Formal languages and grammar, Theory of Computation

The universe of strings is a very useful medium for the representation of information as long as there exists a function that provides the interpretation for the information carried by the strings. An interpretation is just the contrary of the mapping that a representation provides, that is, an interpretation is a function g from Σ* to D for some alphabet Σ and some set D. The string 111, for instance, can be interpreted as the number one hundred and eleven represented by a decimal string, as the number seven represented by a binary string, and as the number three represented by a unary string.

In general, if Σ is an alphabet and L is a subset of Σ*, then L is said to be a language over Σ, or simply a language if Σ is understood. Each element of L is said to be a sentence or a word or a stringof the language.

"Example- {0, 11, 001}, {ε, 10}, and {0, 1}* are subsets of {0, 1}*, and so they are languages over the alphabet {0, 1}.

The empty set Ø and the set {ε} are languages over every alphabet. Ø is a language that contains no string. {ε} is a language that contains just the empty string.

The union of two languages L1 and L2, denoted L1 U  L2, refers to the language that consists of all the strings that are either in L1 or in L2, that is, to { x | x is in L1 or x is in L2 }. The intersection of L1 and L2, denoted L1 ∩  L2, refers to the language that consists of all the strings that are both in L1 and L2, that is, to {x | x is in L1 and in L2}. The complementation of a language L over Σ, or just the complementation of L when Σ is understood, denoted L, refers to the language that consists of all the strings over Σ that are not in L, that is, to { x | x is in Σ* but not in L }".

A set of real values for a problem is called an instance of the problem. So a problem, specifies what an instance is, i.e., what is the input, problem, or output and how the solution is related to the input.

Posted Date: 3/18/2013 1:09:01 AM | Location : United States







Related Discussions:- Formal languages and grammar, Assignment Help, Ask Question on Formal languages and grammar, Get Answer, Expert's Help, Formal languages and grammar Discussions

Write discussion on Formal languages and grammar
Your posts are moderated
Related Questions
Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about

automata of atm machine

what exactly is this and how is it implemented and how to prove its correctness, completeness...


The fact that the Recognition Problem is decidable gives us another algorithm for deciding Emptiness. The pumping lemma tells us that if every string x ∈ L(A) which has length grea

We represented SLk automata as Myhill graphs, directed graphs in which the nodes were labeled with (k-1)-factors of alphabet symbols (along with a node labeled ‘?' and one labeled

Normal forms are important because they give us a 'standard' way of rewriting and allow us to compare two apparently different grammars G1  and G2. The two grammars can be shown to

Prove that Language is non regular TRailing count={aa ba aaaa abaa baaa bbaa aaaaaa aabaaa abaaaa..... 1) Pumping Lemma 2)Myhill nerode

State & prove pumping lemma for regular set. Show that for the language L={ap |p is a prime} is not regular

What is the purpose of GDTR?