Generalization of the interpretation of local automata, Theory of Computation

Assignment Help:

The generalization of the interpretation of strictly local automata as generators is similar, in some respects, to the generalization of Myhill graphs. Again, the set of possible symbols that may appear at any given point depends only on the previous k - 1 symbols. Here this is realized by taking the factors to be tiles and allowing a tile labeled σ2, . . . , σk, σk+1 to be placed over the last k-1 symbols of a tile labeled σ1, σ2, . . . , σk. Again, the process starts with a tile labeled 'x  ' and ends when a tile labeled '  x' is placed. Strings of length less than k - 1 are generated with a single tile.

Note that there is a sense in which this mechanism is the dual of the k-local Myhill graphs. In the graphs, the vertices are labeled with the pre?x of the factors in the automaton and the edges are labeled with the last symbol of the label of the node the edge is incident to. It is those edge labels that call out the string being recognized and the initial k - 1 positions of the string label the edges incident from ‘x'. Here it is the exposed symbols that call out the string being generated and these are the initial symbols of the tiles. And the ?nal k -1 symbols of the string are the symbols labeling the last tile, the one labeled with ‘x'.


Related Discussions:- Generalization of the interpretation of local automata

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

Pumping lemma constant, a) Let n be the pumping lemma constant. Then if L i...

a) Let n be the pumping lemma constant. Then if L is regular, PL implies that s can be decomposed into xyz, |y| > 0, |xy| ≤n, such that xy i z is in L for all i ≥0. Since the le

Numerical integration, what problems are tackled under numerical integratio...

what problems are tackled under numerical integration

#dfa, Give DFA''s accepting the following languages over the alphabet {0,1}...

Give DFA''s accepting the following languages over the alphabet {0,1}: i. The set of all strings beginning with a 1 that, when interpreted as a binary integer, is a multiple of 5.

Strictly local languages, We have now de?ned classes of k-local languages f...

We have now de?ned classes of k-local languages for all k ≥ 2. Together, these classes form the Strictly Local Languages in general. De?nition (Strictly Local Languages) A langu

Operations on strictly local languages, The class of Strictly Local Languag...

The class of Strictly Local Languages (in general) is closed under • intersection but is not closed under • union • complement • concatenation • Kleene- and positive

Mapping reducibility, (c) Can you say that B is decidable? (d) If you someh...

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

Non Regular, Prove that Language is non regular TRailing count={aa ba aaaa...

Prove that Language is non regular TRailing count={aa ba aaaa abaa baaa bbaa aaaaaa aabaaa abaaaa..... 1) Pumping Lemma 2)Myhill nerode

Class of recognizable languages, Proof (sketch): Suppose L 1 and L 2 are ...

Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(

Decision problems of regular languages, We'll close our consideration of re...

We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.

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