Reductions Exercise 31 Suppose L1, L₂ E be two languages. Suppose there exist a computable function f: E → E' such that the following holds: 1. x L₁= f(x) € L₂. Show the following: If L₁, L2 are recognizable languages then L₁ is decidable.

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
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Reductions
Exercise 3
Suppose L₁, L₂ E be two languages. Suppose there exist a computable
function f: E→→ E' such that the following holds:
1. x L₁= f(x) € L₂.
Show the following: If L₁, L2 are recognizable languages then L₁ is decidable.
Transcribed Image Text:Reductions Exercise 3 Suppose L₁, L₂ E be two languages. Suppose there exist a computable function f: E→→ E' such that the following holds: 1. x L₁= f(x) € L₂. Show the following: If L₁, L2 are recognizable languages then L₁ is decidable.
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