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The path function δ : Q × Σ* → P(Q) is the extension of δ to strings:
This just says that the path labeled ε from any given state q goes only to q itself (or rather never leaves q) and that to ?nd the set of states reached by paths labeled wσ from q one ?rst ?nds all the states q′ reached by paths labeled w from q and then takes the set of all the states reached by an edge labeled σ from any of those q′.
We will still accept a string w i? there is a path labeled w leading from the initial state to a ?nal state, but now there may be many paths labeled w from the initial state, some of which reach ?nal states and some of which do not. When thinking in terms of the path function, we need to modify the de?nition of the language accepted by A so it includes every string for which at least one path ends at a ?nal state.
design a turing machine that accepts the language which consists of even number of zero''s and even number of one''s?
The computation of an SL 2 automaton A = ( Σ, T) on a string w is the maximal sequence of IDs in which each sequential pair of IDs is related by |- A and which starts with the in
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 Clo
Theorem The class of ?nite languages is a proper subclass of SL. Note that the class of ?nite languages is closed under union and concatenation but SL is not closed under either. N
write short notes on decidable and solvable problem
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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
examples of decidable problems
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