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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.
Design a Mealy FSM with the input A and an output Z. If 10101 shows up on A, then in same cycle 1 must show up on Z, else Z is 0.
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.
Provide DFA's accepting the following languages over alphabet {0,1}. Set of all strings that, when interpreted as the binary integer, is a multiple of 5.
How many equivalence classes does this relation have and what are they? Use these equivalence classes to construct the minimal DFA for the language.
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.
Express the given correctness properties in LTL. Defne propositions/variables to model the events mentioned in the question. If a parent process calls the blocking waitpid() system call then it is blocked until child process terminates.
Describe the difference between a Deterministic Finite Automata and Non-Deterministic Finite Automata. In general, which one is expected to have less number of states ?
There are four processes that are going to share nine tape drives. Their current and maximum number of allocation numbers. Is system in a safe state? Explain why or why not?
Create and implement a lexical analyzer for C-- as follows: Write the set of token types to be returned by lexical analyzer. Explain regular expressions for this set of token types.
Suppose f is a function that returns the result of reversing the string of symbols given as its input, and g. What ambiguity exists in the statement x?
Write implememnt finite state machine which recognzes input string according to following rules. First character should be either letter(upper or lower case.)
Write down a structural induction principle for the PlayTree free type
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