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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.
Theorem The class of recognizable languages is closed under Boolean operations. The construction of the proof of Lemma 3 gives us a DFA that keeps track of whether or not a give
A.(A+C)=A
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
Perfect shuffle permutation
When we study computability we are studying problems in an abstract sense. For example, addition is the problem of, having been given two numbers, returning a third number that is
Let there L1 and L2 . We show that L1 ∩ L2 is CFG . Let M1 be a decider for L1 and M2 be a decider for L2 . Consider a 2-tape TM M: "On input x: 1. copy x on the second
State & prove pumping lemma for regular set. Show that for the language L={ap |p is a prime} is not regular
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
One might assume that non-closure under concatenation would imply non closure under both Kleene- and positive closure, since the concatenation of a language with itself is included
Find a regular expression for the regular language L={w | w is decimal notation for an integer that is a multiple of 4}
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