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&& Department of nskinfo-i education CS2303-THEORY OF COMPUTATION Chapter: Application of Formal Languages in Computing Environment 1

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Roadmap Introduction Finite Automata and Digital Images Probabilistic Grammar Systems Distributed Processing in Automata Unconventional models of computing L – System and Computer Imagery

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Formal Language Theory Started in 1959 when Noam Chomsky gave a mathematical definition of a grammar. Around the same time FSA were defined. Main motivation for the topic was from compilers – ALGOL 60 complier, parsing, lexical analysis. A. M. Turing defined computability – 1936 Concept of undecidability.

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Earlier Work Array Grammars Parallel Context Free Grammars Graph Grammars L Systems Cellular Automata

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Finite Automata and Digital Images Representation of black and white digital images using Finite State Automata (FSA) Finite State Transducers (FST) as a tool to effect transformations such as scaling, translation, rotation, etc., on images represented by FSAs

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Translation by ½, ¼ Square Scaled Versions of Triangle FST for rotation by 45 °

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3D addressing scheme and Example Automaton Projections of right angled prism Representation of 3D objects using FSA and projections of the 3D object onto the coordinate plane using the FSAs Finite Automata and Digital Images Contd…

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A new O(mn 2 ) algorithm for minimization of DFSAs proposed An efficient O(e 2 ) algorithm to minimize NFSAs proposed Weighted Finite Automata (WFA) as a tool to represent digital gray-scale images Inference and De-inference algorithms for WFA

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Inference Algorithm applied on different images

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Finite Automata and Digital Images Contd… A new incremental inference algorithm for self similar Images proposed --- cut and paste operation Example : Operation Cut-Paste on WFAExample : After Cut-Paste Operation

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Finite Automata and Digital Images Contd… We have defined the distributed version of the WFA, namely Cooperating Distributed Weighted Finite Automata and have analyzed its acceptance power in various modes of acceptance Representation of Images using Distributed Weighted Finite Automata

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Original Image 5%E,26.12%C 10%E,47.92%C 15%E,65.33%C 230 states 190 states 148 states

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Original Image 10%E,55.14%C Original Image 10%E,54.80%C 367 States 1106 States

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Grammar Systems and Distributed Automata Models For Distributed Computing 1.Blackboard Model Cooperative Distributed (CD) Grammar Systems. Modes of Cooperation 2.Classroom Model Parallel Communicating (PC) Grammar Systems. Variants – returning and non returning Centralised and non centralised.

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Probabilistic Grammar Systems We have defined a new model of computation namely, Probabilistic Grammar System and have Studied the generative power of Probabilistic Grammar Systems both in the sequential (PCDGS) and the parallel (PPCGS) sense Studied the syntactic complexity of the sequential construct in terms of the number of productions per component Illustrated an application of the PPCGS in characterizing the workload generated by the user community in computer networks

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Validation of Server 1 Characterization of Workload in a Distributed Environment

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Characterization of Workload in a Distributed Environment Contd … Validation of Server 2

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Characterization of Workload in a Distributed Environment Contd … Validation of Server 3

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Distributed Processing in Automata We have performed an extensive study of distributed processing in automata theory and have investigated the power of the following machine models in distributed environment Finite State Automata (CD) Pushdown Automata (CD & PC) Fuzzy Finite State Automata (CD) Fuzzy Pushdown Automata (CD) - Automata (CD) We have also studied Fuzzy - Automata as accepting devices of the Fuzzy - Languages

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DNA Computing Splicing Systems Sticker Systems E H (Fin, P[1]) = C F Membrane Computing P Systems Peptide Computing Unconventional Models of Computing

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Membrane Systems New field of research, motivated by the way nature computes at the cellular level, introduced by Prof. Gh. Păun. It is also called as P systems. A class of distributed parallel computing devices of biochemical type. The three fundamental features of cells which will be used in our computing model are: The membrane structure, (where) multisets of chemical compounds (evolve according to) (prescribed) rules.

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Membrane Structure Skin Membranes Elementary membranes Regions

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L Systems and Computer Imagery F+ F+ F+ F F draw a line of unit length + turn anti clock wise through 90 degrees

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Kolam Patterns

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L System and Computer Imagery We have implemented several variants like Terminal Weighted L System and Fuzzy L System in Java.

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L System and Computer Imagery Contd…

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References a) List of research publications: 1. Mutyam Madhu and Kamala Krithivasan, Computing with dynamic polarized membranes, Romanian Journal of Information Science and Technology, 4(1), , Mutyam Madhu and Kamala Krithivasan, Inter-membrane communication in P Systems, Romanian Journal of Information Science and Technology, 3(4), , S.V. Ramasubramanian and Kamala Krithivasan, Finite Automata and Digital Images, IJPRAI, Vol. 14, No. 4 (2000),pp Shri Raghav Kaushik and Kamala Krithivasan, Some Results on Contextual Grammars, IJCM, 73, pp , Lakshminarayanan, Muralidhar Talupur, Kamala Krithivasan and C.Pandu Rangan, On the generative power of Simple H Systems, Journal of Automata, Languages and Combinatorics, Vol.5 (2000) 4, pp

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References Contd… 6. Kamala Krithivasan and Arvind Arasu, Simplifed simple H systems, to appear in the commemorative Volume for Gh. Paun's 50th birthday, Muralidhar Talupur and Kamala Krithivasan, On the generative power of Simple H Systems with permitting contexts, submitted to Theoretical Computer Science 8. Rahul Santhanam and Kamala Krithivasan, Graph Splicing systems, submitted to Discrete Applied Mathematics 9. Kamala Krithivasan, M. Sakthi Balan and R. Rama, Array Contextual Grammars, in Recent Topics in Mathematical and Computational Linguistics, ed. C. Martin-Vide and Gheorghe Paun, pp , Kamala Krithivasan, M.Sakthi Balan and P.Harsha, Distributed Processing in Automata, International Journal of Foundations of Computer Science, Vol.10, No.4, 1999, pp

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References Contd… 11. V.T.Chakravarthy and Kamala Krithivasan, Some results on Simple Extended H systems, Romanian Journal of Information Science and Technology, Vol No. 3, pp , Kamala Krithivasan and Shri Raghav Kaushik, Some results on Array Splicing, Computing with Bio Molecules, Ed. G. Paun, Springer, pp , V.Radhakrishnan, V.T.Chakravarthy and Kamala Krithivasan, Pattern Matching in Matrix Grammars, Journal of Automata, Languages and Combinatorics, Vol 3, pp , Mutyam Madhu and Kamala Krithivasan, Contextual P Systems, Workshop on Membrane Computing, Curtea-de Arges, Romania, August, Y. Sivasubramanyam and Kamala Krithivasan, Image representation using Distributed Weighted Finite Automata, 8 th International Workshop on combinatorial Image Analysis, IWCIA2001, Philadelphia, U.S.A.

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References Contd… 16.M. Sakthi Balan, Parallel Communicating Pushdown Automata with filters in Communication, proceedings of DCAGRS, July 2001, Vienna 17. K. Arthi, Kamala Krithivasan and Erzsebet Csuhaj-Varju, On the Number of Rules in Components of Cooperating Distributed Grammar Systems with Probabilities, proceedings of DCAGRS, July 2001,Vienna 18.K.Arthi, Kamala Krithivasan and S.V.Raghavan, A Generative Model for capturing User Behaviour in Comuter Networks, proceedings of SCI2001, Vol.5, pp M. Sakthi Balan, Kamala Krithivasan and Y. Sivasubramanyam, Peptide Computing - Universality and Complexity, 7 th International Conference on DNA based Computers (DNA7), Florida, U.S.A. pp Mutyam Madhu and Kamala Krithivasan, P Systems with membrane creation:Universality and Efficiency, International Conference on Machine, Computation and Universality (MCU'2001), Chesinau, Maldova, 2001, Vol.2055 of LNCS, Springer-Verlag, pp

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21. K. Sharda and Kamala Krithivasan, Distributed Fuzzy Automata, International Conference on Recent Advances in Mathematical Sciences, I.I.T. Kharagpur, 2000, in Applicable Mathematics – Its Perspectives and Challenges, pp Y. Sivasubramanyam and Kamala Krithivasan, Integer Weighted PDA, International Conference on Recent Advances in Mathematical Sciences, I.I.T. Kharagpur, 2000, in Recent Trends in Mathematical Sciences, pp Kamala Krithivasan and M.Sakthi Balan, Distributed Processing in Deterministic PDA, International Workshop on Grammar Systems, Austria, July 2000, pp Prahalad Harsha, Muralidhar Talupur and Kamala Krithivasan, Simple Test Tube Systems, International Workshop on Grammar Systems, Austria, July S.V.Ramasubramanian and Kamala Krithivasan, Weighted Finite Automata, Digital Images and Image Compression, Satellite Conference on Image Analysis in Materials and life Sciences, November 1999, Kalpakkam, India. References Contd…

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26. Kamala Krithivasan, S.V.Raghavan and K.Arthi, Applications of Formal Languages in Global Positioning Systems, ADCOM'99, December 1999, Roorkee, pp V.Radhakrishnan, V.T.Chakravarthy, Kamala Krithivasan, Some properties of Matrix Grammars- Parallel Image Analysis, Sixth International Work shop on Parallel Image Processing and Analysis- Theory and Applications, Jan 15-16, pp , S.V.Ramasubramanian and Kamala Krithivasan, Finite Automata Principles for 2D image and 3D object representation, Sixth International Work shop on Parallel Image Processing and Analysis- Theory and Applications, Jan 15-16, pp , S. N. Krishna, R. Rama and K. Krithivasan, P Systems with Picture Objects, Acta Cybernetica, to appear References Contd…

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Thank You

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