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De?nition (Instantaneous Description) (for both DFAs and NFAs)
An instantaneous description of A = (Q,Σ, δ, q0, F), either a DFA or an NFA, is a pair hq,wi ∈ Q×Σ*, where q the current state and w is the portion of the input under and to the right of the read head.
The directly computes relation is also the same.
De?nition (Directly Computes Relation) (for both DFAs and NFAs without ε-transitions).
Note that while this is de?ned identically for both DFAs and NFAs, in the case of NFAs it is no longer even partial functional; an ID may well have many successors. Moreover, it is no longer true that the only IDs without successors are those in which w = ε. The effect of this is that the transition function (δ(q, σ)) as we de?ned it earlier is no longer total or even functional: there may be some q and σ for which δ(q, σ) is not de?ned (in notation: δ(q, σ)↑) and there may be some q and σ for which there are multiple states which could be the value of δ(q, σ). We can accommodate both of these possibilities by taking the transition function for NFAs to be a function returning a set of states.
proof ogdens lemma .with example i am not able to undestand the meaning of distinguished position .
State & prove pumping lemma for regular set. Show that for the language L={ap |p is a prime} is not regular
Explain the Chomsky's classification of grammar
The fact that the Recognition Problem is decidable gives us another algorithm for deciding Emptiness. The pumping lemma tells us that if every string x ∈ L(A) which has length grea
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advantaeges of single factor trade
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
The initial ID of the automaton given in Figure 3, running on input ‘aabbba' is (A, aabbba) The ID after the ?rst three transitions of the computation is (F, bba) The p
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
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
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