Dungka George Thomas

• Reader at Ahmadu Bello University

This research on the characterization of Angwa-Kede lithium ore, Kokona Local Government Area, Nasarawa State, Nigeria, was carried out to identify the mineralogical content, elemental composition, and the percentage content of lithium(Li) present in the ore. The research employed a systematic sampling method for obtaining lithium ore at various li...

Transition to green energy has made lithium mining one of the biggest venture in the world but this comes with its implications. This research was conducted to check the level of lithium mining contamination on soil quality and on plant in Angwa-Kede community due to observed poor agricultural yield. A systematic sampling method was conducted on bo...

Lithium mining in Nigeria poses lots of concern due to the uncontrolled mining practices used at different mining site as seen in various states where lithium ore is mined. Due to this, water samples were obtained from the host community and lithium mining pits in Angwa-Kede, Kokona LGA, Nasarawa State, Nigeria to check the level of lithium contami...

This research on the characterization of Angwa-Kede lithium ore, Kokona Local Government Area, Nasarawa State, Nigeria, was carried out to identify the mineralogical content, elemental composition, and the percentage content of lithium (Li) present in the ore. The research employed a systematic sampling method for obtaining lithium ore at various l...

Tile pasting system is a parallel generating model which glues two square tiles at their edges to create intricate tiling patterns. It is extended by using three dimensional objects namely tetrahedral tiles and the patterns generated are used to decorate floors and walls. In the literature k-Tabled Tetrahedral Tile Pasting System (k-TTTPS) and Tetr...

A Petri Net is a mathematical model used to generate string languages, which is useful in data analysis, pattern matchings, simulations etc. Array Token Petri Nets were introduced to generate two-dimensional and three-dimensional picture languages. In this paper, we introduce Triangular Array Token Petri Net (TATPN) to generate certain interesting...

The innovative model of partial array languages generated by basic puzzle partial array grammars is available in the literature. Here we define Partial array Token Petri Net Structure (PATPNS) to generate partial array languages. Further we introduce Partial Array Token Petri Net P System (PATPNPS) to generate partial array languages and compared w...

The bene ciation of Gujeni iron ore deposit located in Kagarko Local Government area of Kaduna State, Nigeria has been studied. The ore was prepared to its liberation size of-250 + 180 µm and subjected to double concentration (gravity-magnetic) separation processes, after which XRF analysis was carried out. The gravity concentration reports an upgr...

In literature the innovative model of partial array languages and partial array rewriting rules are existing, earlier we have defined regular partial array grammar and context free partial array grammar to generate partial array languages. Here, the concept of basic puzzle partial array grammar is introduced to generate partial array languages. We...

Splicing systems was first proposed by Head on organic considerations to demonstrate indubitable chimeric behavior of DNA particles and are of current intrigue and study. In this paper, we study some of the chomskian hierarchy of array grammars namely (Regular:Regular)array grammar,(Context Free:Regular)array grammar and (Regular:Context Free)array...

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...

The connection between picture languages and restarting automata has been established in Otto (2014). An interesting class of picture languages generated by parallel contextual array grammars was studied with application in image generation and analysis in Subramanian et al. (2008). In this paper, we introduce a variant of two dimensional restartin...

Siromoney et al. introduced Siromoney matrix grammars (1973) which are of sequential-parallel type in the sense that first a horizontal string of nonterminals is derived sequentially by applying the horizontal production rules and then vertical productions are applied in parallel to get the intended two-dimensional picture. In 1999, Radhakrishnan e...

Chemical, mineralogical and petrological characterization of Gyaza iron ore deposit, Katsina State, Nigeria was carried out. The ore sample was sourced from Gyaza village, Kankiya Local Government Areas of Katsina State and comminuted using laboratory jaw crusher and pulverizing machines respectively. The comminuted sample was analyzed using XRF, X...

Tom Head defined the operation of splicing words while proposing a theoretical model of DNA recombination. Subsequent investigations on splicing on Iso-array pictures have resulted is a number of theoretical properties. In this paper, a different kind of approach of splicing on Iso-array pictures referred to as iso-array that splicing have been int...

We introduce a new grammar, called parallel contextual array insertion deletion grammar and show that it has a strictly higher generative power than a system generating recognizable 2D-picture language and Siromoney context-sensitive matrix grammar.

In this paper, we mainly focus on to prove that the graphs, viz., (i)paths, (ii) comb graphs, (iii) cycles, (iv) ladder graphs and (v) Pn´Pn graphs are k-Zumkeller graphs.

We are systematically discussing finite automata working on rectangularshaped arrays (i.e.,pictures), reading them with different scanning strategies. We show that all 32 different variants only describe two different classes of array languages. Our main proof tool is using the dihedral group D4.

Natural languages contain regular, context-free, and context-sensitive syntactic constructions, yet none of these classes of formal languages can be identified in the limit from positive examples. Mildly context-sensitive languages are capable to represent some context-sensitive constructions such as multiple agreement, crossed agreement, and dupli...

In [2, 16] a new method of description of pictures of digitized rectangular arrays is introduced based on contextual grammars, called parallel internal contextual array grammars. In this paper, we pay our attention on parallel internal column contextual array grammars and observe that the languages generated by these grammars are not inferable from...

We introduce a new P system model called as parallel contextual array insertion deletion P system, based on the modified row and column contextual rules of parallel contextual array grammar. We can generate a family of two-dimensional picture languages using this P system. We discuss some properties of this P system and find its generating power by...

A new type of two-dimensional automaton for accepting two-dimensional languages, called as two-dimensional input-revolving automaton is introduced in this paper. It is an extension of input-revolving automaton for string languages. We bring out all the variants of this automaton which are based on the various types of column-revolving operations co...

We introduce new P system models, called as external and internal parallel contextual hexagonal array P systems, based on the external and internal parallel contextual hexagonal array grammars. We can generate hexagonal arrays using these P system models with the help of Z-direction, X-direction and Y-direction external or internal parallel context...

he possibility of upgrading low grade Manganese ore using gravity and magnetic separation technique was investigated from Wasagu/Danko Local Government Area of Kebbi State, North Western Nigeria. Shaking table gave a concentrate of 48.89 %Mn, spiral concentrator gave a concentrate of 49.34 %Mn while magnetic separation gave a concentrate of 52.63 %...

A new approach to hexagonal array splicing system with respect to directions in uniform and nonuniform ways as an accepting device was proposed in Sheena Christy and Thomas (Proceedings of national conference on mathematics and computer applications 2015). In this paper, we prove the following results (i) \( \mathcal{L}({\text{AHexASSD}}) - {\text{...

Tile Rewriting Grammars (TRG) are a new model for defining picture languages introduced in [1]. A rewriting rule changes a homogeneous rectangular sub-picture into an isometric one tiled with specified tiles. Derivation and language generation with TRG rules are similar to context-free grammars. F. Sweety et al. [4] have introduced Hexagonal Tile R...

A new subclass of infinite triangular arrays called hrl-local infinite triangular arrays is introduced. We introduce infinite triangular domino systems to recognize the infinite triangular picture language. Also we introduce strictly domino testable ωω-triangular array languages.

A new model to generate triangular arrays using petri net structure has been defined. The catenation of an arrowhead to an equilateral triangle results in a similar equilateral triangle. This concept has been used in Triangular Array Token Petri Net Structure (TATPNS). Comparisons with other triangular array models have been made.

Let G = (V, E) be a graph. An injective function f: V → N is said to be a Zumkeller labeling of the graph G, if the induced function f *: E → N defined as f *(xy) = f(x) f(y) is a Zumkeller number for all xy ∈ E, x, y ∈ V. A graph G = (V, E) which admits a Zumkeller labeling is called a Zumkeller graph. In this paper, we provide algorithms for Zumk...

Let G = (V, E) be a graph. An injective function f: V→N is said to be a Zumkeller labeling of the graph G, if the induced function f *: E → N defined as f * (xy) = f(x) f (y) is a Zumkeller number for all xy ∈ E, x, y ∈ V.A graph G= (V, E) that admits a Zumkeller labeling is called a Zumkeller graph. In this paper, we provide polynomial time algori...

Let G=(V,E) be a graph. An injective function f:V→N is said to be a k-Zumkeller labeling of the graph G if the induced function f⁎:E→N defined by f⁎(xy)=f(x)f(y) satisfies the following conditions (i) For every xy∈E, f⁎(xy) is a Zumkeller number. (ii) |f⁎(E)|=k, where |f⁎(E)| denotes the number of distinct Zumkeller numbers on the edges of the grap...

Determination of the work index of Gyel-Buruku columbite ore sample in Plateau state, Nigeria, was investigated. The sample of the columbite ore was sourced from Gyel village in Jos East Local Government Area of Plateau state, Nigeria. The “reference ores (granites)” samples were sourced from Jiche and Gurum villages of Plateau state respectively....

The concept of partial commutation and traces on strings has been recently extended to rectangular picture arrays and languages, motivated by the two-dimensional patterns which appear in studies concerning parallel computing and image analysis. The closure property of Siromoney matrix languages (SML) under partial commutation is already studied. In...

In this paper, we introduce the notion of accepting H iso-array system which is defined by a finite set of permitting iso-arrays as a counter part of the well investigated accepting splicing systems defined by Mitrana et al. (2010). We compare the generative power of this system with that of some existing models such as controlled sequential pastin...

P systems generating two-dimensional languages have been studied. In this paper, the variants of P systems that generate hexagonal pictures have been extended to iso-triangular pictures drawn on triangular grid. Local and recognizable iso-triangular picture languages have been introduced, and an approach of recognizing them by iso-triangular tiling...

Prusa Grammar is a recently introduced rectangular picture languages generating model which exploits the parallel application of two-dimensional context-free rules. We introduce the hexagonal version of Prusa grammar and generate images. We compare this model with other hexagonal array generating devices for the description of its generative power.

Adjunct array token Petri net structure (AATPNS) is a recently introduced rectangular picture generating device which extends Array token Petri net structure. AATPNS generates some of the classical classes of picture languages namely Siromoney matrix languages and kolam array languages, and a recent, pure 2D context-free languages. In this paper we...

In this paper contextual string grammar model is extended to a two dimensional array grammar model, called contextual iso-triangular array grammar. Membrane computing is a computational model and in which í µí±ƒ system is its device. It is a cell like structure model. We continue the study of linking these two areas by introducing contextual iso tr...

Splicing systems were introduced by Tom Head [3] on biological considerations to model certain recombinant behaviour of DNA molecules. An effective extension of this operation to images was introduced by Helen Chandra et al. [5] and H array splicing systems were considered. A new method of applying the splicing operation on images of hexagonal arra...

A computability model based on DNA sequences called sticker systems was introduced by Kari et al. (1998). Sticker systems are language generating devices based on the sticker operation. In this work, a theoretical study about a new class of P system based on the sticker operation has been proposed. In this system, objects are double stranded sequen...

Adjunct Hexagonal Array Token Petri Net Structures (AHPN) are recently introduced hexagonal picture generating devices which extended the Hexagonal Array Token Petri Net Structures. In this paper we consider AHPN model along with a control feature called inhibitor arcs and compare it with some expressive hexagonal picture generating and recognizing...

Motivated by the studies done by G. Siromoney et al. (1973) and Alexan- dru Mateescu et al. (1998) we examine the language theoretic results related to shuf- e on trajectories by making use of Siromoney array grammars such as ( R : R)AG, (R : CF )AG, (CF : R)AG, (CF : CF )AG, (CS : R)AG, (CS : CS)AG and (CF : CS)AG which are more powerful than the...

In this paper we define contextual iso-triangular array P system that make use of iso-array objects and contextual iso-array rules. We examine the generative power of contextual iso-triangular array P system.

Wang automata to recognize rectangular picture languages and iso-picture languages were studied in [6, 7]. In this paper we introduce triangular Wang automata based on triangular Wang tiles to recognize triangular picture languages. We discuss scanning strategies and prove that triangular Wang automata with a specific scanning strategy recognize th...

Adjunct Array Token Petri Net structure (AATPNS) to generate rectangular pictures has been defined in Lalitha et al (Indian J. Math. Math. Sci. 8(1):11–19, 2012) 7]. AATPNS with inhibitor arcs generated context free and context sensitive Kolam Array languages and Tabled 0L/1L languages. In this paper we study the expressiveness of this model by com...

Mitrana et al. (2010) have introduced accepting splicing systems working in uniform and non-uniform way as a counterpart of the well investigated generating splicing systems. In this paper, we have extended these notions to H-array splicing systems studied by Helen Chandra et al. (2004) using parallel splicing on rectangular arrays. We have compare...

In this paper the concept of local languages is extended to infinite triangular arrays and ωω local languages are defined. ωω-recognizable languages of infinite triangular arrays accepted by two direction online tesselation automata are considered. Properties of these languages are studied.

In this paper, we extend the idea of accepting splicing systems on strings which was introduced by Mitrana et al. to string graphs. The input string graph is accepted as soon as the permitting string graph is obtained provided that no forbidding string graph has been obtained so far, otherwise it is rejected. We study the computational power of the...

Splicing systems were introduced by Head [4] on biological considerations to model certain recombinant behaviour of DNA molecules and are of current interest and study [5]. The splicing systems make use of a new operation called splicing on arrays of symbols [9]. Parallel splicing operation has been recently applied to rectangular arrays [6]. Furth...

In the frame work of P systems introduced by Paun (1998), generation of rectangular arrays and hexagonal arrays have been studied in the literature. In this paper, we introduce a new P system generating a family of hexagonal array languages. We compare this new family with the existing families of hexagonal array languages.

Adjunct Array Token Petri Net Structures (AATPNS) are recently introduced rectangular picture generating devices which extended the Array token Petri net Structures. AATPNS generated context free and context sensitive kolam array languages and tabled 0L/1L languages. In this paper we compare AATPNS with some simple and expressive picture grammar mo...

In this paper we construct a marked Petri net for a given symmetric group with a generating set. We show that if this net has a subset of places which are both siphon and trap then the dual of this net has a correspondence with Water Cycle, one of the important biogeochemical cycles.

In this paper we construct a Petri net for a given symmetric group with a generating set. We show that if this net has a subset of places which are both siphon and trap then the dual of this net has a correspondence with carbon cycle, one of the major biogeochemical cycles.

In this paper, we introduce a new concept of trajectory array P system which consists of a membrane structure in which the objects are arrays and the evolutionary rules are given in terms of trajectories. We present some properties of trajectory array P system and compare with certain families of picture languages. We consider a variant of trajecto...

Tree replacement/rewriting systems are an interesting model of computation. They are used in theorem proving, algebraic simplification and language theory. A fundamental property of tree replacement systems is the Church-Rosser property which expresses the fact that interconvertability of two trees can be checked by mere simplification to a common...

Sticker systems, a computability model introduced by L. Kari et al. (1998) are language generating devices based on the sticker operation. In this paper, a theoretical study about a new class of P system based on the sticker operation has been presented. Such a system has double stranded sequences with sticky ends as objects and sticker operations...

Dassow, Paun and Salomaa (1993) defined a generative device called pattern grammar. Abisha, Subramanian and Thomas (2000) introduced a new type of grammar called Pure Pattern grammar, in which they examined parallel communicating grammar systems with all components different from the master being pure pattern grammar. Dersanambika, Krithivasan and...

Parallel composition of words and languages of words appear as a fundamental operation in parallel computation and in the theory of concurrency. Shuffle on trajectories provides a method to handle the operation of parallel composition. In this paper we study the impact of shuffle on trajectories on various finite arrays. We obtain interesting resul...

A new model to generate hexagonal arrays using Petri net structure has been defined. The catenation of an arrowhead to a b-hexagon results in a similar b-hexagon. This concept has been used in Hexagonal Array Token Petri Net Structure (HATPNS). A variation in the position of catenation has been introduced in Adjunct Hexagonal Array Token Petri Net...

The concept of a Parikh matrix of words was introduced by Mateescu et al [3]. It was extended to 2D-rectangular arrays and a polynomial time algorithm was given to reconstruct an unknown 2D-array over {0, 1} from its image under the extended Parikh mapping along a single direction, and reconstruction from projections along three or more directions...

Tree rewriting systems are sets of tree rewriting rules used to compute by repeatedly replacing equal trees in a given formula until the simplest possible form (normal form) is obtained. The Church-Rosser property is certainly one of the most fundamental properties of tree rewriting system. In this system the simplest form of a given tree is unique...

Pattern language learning algorithms within the inductive inference model and query learning setting have been of great interest. In this paper an algorithm to learn a parallel communicating grammar system in which the master component is a regular grammar and the other components are pure pattern grammars is given.

In this paper we introduce a new model called iso-picture splicing system, to generate iso-pictures. We compare the family of languages generated by the proposed system with existing family of languages such as local iso-picture languages and we prove some properties of the family of languages generated by proposed system.

In this paper, we introduce a new concept of trajectory array P system which consists of a membrane structure in which the objects are arrays and the evolutionary rules are given in terms of trajectories. We present some properties of trajectory array P system and compare with certain families of picture languages.

In this paper, we introduce a new model called double splicing and its variants for generating pictures. The family of languages generated by the proposed model is compared with a family of languages generated by an existing model namely H-array splicing, and also compared with family of local picture languages. Closure properties of the family of...

A new operation called collage on one-dimensional (respectively two-dimensional) word languages, obtained by piling up, one on top of the other, words of a given recognizable language on a previously empty one-dimensional (respectively two-dimensional) array, was introduced (2005). In this paper we extend the operation to iso-picture languages. We...

In the context of a syntactic approach to pattern recognition, there have been several studies in the last few decades ontheoretical models for generating or recognizing two-dimensional objects, pictures, and picture languages. Motivated by these studies, we have introduced a new notion of recognizability for a class of picture languages called iso...

We introduce an online tessellation partial automaton to recognize partial array languages. We also introduce two classes of partial array languages viz, Local Partial Array Languages (PAL-LOC), Recognizable Partial Array Languages (PAL-REC) and proved PAL-REC is exactly the family of partial array languages recognizable by online tessellation part...

Public Key Cryptosystems (PKC) based on formal language theory and semi groups have been of interest and study. A PKC based on free group has been presented in [7]. Subsequently another PKC using free partially commutative monoids and groups is studied in [1]. In this paper, we propose a PKC for chain code pictures that uses a finitely presented gr...

Tile rewriting grammars are a new model for defining picture languages. In this paper we propose hexagonal tile rewriting grammars (HTRG) for generating hexagonal picture languages. Closure properties of HTRG are proved for some basic operations. We compare HTRG with hexagonal tiling systems.

A new operation called collage on one-dimensional (respectively two-dimensional) word languages was introduced in [2]. It is obtained by piling up, one on top of the other, words of a given recognizable language on a previously empty one-dimensional (respectively two-dimensional) array. In this paper we extend this operation to hexagonal picture la...

We present a class of coded Petri net languages and study some algebraic properties. The purpose of introducing such languages is to bring out their usefulness in learning theory. We introduce an algorithm for learning a finite coded Petri net language, and its running time is bounded by a polynomial function of given inputs.

We describe two algorithms to identify the repeating subwords in a given partial word w 0 =w 0 [1,⋯,n]. The first algorithm uses the suffix tree and the second algorithm uses the valency tree. Both algorithms take linear time to identify the repeating subwords of a partial word.

Pattern language learning algorithms within the inductive inference model and query learning setting have been of great interest. In this paper, we study the problem of learning pure pattern languages using queries and examples.

In [3], we have provided an algorithm to infer a few subclasses of linear languages through labeled extended Petri nets. The family of equal matrix languages [6] meets both the families of context sensitive languages and context-free languages. In this paper, we prove that an equal matrix language is a Petri net language.We construct labeled extend...

Membrane Computing is a branch of natural computing aiming to abstract computing ideas for the structure and the functioning of living cells as well as from the way the cells are organized in tissues or higher order structures. We consider iso-picture languages introduced in [2,3] and the possibility to handle them with P systems. In this paper we...

Recently F. Blanchet-Sadri introduced Pcodes that play an important role in the study of combinatorics on partial words [Comput. Math. Appl. 47, No. 1, 71–82 (2004; Zbl 1068.68110)]. Pcodes are defined in terms of the compatibility relation which consider two sequences over the same alphabet that are equal except for a number of insertion and/or de...

The subject of tilings is very interesting and has now become an area of study in its own right, with numerous connections and applications to other fields from group theory to topology, from enumerative combinatorics to probability. D. W. Walkup [Am. Math. Mon. 72, 986–988 (1965; Zbl 0132.00603)], M. Korn and I. Pak [Theor. Comput. Sci. 319, No. 1...

Petri nets have been used by several researchers for description and analysis of systems of parallel processes. In a Petri net, actions are modeled by transitions and the occurrence of an action is modeled by the firing of a transition. Such a firing changes the actual marking of the net, which describes the global state of the system. Thus, the dy...

In this paper a probabilistic mechanism is attached to a eight direction sequential / parallel rewriting model generating hexagonal arrays, which are restricted by control tables. Use of stochastic languages for the description of noisy patterns is demonstrated.

The notions of iso-arrays, iso-pictures, local iso-picture languages and recognizable iso-picture languages have been introduced and studied in [6]. In [6] we have provided an algorithm to learn local iso-picture languages through identification in the limit using positive data. In this paper, we construct a two-dimensional on-line tessellation aut...

DNA molecules are known to occur not only as linear strings but also as circular strings. While investigating the recombinant be haviour of DNA molecules in a pioneering work. Tom Head introduced the notion of regularity of circular languages, that are languages of cir cular strings. Pixton has made an interesting study of circular strings accepted...

In the context of a syntactic approach to pattern recognition, there have been several studies in the last few decades on theoretical models for generating or recognizing two-dimensional objects, pictures and picture languages. Motivated by these studies we introduce a new notion of recognizability for a class of picture languages called iso pictur...

In this paper, splicing on images of rectangular arrays is introduced as a simple and effective extension of the operation of splicing on strings extensively studied in the context of DNA computing. A comparison of the resulting class of splicing array languages with the local two-dimensional array languages and two-dimensional right linear languag...

In this paper we propose a block based method of image reconstruction which acts as a generic attack against any block based watermarking scheme in spatial domain. Our reconstruction method relies on the geometric features of the image to discover and modify the inconsistencies in the pixel values introduced due to watermarking. To show its effecti...

In this paper, a public key cryptosystem based on tree replacement system is proposed.

In this paper, we define three classes of languages of bi-infinite words, namely local bi-ω languages, recognizable bi-ω languages and Büchi local bi-ω languages as subclasses of the class of regular bi-ω languages and prove some basic results. We observe that the class of recognizable bi-ω languages coincides with the well-known class of rational...

In this paper, we define three classes of languages of biinfinite words, namelyl ocal bi-¿ languages, recognizable bi-¿ languages and Büchi local bi-¿ languages as subclasses of the class of regular bi-¿ languages and prove some basic results. We observe that the class of recognizable bi-¿ languages coincides with the well-known class of rational b...