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A common approach in solving problems is to transform them to different problems, solve the new ones, and derive the solutions for the original problems from those for the new ones. This approach is helpful when the new problems are simpler to solve, or when they usually have known algorithms for solving them. A similar approach is also very useful in the classification of problems according to their complexity.
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.
Computer has a single LIFO stack containing ?xed precision unsigned integers (so each integer is subject to over?ow problems) but which has unbounded depth (so the stack itself nev
Applying the pumping lemma is not fundamentally di?erent than applying (general) su?x substitution closure or the non-counting property. The pumping lemma is a little more complica
These assumptions hold for addition, for instance. Every instance of addition has a unique solution. Each instance is a pair of numbers and the possible solutions include any third
. On July 1, 2010, Harris Co. issued 6,000 bonds at $1,000 each. The bonds paid interest semiannually at 5%. The bonds had a term of 20 years. At the time of issuance, the market r
The fact that SL 2 is closed under intersection but not under union implies that it is not closed under complement since, by DeMorgan's Theorem L 1 ∩ L 2 = We know that
De?nition Instantaneous Description of an FSA: An instantaneous description (ID) of a FSA A = (Q,Σ, T, q 0 , F) is a pair (q,w) ∈ Q×Σ* , where q the current state and w is the p
Theorem (Myhill-Nerode) A language L ⊆ Σ is recognizable iff ≡L partitions Σ* into ?nitely many Nerode equivalence classes. Proof: For the "only if" direction (that every recogn
De?nition (Instantaneous Description) (for both DFAs and NFAs) An instantaneous description of A = (Q,Σ, δ, q 0 , F) , either a DFA or an NFA, is a pair h q ,w i ∈ Q×Σ*, where
Application of the general suffix substitution closure theorem is slightly more complicated than application of the specific k-local versions. In the specific versions, all we had
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