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

Sketch an algorithm to recognize the language, First model: Computer has a ...

First model: Computer has a ?xed number of bits of storage. You will model this by limiting your program to a single ?xed-precision unsigned integer variable, e.g., a single one-by

Language accepted by a nfa, The language accepted by a NFA A = (Q,Σ, δ, q 0...

The language accepted by a NFA A = (Q,Σ, δ, q 0 , F) is NFAs correspond to a kind of parallelism in the automata. We can think of the same basic model of automaton: an inpu

Vogel Approximation Method(VAM, how to write program Minimum Cost Calculat...

how to write program Minimum Cost Calculation - Vogel Approximation Method(VAM

Strictly local languages, While the SL 2 languages include some surprising...

While the SL 2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless

Turing machine, prove following function is turing computable? f(m)={m-2,if...

prove following function is turing computable? f(m)={m-2,if m>2, {1,if

Mapping reducibility, Can you say that B is decidable? If you somehow know...

Can you say that B is decidable? If you somehow know that A is decidable, what can you say about B?

Qbasic, Ask question #Minimum 100 words accepte

Ask question #Minimum 100 words accepte

Overview of dfa, Explain Theory of Computation ,Overview of DFA,NFA, CFG, P...

Explain Theory of Computation ,Overview of DFA,NFA, CFG, PDA, Turing Machine, Regular Language, Context Free Language, Pumping Lemma, Context Sensitive Language, Chomsky Normal For

Formal language theory, This was one of the ?rst substantial theorems of Fo...

This was one of the ?rst substantial theorems of Formal Language Theory. It's maybe not too surprising to us, as we have already seen a similar equivalence between LTO and SF. But

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