Myhill graphs, Theory of Computation

Assignment Help:

Another way of representing a strictly 2-local automaton is with a Myhill graph. These are directed graphs in which the vertices are labeled with symbols from the input alphabet of the automaton (plus {x,x}), with an edge from a vertex labeled σ1 to a vertex labeled σ2 ix the pair σ1σ2 is included in T. (Note that if we interpret the strings in T as pairs of symbols, then the Myhill graph of A = (Σ, T) is just G = (Σ+, T).) The Myhill graph of the automaton of Figure 2 is given in Figure. For consistency with the graphs we will use later, the entry point to the graph is indicated with an edge "from nowhere" and the exit point is indicated by circling it.

The key property of Myhill graphs is that every path through the graph from the ‘x' node to the ‘x' node corresponds to a computation of the automaton and every computation of the automaton corresponds to such a path. So we can reason about the strings that are accepted by the automaton by reasoning about the sequences of nodes that occur on paths from ‘x' to ‘x'. (For simplicity, we will refer to paths from ‘x' to ‘x' as "paths through the graph".)

For example, the shortest strings in the language recognized by the automaton will those labeling the shortest paths through the graph, which is to say, the acyclic paths from ‘x' to ‘x'. In this particular case, these are the paths (x,x) and (x, a, b,x), corresponding to the strings ε and ab.


Related Discussions:- Myhill graphs

Brain game, If the first three words are the boys down,what are the last th...

If the first three words are the boys down,what are the last three words??

Mealy machine, Construct a Mealy machine that can output EVEN or ODD Accord...

Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.

Algorithm, What is the Best way to write algorithm and construct flow chart...

What is the Best way to write algorithm and construct flow chart? What is Computer? How to construct web page and Designe it?

what is a turing machine, A Turing machine is a theoretical computing mach...

A Turing machine is a theoretical computing machine made-up by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine having of a line of

Distinguish between mealy and moore machine, Distinguish between Mealy and ...

Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1's encountered is even or odd.

Ogdens lemma, proof ogdens lemma .with example i am not able to undestand ...

proof ogdens lemma .with example i am not able to undestand the meaning of distinguished position .

Turing machine, Design a turing machine to compute x + y (x,y > 0) with x a...

Design a turing machine to compute x + y (x,y > 0) with x an y in unary, seperated by a # (descrition and genereal idea is needed ... no need for all TM moves)

Formal languages and grammar, The universe of strings is a very useful medi...

The universe of strings is a very useful medium for the representation of information as long as there exists a function that provides the interpretation for the information carrie

DFA, designing DFA

designing DFA

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