Finiteness of languages is decidable, Theory of Computation

Assignment Help:

To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the Myhill graph is acyclic, then no path from x to x can be longer than card(Σ) + 2, since otherwise some node would have to occur at least twice in the path.

The question of finiteness of L(A), then, can be reduced to the question of acyclicity of the corresponding Myhill graph. And we established that there is an algorithm for testing acyclicity of graphs in Algorithms and Data Structures. Our algorithm for deciding finiteness of L(A) just interprets A as a graph and calls the algorithm for deciding acyclicity as a subroutine.


Related Discussions:- Finiteness of languages is decidable

Xx, Ask queyystion #Minimum 100 words accepted#

Ask queyystion #Minimum 100 words accepted#

Turing machine, design a turing machine that accepts the language which con...

design a turing machine that accepts the language which consists of even number of zero''s and even number of one''s?

Non-regular languages, Suppose A = (Q,Σ, T, q 0 , F) is a DFA and that Q = ...

Suppose A = (Q,Σ, T, q 0 , F) is a DFA and that Q = {q 0 , q 1 , . . . , q n-1 } includes n states. Thinking of the automaton in terms of its transition graph, a string x is recogn

First model of computation, Computer has a single unbounded precision count...

Computer has a single unbounded precision counter which you can only increment, decrement and test for zero. (You may assume that it is initially zero or you may include an explici

Computation of a dfa or nfa, Computation of a DFA or NFA without ε-transiti...

Computation of a DFA or NFA without ε-transitions An ID (q 1 ,w 1 ) computes (qn,wn) in A = (Q,Σ, T, q 0 , F) (in zero or more steps) if there is a sequence of IDs (q 1

Synthesis theorem, Kleene called this the Synthesis theorem because his (an...

Kleene called this the Synthesis theorem because his (and your) proof gives an effective procedure for synthesizing an automaton that recognizes the language denoted by any given r

Alphabets - strings and representation, A finite, nonempty ordered set will...

A finite, nonempty ordered set will be called an alphabet if its elements are symbols, or characters. A finite sequence of symbols from a given alphabet will be called a string ove

Java programming, 1. An integer is said to be a “continuous factored” if it...

1. An integer is said to be a “continuous factored” if it can be expresses as a product of two or more continuous integers greater than 1. Example of continuous factored integers

Computation and languages, When we study computability we are studying prob...

When we study computability we are studying problems in an abstract sense. For example, addition is the problem of, having been given two numbers, returning a third number that is

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