Finiteness of languages is decidable, Theory of Computation

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.

Posted Date: 3/21/2013 6:04:45 AM | Location : United States







Related Discussions:- Finiteness of languages is decidable, Assignment Help, Ask Question on Finiteness of languages is decidable, Get Answer, Expert's Help, Finiteness of languages is decidable Discussions

Write discussion on Finiteness of languages is decidable
Your posts are moderated
Related Questions
Given any NFA A, we will construct a regular expression denoting L(A) by means of an expression graph, a generalization of NFA transition graphs in which the edges are labeled with

Computations are deliberate for processing information. Computability theory was discovered in the 1930s, and extended in the 1950s and 1960s. Its basic ideas have become part of

design a tuning machine for penidrome

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




When we say "solved algorithmically" we are not asking about a speci?c programming language, in fact one of the theorems in computability is that essentially all reasonable program

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

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