On Minimization of Deterministic Automaton with Rough Output

Sharma, Birendra Kumar; Sharan, Shambhu; Tiwari, S. P.

doi:10.1007/978-3-319-64419-6_49

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…Arulprakasam et al examined closure properties of rough regular languages and established equivalence between rough languages generated by rough grammar and rough regular languages accepted by rough finite automata [1]. Sharma et al introduced and examined minimal deterministic automata with rough output for recognizing rough languages [12]. Praba and Saranya introduced non-homogeneous rough finite state automata (NRFSA) to capture system uncertainty and dynamical behavior over time [10].…”

Section: Introductionmentioning

confidence: 99%

Rough Pushdown Automata and Rough Context Free Grammar

Singh

2024

Preprint

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This paper proposes a new computational model, Rough Pushdown Automata (R-PDA), which extends the capabilities of traditional Pushdown Automata by incorporating Rough Set Theory. The proposed R-PDA is designed to handle imprecise and uncertain data, making it effective for decision-making under uncertain conditions. Alongside the R-PDA we further develop rough context free grammar (R-CFG) and rough context free language (R-CFL), and show its equivalence to R-PDA, i.e. for every R-PDA there is an R-CFL and vice versa. Some closure properties of R-CFL are developed to demonstrate the mathematical efficacy of the proposed model. The research provides insights into the use of rough set theory in automata theory and its potential in solving real-world problems. In this era of technological advancement coping with uncertainty is more crucial than ever. Medical domain is no exception. Efficacy of the proposed R-PDA model is demonstrated through a case study of Asthma disease, one of the most common chronic diseases in the world. Although Rough FSA has already been proposed in literature, the concept of R-PDA appears to be novel. Moreover, application of Automata theory is rarely discussed in healthcare system. The proposed model helps in bridging the gap in an effective way.

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Section: Introductionmentioning

confidence: 99%

Rough Pushdown Automata and Rough Context Free Grammar

Singh

2024

Preprint

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“…But this confining demand for equivalence limits the application scope of RST. For application purposes, many extensions of rough sets like fuzzy rough sets, rough fuzzy sets, IT2 fuzzy rough sets, IT2 rough fuzzy sets, tolerance rough fuzzy sets, rough sets based on Galois connections, soft rough fuzzy sets, and soft fuzzy rough sets have been studied (cf., [11,29,30,39,41,62,67]). RST has been proved an essential method in cognitive sciences, decision making, data mining, and artificial intelligence.…”

Section: Introductionmentioning

confidence: 99%

Generalized rough and fuzzy rough automata for semantic computing

Yadav

Tiwari

Kumari

et al. 2022

Int. J. Mach. Learn. & Cyber.

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The classical automata, fuzzy finite automata, and rough finite state automata are some formal models of computing used to perform the task of computation and are considered to be the input device. These computational models are valid only for fixed input alphabets for which they are defined and, therefore, are less user-friendly and have limited applications. The semantic computing techniques provide a way to redefine them to improve their scope and applicability. In this paper, the concept of semantically equivalent concepts and semantically related concepts in information about real-world applications datasets are used to introduce and study two new formal models of computations with semantic computing (SC), namely, a rough finite-state automaton for SC and a fuzzy finite rough automaton for SC as extensions of rough finite-state automaton and fuzzy finite-state automaton, respectively, in two different ways. The traditional rough finite-state automata can not deal with situations when external alphabet or semantically equivalent concepts are given as inputs. The proposed rough finite-state automaton for SC can handle such situations and accept such inputs and is shown to have successful real-world applications. Similarly, a fuzzy finite rough automaton corresponding to a fuzzy automaton is also failed to process input alphabet different from their input alphabet, the proposed fuzzy finite rough automaton for SC corresponding to a given fuzzy finite automaton is capable of processing semantically related input, and external input alphabet information from the dataset obtained by real-world applications and provide better user experience and applicability as compared to classical fuzzy finite rough automaton.

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