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# assign1 - with O n states 4 Show that L = x x | x ∈ 1 is...

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University of California, Santa Barbara CS 220 Winter 2011: Assignment 1, Due: January 20 Notation: 1DFA = one-way deterministic fnite automaton, 2DFA = two-way deterministic fnite au- tomaton, 1DPDA = one-way deterministic pushdown automaton, 1NPDA = one-way nondeterministic pushdown automaton, 2DPDA = two-way deterministic pushdown automaton, 2NPDA = two-way nondeterministic pushdown asutomaton. 1. Show that the set L = { x | x is a nonnull binary number with leading bit (the frst bit) the most signifcant bit, and x is divisible by 5 } is a regular set (i.e., accepted by a 1DFA). 2. Suppose in L o± problem 1, the leading bit o± x is the least signifcant bit. Is L a regular set? Why? 3. Let n 1, and L n = { x # x | x ∈ { 0 , 1 } + , | x | = n } . Show that L n can be accepted by a 2DFA
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Unformatted text preview: with O ( n ) states. 4. Show that L = { x # x | x ∈ { , 1 } + } is not a regular set. 5. Describe (in English) a 1DPDA that accepts the language L = set o± binary strings such that the number o± 0’s = number o± 1’s. 6. Describe (in English) a 1NPDA that accepts the language L = { x # y | x,y ∈ { , 1 } * ,x n = y } . (It can be shown that this language cannot be accepted by a 1DPDA.) 7. Describe in English a 2DPDA accepting the language L = { xx r | x ∈ { , 1 } * } , where x r denotes the reverse o± x . (This language cannot be accepted by a 1DPDA.) 8. Describe (in English) a 2DPDA accepting the language L = { a n b 2 n | n > } ....
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## This note was uploaded on 01/28/2012 for the course CS 220 taught by Professor Ibarra,o during the Winter '08 term at UCSB.

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