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303sol1 - 1 CSE303 Spring 2010 Solutions to Homework 1...

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1 CSE303, Spring 2010 Solutions to Homework 1 Section 1.1 3 (c). False. Counterexample : Let A = { ab,cd } . Then, we have A R = { ba,dc } , and x = abdc ( A A R ) * . On the other hand, any nonempty string in A * must end with b or d , and any nonempty string in ( A * ) R must start with b or d . Thus x / A * ( A * ) R . 6 . 0 13 . Section 1.2 3 (a). (0+1) * 0(0+1) 4 ; or, more formally, (0+1) * 0(0+1)(0+1)(0+1)(0+1). 3 (c). In general, we divide a string w into blocks of 0’s and 1’s like 0 · · · 01 · · · 10 · · · 01 · · · 1 · · · Then, a string w in the set under considertation has the property that each block has length either 1 or 2. So, we may express it by (0 + 00)(1 + 11)(0 + 00)(1 + 11) · · · In other words, each substring of
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