Decision Properties of Languages

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SUMMARY

The discussion centers on the decision properties of formal languages, specifically Regular Languages (RL), Deterministic Context-Free Languages (DCFL), Context-Free Languages (CFL), Context-Sensitive Languages (CSL), and Recursively Enumerable Languages (RE). A user created a table to clarify the decidability of various properties, including membership, emptiness, infiniteness, equality, and subset relations. The community seeks to verify the accuracy of the table and expand on the acronyms used. Key concepts such as "Is L = ∅?" and the meanings of L1 and L2 are also discussed.

PREREQUISITES
  • Understanding of formal languages and automata theory
  • Familiarity with decidability concepts in computational theory
  • Knowledge of language classifications: Regular, Context-Free, Context-Sensitive, and Recursively Enumerable
  • Basic understanding of formal proofs and logical reasoning
NEXT STEPS
  • Research the properties of Regular Languages and their decision problems
  • Study Deterministic Context-Free Languages and their decidability
  • Explore Context-Free Languages and the implications of the Pumping Lemma
  • Investigate Recursively Enumerable Languages and their relationship to Turing machines
USEFUL FOR

Students and professionals in computer science, particularly those focusing on theoretical computer science, formal language theory, and automata. This discussion is beneficial for anyone looking to deepen their understanding of language decision properties and their implications in computational theory.

22990atinesh said:
I'd trouble remembering decision properties of languages like Regular, CFL, RE, etc. So I made a table of it. Are all the entries of table correct or has some errors

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Decision_Property.jpg
I don't think that we have much expertise in this somewhat esoteric area, which is probably why no one has responded.

You could help us out, though, but expanding the acronyms in your table.
RL = ?
DCFL = ?
CFL = ? (context-free language?)
CSL = ?
RE = ?

What does "Is L = ##\Phi ?## mean?
What do the other columns in the table mean?
What are L1 and L2?
 
Last edited by a moderator:
Mark44 said:
I don't think that we have much expertise in this somewhat esoteric area, which is probably why no one has responded.

You could help us out, though, but expanding the acronyms in your table.
RL = ?
DCFL = ?
CFL = ? (context-free language?)
CSL = ?
RE = ?

What does "Is L = ##\Phi ?## mean?
What do the other columns in the table mean?
What are L1 and L2?
Here
RL=Regular Languages
DCFL=Deterministic Context Free Languages
CFL=Context Free Languages
CSL=Context Sensitive Languages
RE=Recursively Enumerable Languages

##1^{st}## Column "Membership" corresponding to a particular row says that, is it decidable that a given string belong to a given language.

##2^{nd}## Column "##L=\phi##" corresponding to a particular row says that, is it decidable that a given language empty or not "i.e Emptiness Test".

##3^{rd}## Column "##L=\sum##*" corresponding to a particular row says that, is it decidable that a given language infinite.

##4^{th}## Column "Is ##L_1=L_2##" corresponding to a particular row says that, is it decidable that a given languages ##L_1, L_2## are equal.

##5^{th}## Column "Is ##L_1 \subset L_2##" corresponding to a particular row says, is it decidable that a given language ##L_1## a subset of another given language ##L_2##.
 
Thank you. Your question deals with things I don't know much about, but maybe the clarifications will help others to provide you with some insight.
 

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