# UE23CS242A: Automata Formal Languages and Logic

The course introduces fundamental concepts in Automata and Formal Languages and their application to Logic. The course covers the notions of Finite State Automaton, Regular expression, Push down Automaton, Context Free Languages and Turing Machines. These abstract and formal models and their usage in Propositional and First Order Predicate Logic, allow for solving problems in Formal language Generation and Recognition.

### Course Objectives:

- Teach students to construct basic machines like DFA, NFA which represent Regular Languages, Regular Expressions, and Regular Grammars and to identify Non â€“ Regular Languages.
- To familiarize students to construct Teach students to identify Context Free Languages, to construct Push down Automata which represent Context Free Languages, to convert the given grammar to various normal forms and to make use of Membership Algorithm.
- Teach students to understand closure properties of Context Free Languages, to identify Non â€“ Context Free Languages and to construct Turing Machines and
- To familiarize students with concepts like Recursively Enumerable languages, Recursive Languages, Undecidable Problems. And to familiarize notions of mathematical logic: logical notations (syntax) and how to assign meaning to them (semantics).

### Course Outcomes:

- Design simple machines like DFA, NFA, convert NFA to DFA and minimize a given DFA, construct regular expressions for different languages, verify that some languages are regular and some are not.
- Analyze the difference between Regular Languages and Context Free Languages, design Push Down automata,construct Context Free Grammars, and convert one form of the grammar to another form.
- Enumerate the properties of Context Free Grammars, verify that some languages are context free and some are not, design Turing Machines, and analyze the difference between acceptability and decidability
- Analyze the difference between Recursive and Recursively Enumerable Languages, Decidable Languages,Turing â€“ Recognizable and Co â€“ Turing â€“ Recognizable, some problems that cannot be solved by Turing Machines, reduce one Undesirables Problem to another, Undeniable Problems for Recursively Enumerable Languages. And make use of Propositional Logic and Predicate Logic in knowledge representation and truth verification.

## Course Contents:

Unit 1: Introduction

Mathematical Preliminaries and Notation, Three Basic Concepts. Finite Automata: Deterministic Finite Accepters, Non- Deterministic Finite Accepters, Equivalence of Deterministic and Non-Deterministic Finite Accepters, Reduction of the number of states in Finite Automata. Regular Expressions, Connection between Regular Expressions and Regular Languages Regular Grammars.

Properties of Regular Languages: Closure Properties of Regular Languages, Elementary Questions about Regular Languages, Identifying Non Regular Languages. Definitions of PDA and CFL, Deterministic Pushdown Automata, Non-Deterministic Pushdown Automata, Pushdown Automata and Context Free Languages, Context Free Grammars.

Unit 3: Properties of Context Free Languages and Turing Machines

Parsing and Ambiguity. Simplification of Contextâ€“Free Grammars and Normal Forms: Methods for Transforming Grammars, Two Important Normal Forms, A Membership algorithm for Context Free Grammar. Properties of Context-Free Languages: Closure Properties and Questions about Contextâ€“Free Languages, Pumping Lemma for Contextâ€“Free Languages. Turing Machines: The Standard Turing Machine, Constructing Turing Machines, Combining Turing Machines for Complicated Tasks, Turingâ€™s Thesis, Rice theorem.

Hierarchy of Formal Languages and Automata: Recursive and Recursively Enumerable Languages, the Chomsky Hierarchy. Limits of Algorithmic Computation: Some Problems that cannot be solved by Turing Machines,Undecidable Problem for Recursively Enumerable Languages, idea of reduction. A very simple Logic, Syntax, Semantics, A simple knowledge Base, A simple inference procedure. Propositional Theorem Proving: Inference and Proofs, Proof by Resolution, Conjunctive Normal Form, A resolution algorithm.Syntax and Semantics of First Order Logic: Models for First Order Logic Symbols and interpretations, Terms,Atomic Sentences, Complex Sentences Quantifiers, Equality, Numbers, sets and Lists. Example - The electronic circuitsâ€™ domain.