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

Decision problems, In Exercise 9 you showed that the recognition problem an...

In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems

Algorithm for the universal recognition problem, Sketch an algorithm for th...

Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi

Exhaustive search, A problem is said to be unsolvable if no algorithm can s...

A problem is said to be unsolvable if no algorithm can solve it. The problem is said to be undecidable if it is a decision problem and no algorithm can decide it. It should be note

Pushdown automator, draw pda for l={an,bm,an/m,n>=0} n is in superscript

draw pda for l={an,bm,an/m,n>=0} n is in superscript

Positiveness problem - decision problems, For example, the question of whet...

For example, the question of whether a given regular language is positive (does not include the empty string) is algorithmically decidable. "Positiveness Problem". Note that

Transition and path functions, When an FSA is deterministic the set of trip...

When an FSA is deterministic the set of triples encoding its edges represents a relation that is functional in its ?rst and third components: for every q and σ there is exactly one

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.

Automaton for finite languages, We can then specify any language in the cla...

We can then specify any language in the class of languages by specifying a particular automaton in the class of automata. We do that by specifying values for the parameters of the

Closure properties to prove regularity, The fact that regular languages are...

The fact that regular languages are closed under Boolean operations simpli?es the process of establishing regularity of languages; in essence we can augment the regular operations

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