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

Transition graphs, We represented SLk automata as Myhill graphs, directed g...

We represented SLk automata as Myhill graphs, directed graphs in which the nodes were labeled with (k-1)-factors of alphabet symbols (along with a node labeled ‘?' and one labeled

#title., distinguish between histogram and historigram

distinguish between histogram and historigram

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.

Decision Theroy, spam messages h= 98%, m= 90%, l= 80% non spam h=12%, m = 8...

spam messages h= 98%, m= 90%, l= 80% non spam h=12%, m = 8%, l= 5% The organization estimates that 75% of all messages it receives are spam messages. If the cost of not blocking a

Computations of sl automata, We will specify a computation of one of these ...

We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea

Concatenation, We saw earlier that LT is not closed under concatenation. If...

We saw earlier that LT is not closed under concatenation. If we think in terms of the LT graphs, recognizing the concatenation of LT languages would seem to require knowing, while

Tuning machine, design a tuning machine for penidrome

design a tuning machine for penidrome

Regular languages, LTO was the closure of LT under concatenation and Boolea...

LTO was the closure of LT under concatenation and Boolean operations which turned out to be identical to SF, the closure of the ?nite languages under union, concatenation and compl

#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.

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