U.C. Berkeley — CS172: Automata, Computability and Complexity Practice Midterm 1
Professor Luca Trevisan October 2, 2009
Practice Midterm 1
1. Show that the intersection of infinitely many regular languages may not be regular.
2. Consider the language
L:= {1k#y:k≥1, y ∈ {0,1}∗and ycontains at least k ones }
defined over the alphabet {0,1,#}. Prove or disprove that Lis regular.
3. Consider the language
L:= (1101 ∪11)∗
Give a minimal DFA for Land prove that it is minimal
4. Show that every infinite Turing-recognizable language has an infinite decidable subset.
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