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Let the following "gold-digger problem" (GDP). You are given the map of territory consisting of set of towns connected by trails. Each trail (u, v) connecting towns u and v is labeled with dollar value w(u, v), which is value of gold you will find along that trail. You can traverse trail as frequently as you want, but you only get value of trail the first time you traverse it; subsequent traversals have no value. Each town v has lodging cost c(v), which you pay each time you enter the town.
Expedition is cyclic path which starts and ends at given town. Expedition has profit k if total value of gold found, minus cost of all the town visits, is k. Goal is to find expedition of maximum profit. Either show that there exists polynomial-time algorithm for GDP, or show that corresponding decision problem is NP-complete. If you want to illustrate that problem is hard, you may decrease from any of: SAT, 3-CNF-SAT, CLIQUE, VERTEX-COVER, SUBSET-SUM, PARTITION, HAM-CYCLE, TSP.
If you perform reduction in proof of Rice's theorem for special case of property P: "infinite language", does this reduction also show that language P L = { | N is Turing machine.
Rewrite the productions for each of the following nonterminals as right regular grammars: Identifier, Float. Show the moves made using the DFSA for identifiers in accepting.
Create and DFA or LR(0) items for this grammar. Is this grammar LR(0) parsing table? If not, explain LR(0) conflict. If so create LR(0) parsing table.
What does the term solvable mean to you? What does it mean to say that "you solved a problem"? Determine examples of problems for which you believe there are no solutions.
Show that the language F = {a^i b^j c^k | i, j, k greater than or equal to 0 and if i = 1 then j = k} is not regular. Show, however, that it satisfies the statement of the pumping lemma
Write down the algorithm for finding useless/productive nonterminals. Describe how this gives you the algorithm for whether language generated by grammar is empty.
Think about the following Turing-machine model, A tape that is infinitely long in both directions and is divided into cells; at any given step, each cell either is blank or contains a 1.
Show that the following identities hold for regular expressions over any alphabet: epsilon + R*R = R*. These should be done by interpreting the regular expressions as languages.
Use undecidability of ALLCFG to illustrate that following problem is also undecidable: Given PDA M1 and FA M2, is L(M1) = L(M2)?
Discuss the impact of Moore's law on data center costs on such things as servers and communications equipment. List at least 3 steps or recommendations your data center can take to offset some or all of the effect of Moore's law.
Write a program would read two numbers and then print all numbers between the first and the second, inclusive. Design unambiguous grammar to parse expressions
Write down the set of token types to be returned by your lexical analyzer. Describe regular expressions for this set of token types.
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