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Sketch an algorithm for the universal recognition problem for SL2. This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwise. Assume the automaton is given just as a sequence of pairs of symbols and that the automaton and string are both over the same language. Give an argument justifying the correctness of your algorithm.
a) Let n be the pumping lemma constant. Then if L is regular, PL implies that s can be decomposed into xyz, |y| > 0, |xy| ≤n, such that xy i z is in L for all i ≥0. Since the le
What is the purpose of GDTR?
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
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Our primary concern is to obtain a clear characterization of which languages are recognizable by strictly local automata and which aren't. The view of SL2 automata as generators le
Exercise Show, using Suffix Substitution Closure, that L 3 . L 3 ∈ SL 2 . Explain how it can be the case that L 3 . L 3 ∈ SL 2 , while L 3 . L 3 ⊆ L + 3 and L + 3 ∈ SL
Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con
how many pendulum swings will it take to walk across the classroom?
S-->AAA|B A-->aA|B B-->epsilon
You are required to design a system that controls the speed of a fan's rotation. The speed at which the fan rotates is determined by the ambient temperature, i.e. as the temperatur
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