generated are interesting, new and are applicable in floor design, wall design and tiling. We compare the generative power of these Petri Nets with that of other recent models [9, 16] developed by our group.
Contextual array P systems generate two-dimensional picture arrays by sequential application of contextual array rules on picture arrays. Here we consider a parallel mode of application of the contextual array rules in the regions of such an array P system. We call the resulting array P system as parallel contextual array P system (PCAP) and we study the generative power of these systems. A main advantage is that the number of membranes needed in the constructions of the PCAP for picture array generation is reduced in comparison with the sequential counterpart.
