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

Myhill graph of the automaton, Exercise:  Give a construction that converts...

Exercise:  Give a construction that converts a strictly 2-local automaton for a language L into one that recognizes the language L r . Justify the correctness of your construction.

Chomsky-schutzenberger, The upper string r ∈ Q+ is the sequence of states v...

The upper string r ∈ Q+ is the sequence of states visited by the automaton as it scans the lower string w ∈ Σ*. We will refer to this string over Q as the run of A on w. The automa

Trees and graphs , Trees and Graphs Overview: The problems for this ...

Trees and Graphs Overview: The problems for this assignment should be written up in a Mircosoft Word document. A scanned hand written file for the diagrams is also fine. Be

Equivalence of nfas and dfas, In general non-determinism, by introducing a ...

In general non-determinism, by introducing a degree of parallelism, may increase the accepting power of a model of computation. But if we subject NFAs to the same sort of analysis

A composable-reset DFA (CR-DFA) is a five-tuple, Question 2 (10 pt): In thi...

Question 2 (10 pt): In this question we look at an extension to DFAs. A composable-reset DFA (CR-DFA) is a five-tuple, (Q,S,d,q0,F) where: – Q is the set of states, – S is the alph

Programming languages, Different types of applications and numerous program...

Different types of applications and numerous programming languages have been developed to make easy the task of writing programs. The assortment of programming languages shows, dif

Assignment, Consider a water bottle vending machine as a finite–state autom...

Consider a water bottle vending machine as a finite–state automaton. This machine is designed to accept coins of Rs. 2 and 5 only. It dispenses a single water bottle as soon as the

Differentiate between dfa and nfa, Differentiate between DFA and NFA. Conve...

Differentiate between DFA and NFA. Convert the following Regular Expression into DFA. (0+1)*(01*+10*)*(0+1)*. Also write a regular grammar for this DFA.

Context free grammar, A context free grammar G = (N, Σ, P, S)  is in binary...

A context free grammar G = (N, Σ, P, S)  is in binary form if for all productions A we have |α| ≤ 2. In addition we say that G is in Chomsky Normaml Form (CNF) if it is in bi

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