Question: 1. Pushdown Automata ( 30 points - 10 each) Give pushdown automata for the following languages. (a) L1={aibjcki,j,kZ0,i+j is odd and i+j>2k} Note that 0

1. Pushdown Automata ( 30 points - 10 each) Give pushdown

1. Pushdown Automata ( 30 points - 10 each) Give pushdown automata for the following languages. (a) L1={aibjcki,j,kZ0,i+j is odd and i+j>2k} Note that 0 is an even number, so strings in this language must have at least one a or one b. (b) L2={ww is a binary string with the same number of occurrences of 00 and 11 as substrings Note that 000 has exactly two substrings equal to 00 . Thus 1100011 is a string in L2. (c) L3={ww=wR,w is odd with 010 as the middle three characters, and w{0,1}}

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1. Who is responsible for resolving this dilemma?

3. What is at stake for you? What are your values? Are there motives that may be persuading you in one direction instead of another?

7. How might you go about testing these assumptions?