Formal languages and grammar, Theory of Computation

Assignment Help:

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.


Related Discussions:- Formal languages and grammar

Strictly 2-local languages, The fundamental idea of strictly local language...

The fundamental idea of strictly local languages is that they are speci?ed solely in terms of the blocks of consecutive symbols that occur in a word. We'll start by considering lan

Non deterministic finite state automaton, Automaton (NFA) (with ε-transitio...

Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q 0 , F i where Q, Σ, q 0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}). We must also modify the de?nitions of th

Give a strictly 2-local automaton, Let L 3 = {a i bc j | i, j ≥ 0}. Give ...

Let L 3 = {a i bc j | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L 3 . Use the construction of the proof to extend the automaton to one that recognizes L 3 . Gi

Computer achitecture, what is a bus and draw a single bus structure

what is a bus and draw a single bus structure

Local suffix substitution closure, The k-local Myhill graphs provide an eas...

The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages. Lemma (k-Local Suffix Substitution Clo

Boolean operations - class of recognizable languages, Theorem The class of ...

Theorem The class of recognizable languages is closed under Boolean operations. The construction of the proof of Lemma 3 gives us a DFA that keeps track of whether or not a give

Strictly 2 - local automata, We will assume that the string has been augmen...

We will assume that the string has been augmented by marking the beginning and the end with the symbols ‘?' and ‘?' respectively and that these symbols do not occur in the input al

Path function of a nfa, The path function δ : Q × Σ*→ P(Q) is the extension...

The path function δ : Q × Σ*→ P(Q) is the extension of δ to strings: Again, this just says that to ?nd the set of states reachable by a path labeled w from a state q in an

Automata and compiler, Automata and Compiler (1) [25 marks] Let N be the...

Automata and Compiler (1) [25 marks] Let N be the last two digits of your student number. Design a finite automaton that accepts the language of strings that end with the last f

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd