Chapter 3, Problem 1PS

The two mathematical models for language description are:

• Recognition
• Generation

These two mathematical models can define the syntax of programming language in the given manner,

Recognition:

• It works on yes or no basis. In this method, a mechanism called recognition device (R) is used that can read strings from the given alphabet.
• This would indicate whether the input string is in language or not. That means, it will either accept the string or reject the string.
• Recognition device filters the correctly formed sentences from those that are incorrectly formed.
• In recognition, recognizer is used for syntax. analysis. Recognizer does not check for all possible strings but it simply check if the given programs are in the language or not.
• It checks the syntactical part of the program.

Generation:

• In this method, a device named generator is used to generate the sentences in a language.
• Whenever a generator is called, it generator a sentence which is unpredictable.
• When a string is to be checked if it is a correct or incorrect, first of all, it calls the generator to generate a correct sentence.
• Then, it compares the correct generated string with the input string.
• Hence, it determines the correction in string.