1. Let L be any language. We define I = {reverse(x)/x 2 L). (For example, if L = {b, baa, aaabb, aabba}, then L = {b, aab, bbaaa, abbaa}.) (a) Prove that for any language L, if there is an FA that accepts L, then there is a TG that accepts L'. (b) Prove that for any language L, if there is a TG that accepts L, then there is a TG that accepts Lº.

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
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1. Let L be any language. We define L = {reverse(x)/x 2 L}. (For example, if
L = {b, baa, aaabb, aabba), then I = {b, aab, bbaaa, abbaa}.)
(a) Prove that for any language L, if there is an FA that accepts L, then there is a
TG that accepts L'.
(b) Prove that for any language L, if there is a TG that accepts L, then there is a TG
that accepts L'.
Transcribed Image Text:1. Let L be any language. We define L = {reverse(x)/x 2 L}. (For example, if L = {b, baa, aaabb, aabba), then I = {b, aab, bbaaa, abbaa}.) (a) Prove that for any language L, if there is an FA that accepts L, then there is a TG that accepts L'. (b) Prove that for any language L, if there is a TG that accepts L, then there is a TG that accepts L'.
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