1. FORMAL LANGUAGES AND AUTOMATA THEORY
C K Nagpal
M.Tech. Ph.D.
Associate Professor
Computer Engg.
YMCA University of Science & Technology

2. Chapter 1 Automata, Formal Languages, and Computability
In these slides, we will cover the following topics:
Why study automata theory
Basic constituents of phrase structure grammar
Chomsky hierarchy of grammars
Basic aspects of computability

3. Automata
Automata →plural of the word ‘ automaton’ which means to automate or mechanize.
Mechanization of a process means performing it on a machine without human intervention.
Mechanized Environment & its advantages

4. Automata Theory in Computer Science
What is computable?
If computable how it can be implemented on a machine?
Study of abstract machines that can perform computing.

5. Formal Language
Meta language to describe the formal or official description of a language

6. Phrase Structure Grammar
Formal structure of English Sentences can be defined in terms of phrases, it is a phrase structure grammar.
For example, the structure of a declarative sentence can be defined in terms of two phrases Noun Phrase and Verb Phrase

7. Phrase Structure Grammar (Constituents)
A set of terminals Σ
(Ultimate participants in the sentence)
2. A set of nonterminals V
(Syntactic categories)
3. A set of productions P
(Description of sentence construction process)
4. A special nonterminal S, known as starting symbol or starting sentential form
(describe from where to start the sentence construction process)

8. Structure of a Declarative Sentence in English
sentence →noun phrase + verb phrase
noun phrase → article + common noun
noun phrase → proper noun
verb phrase → transitive verb phrase
verb phrase → intransitive verb phrase
transitive verb phrase → transitive verb + noun phrase
intransitive verb phrase → intransitive verb
intransitive verb phrase → intransitive verb + adverb
article → {a, the}
common noun → {cow, elephant, dog, cat, door}
proper noun → {Ram, Shyam, Hari, Govind, Rakesh}
transitive verb →{chases, meets, hits, opens}
intransitive verb → {runs, plays, eats}
adverb → {slowly, rapidly}

9. Chomsky Classification of Grammars
Chomsky classified the languages into 4 categories depending upon their production system
Type 0→ Unrestricted Grammar → Turing Recognizable Language → Turing Machine
Type 1→ Context Sensitive Grammar → Context Sensitive Language → Linear Bound Automaton
Type 2→ Context Free Grammar → Context Free Language → Push Down Automation
Type 3→ Regular Grammar → Regular Language → Finite Automaton
( All grammars except Type 0 are monotonically increasing grammars)

10. Containment Relationship Among Languages
Turing Recognizable Languages
Context Sensitive languages
Context Free Languages
Regular Languages

11. Computability
All primitive recursive functions are computable but vice versa is not true
All µ recursive functions are computable and vice versa is also true