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

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

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

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.

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

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

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)

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}

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)

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

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