a system built of a finite sets of symbols (the alphabet) and a finite set of rules that defines what types of words or sentences (strings of characters from the alphabet) are allowed in this language

a system for defining the syntax of a language by specifying the strings of symbols or sentences that are considered grammatical

In computer science and linguistics, a formal grammar, or sometimes simply grammar, is a precise description of a formal language — that is, of a set of strings. The two main categories of formal grammar are that of generative grammars, which are sets of rules for how strings in a language can be generated, and that of analytic grammars, which are sets of rules for how a string can be analyzed to determine whether it is a member of the language. In short, an analytic grammar describes how to recognize when strings are members in the set, whereas a generative grammar describes how to write only those strings in the set.