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The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages.
Lemma (k-Local Suffix Substitution Closure) If L is a strictly k-local language then for all strings u1, v1, u2, and v2 in Σ* and all strings x in Σk-1 :
u1xv1 ∈ L and u2xv2 ∈ L ⇒ u1xv2 ∈ L.
The justi?cation is essentially identical to that of our original suffix substitution closure lemma. If L ∈ SLk then it is recognized by an SLk automaton. In the k-local Myhill graph of that automaton, any path from ‘?' to the vertex labeled x can be put together with any path from that vertex to ‘?' to produce a path that represents a string in L.
Differentiate between DFA and NFA. Convert the following Regular Expression into DFA. (0+1)*(01*+10*)*(0+1)*. Also write a regular grammar for this DFA.
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
how to convert a grammar into GNF
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.
1. An integer is said to be a “continuous factored” if it can be expresses as a product of two or more continuous integers greater than 1. Example of continuous factored integers
Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
Suppose A = (Σ, T) is an SL 2 automaton. Sketch an algorithm for recognizing L(A) by, in essence, implementing the automaton. Your algorithm should work with the particular automa
S-->AAA|B A-->aA|B B-->epsilon
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
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