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Ijraset Journal For Research in Applied Science and Engineering Technology

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A New Direction Towards Plus weighted Grammar

Authors: Dr. S. Saridha, S. Haridha Banu

DOI Link: https://doi.org/10.22214/ijraset.2023.49129

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Abstract

The core of this paper is to establish plus weighted grammar and to illustrate the language accepted by the pwfa and pwg are equivalent.

Introduction

I. INTRODUCTION

Weighted context free grammars and weighted finite automata were initially introduced in significant articles by Marcel-Paul Schutzenberger (1961) and Noam Chomsky (1963), respectively.Weighted finite automata are standard nondeterministic finite automata in which the transitions have weights.We consider the following scenarios to demonstrate the variation of weighted finite automata. We may determine the wide range of a word by counting the number of paths that can be used to represent it as follows: Let each transition have a weight of 1, and for a path that is taken again, the sum of the weights of its successful paths. The wide range of a word equals the sum of its successful paths' weights. The algebraic structures of a semiring involve the computations with weights in the previously mentioned illustration. Here the multiplication of semiring is utilised for estimating the weights of the paths and the weight of the word is successively predicted by the sum of the weights of its successful paths.Applications for weighted automata are numerous. Weighted automata and their accompanying algorithm are developed by contemporary spoken-dialog or handheld speech recognition systems to express their concepts and promote successful combination and search [1,7].

A plus weighted automata [8,9,10,11] is an automata that deals with plus weights up to infinity. Many algebraic structures of plus weighted automata has been discussed in [8,9,10]. A grammar related to this automata is proposed in this paper. This study is a generalisation of plus weighted multiset grammar [9].Plus weighted grammar (pwg) can also be extended further in right linear and left linear grammar. The plus weighted automata can be applied in max weighted automata cited as[2,3,4,5,6]. This work   can  be further motivated to work  in  field of graph theory [13,14,15,16].

In addition to this section, this paper comprises four more. Basic concepts and notions are discussed in Section 2 for usage in later parts. In Section 3, a new grammar called pwg is proposed which offers a fresh perspective on pwfa and it elaborates with illustration that for every plus weighted regular grammar there exists a pwfa. The final section, Section 4, concludes and describes the future extension of pwg.

Conclusion

This paper introduces a different approach on plus weighted grammar, this proposal can be applied in numerous works done in fuzzy grammar and fuzzy multiset grammar. Further plus weighted algebra-related tasks can be extended in the future.

References

[1] Allauzen. C., Benson, E., Chelba, C., Riley, M., and Schalkwyk, J. (2012) Voice query refinement. In \\\"Interspeech\\\" [2] Chitra, K., \\\"A Study on Recognizability Of Max Weighted Finite State Automaton\\\", Journal Of Computer and Mathematical Sciences, Volume 8, Issue 11, December 2017, Pg. No. 658-673, Impact Factor: 4.655,ISSN NO: 0976-5727. [3] Chitra, K., \\\"Algerbraic Properties Of Max Weighted Finite State Mealy Machines\\\", International Journal Of Information And Computing Science, Volume 6, Issue 1, January 2019. Pg. No. 69-83, Impact Factor: 5.2, ISSN No:0972-1347. [4] Chitra, K., \\\"Homomorphism On Max Weighted Finite State Mealy Machine\\\", Journal Of Applied Science And Computations, Volume 5, Issue XII, December 2018. Pg. No: 96-103, Impact Factor: 5.8, ISSN No: 1076-5131. [5] Chitra, K., \\\"Minimal Machines On Max Weighted Finite State Mealy Machines\\\", International Journal Of Information And Computing Science, Volume 6, Issue 5, May 2019. Pg No. 4-23, Impact Factor: 5.2, ISSN No: 0972-1347. [6] Chitra, K., \\\"Some Products On Max Weighted Finite State Automaton\\\", International Journal Of Applied Engineering Research, Volume 13, Number 22, 2018. Pg.No. 15806-15803, Impact Factor: 2.28, ISSN No: 0973-4562. [7] Mohri, M., Pereira, F. C. N., and Riley, M. (2008) Speech recognition with weighted finite state transducers, in \\\"Handbook on speech proc. and speech commm.\\\",Springer. [8] Saridha, S. and Rajaretnam, T., \\\"Algebraic Properties of Plus Weighted Finite State Machine\\\", International Journal Of Applied Engineering Research, e-ISSN:0973-9769, p-ISSN:0973-4652, Vol.13, Number 21, 2018, 14974-14982. [9] Saridha, S. and Rajaretnam, T., \\\"A Study On Plus Weighted Multiset Transformation Semigroups\\\", International Journal Of Information And Computing Science, e-ISSN:0972-1347, Vol.6, Issue I, January 2019, 84-98. [10] Saridha, S. and Rajaretnam, T., \\\"On Regular Properties Of Plus Weighted Multiset Finite State Automaton\\\", Journal Of Applied Science And Computations, e-ISSN:1076-5131, Vol.5, Issue XII, December 2018, 87-95. [11] Saridha, S., Rajaretnam, T., Plus weighted finite state automaton, in Journal Of Computer And Mathematical Sciences (JCMS 2017), Vol.8, Issue 11, ISSN 0976-5727, pp674-690. [12] Saridha, S. and Rajaretnam, T., \\\"Some properties of plus weighted multiset grammars\\\", International Journal Of Information And Computing Science, e-ISSN:0972-1347, Vol.6, Issue 5, May 2019, 24-37. [13] Shalini. P, Paul Dhayabaran. D, \\\"An Absolute Differences of Cubic and Square Difference Labelling\\\", International Journal of Advanced Scientific and Technical Research, May-June 2015, Issue-5, Volume-3, Pages 1-8. [14] Shalini. P, Paul Dhayabaran. D, \\\"A Study on Root Mean Square Labelling in Graphs\\\", International Journal of Engineering Science and Innovative Technology, May 2015, Volume-4, Issue-3, Pages 305-309. [15] Shalini. P, S.A.Meena, \\\"Lehmer-4 Mean Labelling of Graphs\\\", Volume 10, Issue XII, International Journal for Research in Applied Science and Engineering Technology (IJRASET), Page No: 1348-1351, ISSN: 2321-9653. [16] Shalini. P, S.Tamizharasi, \\\"Power-3 Heronian Mean Labelling Graphs\\\", Volume 10, Issue XII, International Journal for Research in Applied Science and Engineering Technology (IJRASET), Page No: 1605-1608, ISSN: 2321-9653.

Copyright

Copyright © 2023 Dr. S. Saridha, S. Haridha Banu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Paper Id : IJRASET49129

Publish Date : 2023-02-16

ISSN : 2321-9653

Publisher Name : IJRASET

DOI Link : Click Here