Grammars are the finite set of formal rules that are used to generate syntactically meaningful sentences. It is used to define a language. Given a grammar G, its corresponding language L(G) represents the set of all strings generated from G. Chomsky’s containment classification on grammar provides a hierarchical representation. Ever since then several subclasses of conceptual grammars are defined and studied. Restricted linear languages are one such subclass of context-free languages that tend to possess properties comparable to linear languages. We will find that the languages of RLIN mainly consist of pattern matching languages ( \(a^nb^n, ww^r\) etc.) that are widely used in compilers and searching operations. It also enables us to establish new methods for solving the analysis and synthesis problems related to pattern understanding. The exclusive properties of RLIN can be used to define them to be a unique class of grammars under linear languages. In this work, we aim at studying RLIN along with its properties which includes designing restricted automata that can be used to recognize RLIN. The computational complexity analysis allows us to check for the possibility to place RLIN under a small class of log space. We prove that the RLIN is contained in the complexity class \(AC^0\) .