Material covered in class - accepted of length between n...

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Monday Sept 14 Conversion of finite automaton to regular expression Conversion of regular expression to finite automaton Closure properties for regular sets 1) union, concatenation, and star 2) intersection and complement 3) set difference 4) reversal of strings machine construction Wednesday Sept 16 definitions of homomorphisms and inverse homomorphisms the class of regular sets is closed under homomorphisms and inverse homomorphisms Friday Sept 18 working with homomorphisms and intersection with regular sets Monday Sept 21 pumping lemma for regular sets proving some sets not regular Wednesday Sept 23 decision problems for regular expressions, NFAs and DFAs: membership, emptiness, finiteness, universality (whether L(M)=Sigma*). I showed them - that there is a string accepted iff there is one accepted of length at most n, the number of states; - that there are infinitely many strings accepted iff there is one
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Unformatted text preview: accepted of length between n and 2n;- that for NFAs, there is an NFA that is not universal, but the shortest string rejected is exponential in the number of states. We discussed the representation of FAs as labeled directed graphs and DFS and BFS as techniques for answering these questions. I also proved that a set over a single-letter alphabet is regular iff it is ultimately periodic. I also mentioned (but did not prove) that over any alphabet, the number of strings of each length in a regular set satisfy a linear recurrence. There was a little time left at the end, so I showed them that the set of first halves of strings in a regular set is regular. Monday Oct 5 definition of pushdown automata, acceptance by finalstate and by empty store equivalence of acceptance by final state and empty store acceptance of context-free language by pushdown automaton...
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