## 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.

#### REGULAR GRAMMAR, Find the Regular Grammar for the following Regular Express...

Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.

#### Intelligent computing, unification algorithm

unification algorithm

#### Myhill-nerode theorem, This close relationship between the SL2 languages an...

This close relationship between the SL2 languages and the recognizable languages lets us use some of what we know about SL 2 to discover properties of the recognizable languages.

#### Example of finite state automaton, The initial ID of the automaton given in...

The initial ID of the automaton given in Figure 3, running on input ‘aabbba' is (A, aabbba) The ID after the ?rst three transitions of the computation is (F, bba) The p

#### Kleene closure, So we have that every language that can be constructed from...

So we have that every language that can be constructed from SL languages using Boolean operations and concatenation (that is, every language in LTO) is recognizable but there are r

#### Complement - operations on languages, The fact that SL 2 is closed under i...

The fact that SL 2 is closed under intersection but not under union implies that it is not closed under complement since, by DeMorgan's Theorem L 1 ∩ L 2 = We know that

#### 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

#### Binary form and chomsky normal form, Normal forms are important because the...

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

#### Kleenes theorem, All that distinguishes the de?nition of the class of Regul...

All that distinguishes the de?nition of the class of Regular languages from that of the class of Star-Free languages is that the former is closed under Kleene closure while the lat

#### Algorithm, What is the Best way to write algorithm and construct flow chart...

What is the Best way to write algorithm and construct flow chart? What is Computer? How to construct web page and Designe it?  