(2) {w € [0, 1]* : w corresponds to the binary encoding, without leading O's, of natural numbers that are powers of 4} Testing strings: €, 0, 1, 01, 10, 11, 100, 101, 1000, 1010, 10000 The accepted strings are:

(2) {w € [0, 1]* : w corresponds to the binary encoding, without leading O's, of natural numbers that are powers of 4} Testing strings: €, 0, 1, 01, 10, 11, 100, 101, 1000, 1010, 10000 The accepted strings are:

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

For each question, build a deterministic FSM for the given language.

(2) {w € {0, 1}* : w corresponds to the binary encoding, without leading O's, of natural numbers that
are powers of 4}
Testing strings: €, 0, 1, 01, 10, 11, 100, 101, 1000, 1010, 10000
The accepted strings are:
L
U
E
1
01
11
100
101
1000
1010
10000

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9. Give a context-free grammar for a context-free language. Let L be the language of all algebraic expres- sions where The operations are addition, subtraction and multiplication, there are parentheses, and the only variables are x, y, and z. Give an unambiguous CF grammar for L, where addition and subtrac- tion have equal precedence, multiplication has precedence over addition and subtraction, and all three operations are left associative.
For each of the following languages L, state whether or not L is regular. Prove your answer. You can prove it by finding a regular expression that describes the language or by finding an FSM that recognizes it. {w {a, b, c}* : w contains at least two occurrences of the substring ac or w contains no more than 3 c’s}.
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