Rough Finite State Automata and Rough Languages

Arulprakasam, R.; Perumal, R.; Radhakrishnan, M.; Dare, V. R.

doi:10.1088/1742-6596/1000/1/012155

Cited by 2 publications

(8 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[ 3 , 5 , 40 ] Let be a RFSA and be the class of all definable sets in ( Q , R ). Then the block transition map of M can be extended to such that for all : …”

Section: Preliminariesmentioning

confidence: 99%

“…Like classical automata and FFA, RFSA is also a mathematical model used for computation purposes in computational theory where data is given in the form of decision table having incomplete information. The automaton was presented as a recognizer of rough sets that accepts rough regular languages [ 3 ]. Formally, after an input set is provided the rough finite state automaton permits a state to transit to a rough set of states.…”

Section: Preliminariesmentioning

confidence: 99%

“…It differs from both the concept of automaton and fuzzy automaton in the sense that input in a state in these cases results in a single state/subset of Q, or a fuzzy (sub)set of Q. Definition 2.10 [3,5,40] Let M = (Q, R, X, , I, H) be a RFSA and D be the class of all definable sets in (Q, R). Then, for any D � ∈ D , the block transition map of M is a map D ∶ D × X → A defined as follows:…”

Section: Remark 25mentioning

confidence: 99%

“…Definition 2.11 [5,40] The transition map of M can be extended to * ∶ Q × X * → A in the following way: (i) * (q, ) = [q], [q] , for all q ∈ Q and empty string ∈ X * . (ii) For all q ∈ Q, w ∈ X * , and x ∈ X , * (q, wx) = * (q, wx), * (q, wx) , where * (q, wx) = D ( * (q, w), x) and * (q, wx) = D ( * (q, w), x) Definition 2.12 [3,5,40] Let M = (Q, R, X, , I, H) be a RFSA and D be the class of all definable sets in (Q, R). Then the block transition map D of M can be extended to * D ∶ D × X * → A such that for all D � ∈ D and w ∈ X * :…”

Section: Remark 25mentioning

confidence: 99%

“…The concept of rough finite-state machine introduced by Basu [5] is further studied by Sharan, Srivastava, and Tiwari [40] to characterize rough finite state automata, by Tiwari, Sharan and Singh [49] to discuss coverings of product of rough transformation semigroup, and by Tiwari and Sharan [48] to introduce the concept of product of rough finite state machine. R. Arulprakasam et al [3] established a correspondence between rough languages generated by rough grammar and rough languages accepted by rough finite-state automata. Tyagi and Tripathi [56,58], introduced rough automata, rough grammar, and rough languages into a fuzzy environment.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Generalized rough and fuzzy rough automata for semantic computing

Yadav

Tiwari

Kumari

et al. 2022

Int. J. Mach. Learn. & Cyber.

View full text Add to dashboard Cite

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.

show abstract

“…[ 3 , 5 , 40 ] Let be a RFSA and be the class of all definable sets in ( Q , R ). Then the block transition map of M can be extended to such that for all : …”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Remark 25mentioning

confidence: 99%

Section: Remark 25mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Generalized rough and fuzzy rough automata for semantic computing

Yadav

Tiwari

Kumari

et al. 2022

Int. J. Mach. Learn. & Cyber.

View full text Add to dashboard Cite

show abstract

Rough Pushdown Automata and Rough Context Free Grammar

Singh

2024

Preprint

View full text Add to dashboard Cite

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.

show abstract

Rough Finite State Automata and Rough Languages

Cited by 2 publications

References 3 publications

Generalized rough and fuzzy rough automata for semantic computing

Generalized rough and fuzzy rough automata for semantic computing

Rough Pushdown Automata and Rough Context Free Grammar

Contact Info

Product

Resources

About