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

2. Application of Formal Languages in Computing Environment

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

4. 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.

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

6. 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

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

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

9. Finite Automata and Digital Images Contd…
A new O(mn2) algorithm for minimization of DFSAs proposed
An efficient O(e2 ) 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

10. Inference Algorithm
applied on different
images

11. 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 WFA
Example : After Cut-Paste Operation

12. 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

13. Original Image 5%E,26.12%C 10%E,47.92%C 15%E,65.33%C
230 states states states

14. Original Image 10%E,55.14%C Original Image 10%E,54.80%C
367 States States

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

16. 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

19. Characterization of Workload in a Distributed Environment
Validation of Server 1

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

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

22. 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

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

24. 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.

25. Membrane Structure 1 5 7 6 4 10 3 9 Skin 2 8 Membranes Elementary
Regions 3 9
Skin 2 8

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

27. Kolam Patterns

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

29. L System and Computer Imagery Contd…

30. L System and Computer Imagery Contd…

31. L System and Computer Imagery Contd…

32. References List of research publications:
1. Mutyam Madhu and Kamala Krithivasan, Computing with
dynamic polarized membranes, Romanian Journal of Information
Science and Technology, 4(1), , 2001
2. Mutyam Madhu and Kamala Krithivasan, Inter-membrane
communication in P Systems, Romanian Journal of Information
Science and Technology, 3(4), , 2000
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 , 2000
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

33. References Contd…
Kamala Krithivasan and Arvind Arasu, Simplifed simple
H systems, to appear in the commemorative Volume for Gh. Paun's
50th birthday, 2000
7. Muralidhar Talupur and Kamala Krithivasan, On the generative power of Simple H Systems with permitting contexts, submitted to Theoretical Computer Science
Rahul Santhanam and Kamala Krithivasan, Graph Splicing systems,
submitted to Discrete Applied Mathematics
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 , 2000.
10. 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

34. 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 , 1998
12. Kamala Krithivasan and Shri Raghav Kaushik, Some results
on Array Splicing, Computing with Bio Molecules, Ed. G. Paun,
Springer, pp , 1998
13. V.Radhakrishnan, V.T.Chakravarthy and Kamala Krithivasan,
Pattern Matching in Matrix Grammars, Journal of Automata,
Languages and Combinatorics, Vol 3, pp , 1998
14. Mutyam Madhu and Kamala Krithivasan, Contextual P Systems,
Workshop on Membrane Computing, Curtea-de Arges, Romania,
August, 2001
Y. Sivasubramanyam and Kamala Krithivasan, Image representation using Distributed Weighted Finite Automata, 8th International Workshop on combinatorial Image Analysis, IWCIA’2001, Philadelphia, U.S.A.

35. References Contd…
M. Sakthi Balan, Parallel Communicating Pushdown Automata with filters in Communication, proceedings of DCAGRS, July 2001, Vienna
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
K.Arthi, Kamala Krithivasan and S.V.Raghavan, A Generative Model for capturing User Behaviour in Comuter Networks, proceedings of SCI’2001, 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

36. References Contd…
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
22. 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
23. Kamala Krithivasan and M.Sakthi Balan, Distributed Processing
in Deterministic PDA, International Workshop on Grammar
Systems, Austria, July 2000, pp
24. Prahalad Harsha, Muralidhar Talupur and Kamala Krithivasan,
Simple Test Tube Systems, International Workshop on Grammar
Systems, Austria, July 2000.
25. 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.

37. References Contd…
26. Kamala Krithivasan, S.V.Raghavan and K.Arthi, Applications
of Formal Languages in Global Positioning Systems, ADCOM'99,
December 1999, Roorkee, pp
27. 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 , 1999.
28. 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 , 1999
29. S. N. Krishna, R. Rama and K. Krithivasan, P Systems with Picture
Objects, Acta Cybernetica, to appear

38. Thank You