Presentation on theme: "CS2303-THEORY OF COMPUTATION"— Presentation transcript:
1CS2303-THEORY OF COMPUTATION && Department of nskinfo-i educationCS2303-THEORY OF COMPUTATIONChapter:Application of Formal Languages in Computing Environment
2Application of Formal Languages in Computing Environment
3Roadmap Introduction Finite Automata and Digital Images Probabilistic Grammar SystemsDistributed Processing in AutomataUnconventional models of computingL – System and Computer Imagery
4Formal 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 – 1936Concept of undecidability.
6Finite 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
7Translation by ½ , ¼ Square Scaled Versions of TriangleFST for rotation by 45°
8Finite Automata and Digital Images Contd… Representation of 3D objects using FSA andprojections of the 3D object onto the coordinateplane using the FSAs3D addressing schemeandExample AutomatonProjections of rightangled prism
9Finite Automata and Digital Images Contd… A new O(mn2) algorithm for minimization of DFSAs proposedAn efficient O(e2 ) algorithm to minimize NFSAs proposedWeighted Finite Automata (WFA) as a tool to represent digital gray-scale imagesInference and De-inference algorithms for WFA
11Finite Automata and Digital Images Contd… A new incremental inference algorithm for self similarImages proposed --- cut and paste operationExample : Operation Cut-Paste on WFAExample : After Cut-Paste Operation
12Finite 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 acceptanceRepresentation of Images using Distributed Weighted Finite Automata
13Original Image 5%E,26.12%C 10%E,47.92%C 15%E,65.33%C 230 states states states
14Original Image 10%E,55.14%C Original Image 10%E,54.80%C 367 States States
15Grammar Systems and Distributed Automata Models For Distributed ComputingBlackboard ModelCooperative Distributed (CD) Grammar Systems.Modes of CooperationClassroom ModelParallel Communicating (PC) Grammar Systems.Variants – returning and non returningCentralised and non centralised.
16Probabilistic Grammar Systems We have defined a new model of computation namely, Probabilistic Grammar System and haveStudied the generative power of Probabilistic Grammar Systems both in the sequential (PCDGS) and the parallel (PPCGS) senseStudied the syntactic complexity of the sequential construct interms of the number of productions per componentIllustrated an application of the PPCGS in characterizing theworkload generated by the user community in computer networks
19Characterization of Workload in a Distributed Environment Validation of Server 1
20Characterization of Workload in a Distributed Environment Contd … Validation of Server 2
21Characterization of Workload in a Distributed Environment Contd … Validation of Server 3
22Distributed 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 environmentFinite 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
23Unconventional Models of Computing DNA ComputingSplicing SystemsSticker SystemsE H (Fin, P) = C FMembrane ComputingP SystemsPeptide Computing
24Membrane SystemsNew 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.
32References List of research publications: 1. Mutyam Madhu and Kamala Krithivasan, Computing withdynamic polarized membranes, Romanian Journal of InformationScience and Technology, 4(1), , 20012. Mutyam Madhu and Kamala Krithivasan, Inter-membranecommunication in P Systems, Romanian Journal of InformationScience and Technology, 3(4), , 2000S.V. Ramasubramanian and Kamala Krithivasan,Finite Automata and Digital Images, IJPRAI, Vol. 14, No. 4(2000),ppShri Raghav Kaushik and Kamala Krithivasan, Some Results onContextual Grammars, IJCM, 73, pp , 2000Lakshminarayanan, Muralidhar Talupur, Kamala Krithivasanand C.Pandu Rangan, On the generative power of Simple HSystems, Journal of Automata, Languages and Combinatorics,Vol.5 (2000) 4, pp
33References Contd…Kamala Krithivasan and Arvind Arasu, Simplifed simpleH systems, to appear in the commemorative Volume for Gh. Paun's50th birthday, 20007. Muralidhar Talupur and Kamala Krithivasan, On the generative power of Simple H Systems with permitting contexts, submitted to Theoretical Computer ScienceRahul Santhanam and Kamala Krithivasan, Graph Splicing systems,submitted to Discrete Applied MathematicsKamala Krithivasan, M. Sakthi Balan and R. Rama, ArrayContextual Grammars, in Recent Topics in Mathematical andComputational Linguistics, ed. C. Martin-Vide and GheorghePaun, pp , 2000.10. Kamala Krithivasan, M.Sakthi Balan and P.Harsha, DistributedProcessing in Automata, International Journal of Foundationsof Computer Science, Vol.10, No.4, 1999, pp
34References Contd…11. V.T.Chakravarthy and Kamala Krithivasan, Some resultson Simple Extended H systems, Romanian Journal of InformationScience and Technology, Vol No. 3, pp , 199812. Kamala Krithivasan and Shri Raghav Kaushik, Some resultson Array Splicing, Computing with Bio Molecules, Ed. G. Paun,Springer, pp , 199813. V.Radhakrishnan, V.T.Chakravarthy and Kamala Krithivasan,Pattern Matching in Matrix Grammars, Journal of Automata,Languages and Combinatorics, Vol 3, pp , 199814. Mutyam Madhu and Kamala Krithivasan, Contextual P Systems,Workshop on Membrane Computing, Curtea-de Arges, Romania,August, 2001Y. Sivasubramanyam and Kamala Krithivasan, Image representation using Distributed Weighted Finite Automata, 8th International Workshop on combinatorial Image Analysis, IWCIA’2001, Philadelphia, U.S.A.
35References Contd…M. Sakthi Balan, Parallel Communicating Pushdown Automata with filters in Communication, proceedings of DCAGRS, July 2001, ViennaK. 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,ViennaK.Arthi, Kamala Krithivasan and S.V.Raghavan, A Generative Model for capturing User Behaviour in Comuter Networks, proceedings of SCI’2001, Vol.5, ppM. 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. ppMutyam Madhu and Kamala Krithivasan, P Systems withmembrane creation:Universality and Efficiency, InternationalConference on Machine, Computation and Universality (MCU'2001),Chesinau, Maldova, 2001, Vol.2055 of LNCS, Springer-Verlag,pp
36References Contd…21. K. Sharda and Kamala Krithivasan, Distributed Fuzzy Automata, International Conference on Recent Advances in MathematicalSciences, I.I.T. Kharagpur, 2000, in Applicable Mathematics –Its Perspectives and Challenges, pp22. Y. Sivasubramanyam and Kamala Krithivasan, Integer WeightedPDA, International Conference on Recent Advances in MathematicalSciences, I.I.T. Kharagpur, 2000, in Recent Trends in MathematicalSciences, pp23. Kamala Krithivasan and M.Sakthi Balan, Distributed Processingin Deterministic PDA, International Workshop on GrammarSystems, Austria, July 2000, pp24. Prahalad Harsha, Muralidhar Talupur and Kamala Krithivasan,Simple Test Tube Systems, International Workshop on GrammarSystems, Austria, July 2000.25. S.V.Ramasubramanian and Kamala Krithivasan, WeightedFinite Automata, Digital Images and Image Compression, SatelliteConference on Image Analysis in Materials and life Sciences, November 1999, Kalpakkam, India.
37References Contd…26. Kamala Krithivasan, S.V.Raghavan and K.Arthi, Applicationsof Formal Languages in Global Positioning Systems, ADCOM'99,December 1999, Roorkee, pp27. V.Radhakrishnan, V.T.Chakravarthy, Kamala Krithivasan,Some properties of Matrix Grammars- Parallel Image Analysis, SixthInternational Work shop on Parallel Image Processing and Analysis-Theory and Applications, Jan 15-16, pp , 1999.28. S.V.Ramasubramanian and Kamala Krithivasan, FiniteAutomata Principles for 2D image and 3D object representation,Sixth International Work shop on Parallel Image Processingand Analysis- Theory and Applications, Jan 15-16, pp , 199929. S. N. Krishna, R. Rama and K. Krithivasan, P Systems with PictureObjects, Acta Cybernetica, to appear