Automata Problems

There are nine problems from the subject Theory of Computation or Automata. I have written three problems in text here for search purposes. Please view the attached image for exact nine Questions. Problem1. Let TSP (Traveling Salesman Problem) be the language {[G],{K}|G is a weighted complete graph with a Hamiltonian cycle of weight at most integer K. Prove the TSP is NP-Complete. Problem 2. Given that the Clique problem, i.e. the problem finding a clique of size k, is NP-Hard (by a reduction from 3-SAT) show that the independent set (IS), the problem of finding an independent set of size l, is NP-Hard. A set of Vertices is independent if there is no edge between any two vertices in the set. Show that there exists a polynomial time reduction from IS to 3-SAT Problem 3. Let C be a language over an alphabet sigma and assume the sysmbol ";" does not belong to sigma. Prove that C is Turing-recognizable if and only if a decidabl language D exists such that C={x|}. Here x;y denotes the concatenation of the word x, the symbol;, and the word y. ## Deliverables 1) Complete and fully-functional working program(s) in executable form as well as complete source code of all work done. 2) Deliverables must be in ready-to-run condition, as follows (depending on the nature of the deliverables): a) For web sites or other server-side deliverables intended to only ever exist in one place in the Buyer's environment--Deliverables must be installed by the Seller in ready-to-run condition in the Buyer's environment. b) For all others including desktop software or software the buyer intends to distribute: A software installation package that will install the software in ready-to-run condition on the platform(s) specified in this bid request. 3) All deliverables will be considered "work made for hire" under U.S. Copyright law. Buyer will receive exclusive and complete copyrights to all work purchased. (No GPL, GNU, 3rd party components, etc. unless all copyright ramifications are explained AND AGREED TO by the buyer on the site per the coder's Seller Legal Agreement). ## Platform Windows