Mathematical Foundation of Computer Science

DHARM 164 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Sol. We assume that element x has complement z other than x. So, we have, ...

DHARM LATTICE THEORY 165 l Also, GLB(x 5 , x 4 ) = x 6 ∉ X 3 ; so subset X 3 is not closed under operations GLB and LUB therefor ...

DHARM 166 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE 6.7 Prove that every chain is a distributive lattice. 6.8 Prove De Morgan’ ...

INTRODUCTION TO LANGUAGES AND FINITE AUTOMATA 7.1 Basic Concepts of Automata Theory............................................. ...

7.1 BASIC CONCEPTS OF AUTOMATA THEORY Before begin to the study of automata theory we shall first introduce the basic concepts a ...

DHARM INTRODUCTION TO LANGUAGES AND FINITE AUTOMATA 169 The set of all possible strings over Σ is denoted by Σ, where operator ...

DHARM 170 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Strings, by definition, are finite but the language contains infinite numb ...

DHARM INTRODUCTION TO LANGUAGES AND FINITE AUTOMATA 171 movement is restricted only in forward/ right direction. Once it moves f ...

DHARM 172 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE 7.2.2 Representation of a DFA Obviously, A Deterministic Finite State Auto ...

DHARM INTRODUCTION TO LANGUAGES AND FINITE AUTOMATA 173 Example 7.2. A Deterministic Finite Automata M = (Q, Σ, δ, q 0 , F) has ...

DHARM 174 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE q 0 q 1 a a q 2 1 4 (^2) b 3 b Fig. 7.6 If there is a string containing s ...

DHARM INTRODUCTION TO LANGUAGES AND FINITE AUTOMATA 175 For example, following transition function δ (q, a) = p ; has the transi ...

DHARM 176 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE III. Similarly, any string starting with symbol 1 and followed by any numb ...

DHARM INTRODUCTION TO LANGUAGES AND FINITE AUTOMATA 177 Example 7.5. Give a DFA that accepts the language over alphabet a and th ...

DHARM 178 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE Let automata M is in state q, after reading the string x (tape cells entri ...

DHARM INTRODUCTION TO LANGUAGES AND FINITE AUTOMATA 179 a M q M p Þ ............y............ a ............y............ Here δ ...

DHARM 180 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE State Input symbol a q 1 q q q 0 3 2 q q q q 0 1 2 3 b q q q q 3 2 1 1 Fig ...

DHARM INTRODUCTION TO LANGUAGES AND FINITE AUTOMATA 181 where LM contains those set of strings that are accepted by automaton M, ...

DHARM 182 MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE l More state transitions means, there is the possibility of two/more trans ...

DHARM INTRODUCTION TO LANGUAGES AND FINITE AUTOMATA 183 Thus, δ-head is the transition function which is a mapping of a state (∈ ...