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As de?ned the powerset construction builds a DFA with many states that can never be reached from Q′0. Since they cannot be reached from Q′0 there is no path from Q′0 to a state in F′ which passes through them and they can be deleted from the automaton without changing the language it accepts. In practice it is much easier to build Q′ as needed, only including those state sets that actually are needed.
To see how this works, lets carry out an example. For maximum generality, let's start with the NFA with ε-transitions given above, repeated here:
Because it is simpler to write the transition function (δ) out as a table than it is to write out the transition relation (T) as a set of tuples, we will work with the δ representation. When given a transition graph of an NFA with ε-transitions like this there are 6 steps required to reduce it to a DFA:
1. Write out the transition function and set of ?nal states of the NFA.
2. Convert it to an NFA without ε-transitions.
(a) Compute the ε-Closure of each state in the NFA.
(b) Compute the transition function of the equivalent NFA without ε-transitions.
(c) Compute the set of ?nal states of the equivalent NFA without ε- transitions.
To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the
This close relationship between the SL2 languages and the recognizable languages lets us use some of what we know about SL 2 to discover properties of the recognizable languages.
We got the class LT by taking the class SL and closing it under Boolean operations. We have observed that LT ⊆ Recog, so certainly any Boolean combination of LT languages will also
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.
How useful is production function in production planning?
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We developed the idea of FSA by generalizing LTk transition graphs. Not surprisingly, then, every LTk transition graph is also the transition graph of a FSA (in fact a DFA)-the one
Computer has a single unbounded precision counter which you can only increment, decrement and test for zero. (You may assume that it is initially zero or you may include an explici
Give the Myhill graph of your automaton. (You may use a single node to represent the entire set of symbols of the English alphabet, another to represent the entire set of decima
The objective of the remainder of this assignment is to get you thinking about the problem of recognizing strings given various restrictions to your model of computation. We will w
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