Abstract
In real-world applications like network software design, pattern recognition, compiler construction moreover in some of the applications of formal and natural language like accepter, spell checker and advisor, language dictionary, the Deterministic Finite Automata (DFA) plays an important role. For such applications, specification rules to construct DFA are more complex in nature. More generally, the rules consist of the intricate words like ‘and’, ‘or’, ‘not having’, ‘followed by’. Constructing DFA for such rules is time-consuming and tedious process. To make the construction process easier, simple DFA construction algorithm is proposed. The proposed algorithm is based on divide-and-conquer (D&C) algorithm design strategy. To apply D&C, the first step is to divide given language specification rule into a number of manageable pieces of sub-language specification rules, second construct DFA for each sub-language by any efficient method and at last, combine the DFA using closure properties of the regular set to obtain resultant DFA. To verify the correctness of the proposed algorithm, the obtained resultant DFA is compared with DFA constructed by a conventional method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Martin, J.C.: Introduction to Languages and the Theory of Computation, vol. 4. McGraw-Hill NY, USA (1991)
Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. Dev. 3(2), 114–125 (1959)
Hopcroft, J.E.: Introduction to Automata Theory, Languages, and Computation. Pearson Education India (2008)
Chomsky, N.: On certain formal properties of grammars. Inf. Control 2(2), 137–167 (1959)
Myers, G.: A four Russians algorithm for regular expression pattern matching. J. ACM (JACM) 39(2), 432–448 (1992)
Lochan, M., Garhwal, S., Kumar, A.: Closure properties of prefix-free regular languages. Int. J. Comput. Appl. 52(8) (2012)
Stearns, R.E., Hartmanis, J.: Regularity preserving modifications of regular expressions. Inf. Control 6(1), 55–69 (1963)
Ben-David, S., Fisman, D., Ruah, S.: Embedding finite automata within regular expressions. Theor. Comput. Sci. 404(3), 202–218 (2008)
Berry, G., Sethi, R.: From regular expressions to deterministic automata. Theor. Comput. Sci. 48, 117–126 (1986)
Daciuk, J., Mihov, S., Watson, B.W., Watson, R.E.: Incremental construction of minimal acyclic finite-state automata. Comput. Linguist. 26(1), 3–16 (2000)
Omlin, C.W., Giles, C.L.: Constructing deterministic finite-state automata in recurrent neural networks. J. ACM (JACM) 43(6), 937–972 (1996)
Parekh, R., Honavar, V.: Learning DFA from simple examples. In: International Workshop on Algorithmic Learning Theory, pp. 116–131. Springer (1997)
Tomita, M.: Learning of construction of finite automata from examples using hill-climbing: RR: Regular Set Recognizer (1982)
Lucas, S.M., Reynolds, T.J.: Learning deterministic finite automata with a smart state labeling evolutionary algorithm. IEEE Trans. Pattern Anal. Mach. Intell. 27(7), 1063–1074 (2005)
Kumar KS, M.D.: A novel method to construct deterministic finite automata from a given regular grammar. Int. J. Sci. Eng. Res. 6(3), 106–111 (2015)
Horowitz, E., Sahni, S.: Fundamentals of Computer Algorithms. Google Scholar (1978)
Nerode, A.: Linear automaton transformations. Proc. Am. Math. Soc. 9(4), 541–544 (1958)
Högberg, J., Larsson, L.: DFA minimisation using the Myhill-Nerode theorem. a a 1(q2) q3
Acknowledgements
The first author thanks the Ministry of Electronics and Information Technology (MeitY), New Delhi for granting Visvesvaraya Ph.D. fellowship through file no. PhD-MLA\(\backslash \)4(34)\(\backslash \)201-1 Dated: 05/11/2015.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Ruikar, D.D., Hegadi, R.S. (2019). Simple DFA Construction Algorithm Using Divide-and-Conquer Approach. In: Nagabhushan, P., Guru, D., Shekar, B., Kumar, Y. (eds) Data Analytics and Learning. Lecture Notes in Networks and Systems, vol 43. Springer, Singapore. https://doi.org/10.1007/978-981-13-2514-4_21
Download citation
DOI: https://doi.org/10.1007/978-981-13-2514-4_21
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-2513-7
Online ISBN: 978-981-13-2514-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)