Rough Pushdown Automata and Rough Context Free Grammar

Abstract

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.