Answer:
3. (9 points) The goal of this problem is to show that our formal definitions of P and NP imply that P = NP cannot have a non-constructive proof. Throughout this problem we assume a consistent, binary, encoding of both Turing machines and 3-SAT instances. Note that the complexities are intentionally not tight to address potential overheads from scan- ning the tape linearly in order to look for certain symbols. (a) (3 points) Show that for any constant cı, there is a constant c2 such that if Mi is a Turing machine encoded by at most bits that correctly decides 3-SAT in O(n10) time (aka. 3-SAT E TIME(n10), then there is a Turing machine M, encoded by at most most c2 bits that runs in O(n100) time such that if the 3-SAT instance has a satisfying assignment, M, accepts and writes a satisfying assignment at the end of the tape. (b) (3 points) Let M ...Mbe Turing machines show that the language {(k, M... Mk,t,w) | w is an instance of 3-SAT and one of M, writes a satisfying assignment to w in at most t steps can be decided by a Turing machine in (k2107 10) time. (c) (3 points) Under the assumption that there exists an unknown Turing machine encodable in c bits that decides 3-SAT is in O(n10) time, give implementation details for a Turing Machine M that decides 3-SAT in O(n10000) time. Hint: the constant factor in the big-O is able to hide any function related ci and c2, which independent of input sizes, and thus constants.
Explanation:
3. (9 points) The goal of this problem is to show that our formal definitions of P and NP imply that P = NP cannot have a non-constructive proof. Throughout this problem we assume a consistent, binary, encoding of both Turing machines and 3-SAT instances. Note that the complexities are intentionally not tight to address potential overheads from scan- ning the tape linearly in order to look for certain symbols. (a) (3 points) Show that for any constant cı, there is a constant c2 such that if Mi is a Turing machine encoded by at most bits that correctly decides 3-SAT in O(n10) time (aka. 3-SAT E TIME(n10), then there is a Turing machine M, encoded by at most most c2 bits that runs in O(n100) time such that if the 3-SAT instance has a satisfying assignment, M, accepts and writes a satisfying assignment at the end of the tape. (b) (3 points) Let M ...Mbe Turing machines show that the language {(k, M... Mk,t,w) | w is an instance of 3-SAT and one of M, writes a satisfying assignment to w in at most t steps can be decided by a Turing machine in (k2107 10) time. (c) (3 points) Under the assumption that there exists an unknown Turing machine encodable in c bits that decides 3-SAT is in O(n10) time, give implementation details for a Turing Machine M that decides 3-SAT in O(n10000) time. Hint: the constant factor in the big-O is able to hide any function related ci and c2, which independent of input sizes, and thus constants.
Answer:
This is not plagiarism
Explanation:
The student has properly referenced the original source material, therefore, it is not plagiarism. Also, it is sufficient to just reference the attached source material author. Although it is implied that several other authors' material has been used in the source material, there is no need for the student to reference the other authors too.
During the Great Depression. ... introduced as they study the Great Depression. Review the ... 1989-1999 appears to have a high degree of price stability with low
Answer:
COUNTIF
Explanation:
the Countif function counts the number of cells in range that meets a given criteria.
Answer:
TCP/IP
Explanation:
TCP/IP which stands for Transmission Control Protocol and Internet Protocol are network protocols which divide your message into smaller chunks or fragments known as network packets and sends them out onto the Internet. When the chunks arrive at the intended destination, TCP/IP on the receiving end reassembles the network packets into the original message.
TCP/IP are the main protocols used for sending data over the internet.
