In computational complexity theory, a decision problem is P-complete if it is in P and every problem in P can be reduced to it by an appropriate reduction. The notion of P-complete decision problems is useful in the analysis of: which problems are difficult to parallelize which problems are difficult to solve in limited space; the specific type of reduction used may affect the exact set of problems. If we use NC reductions, that is, reductions which can operate in polylogarithmic time on a parallel computer with a polynomial number of processors all P-complete problems lie outside NC and so cannot be parallelized, under the unproven assumption that NC ≠ P. If we use the weaker log-space reduction, this remains true, but additionally we learn that all P-complete problems lie outside L under the weaker unproven assumption that L ≠ P. In this latter case the set P-complete may be smaller; the class P taken to consist of all the "tractable" problems for a sequential computer, contains the class NC, which consists of those problems which can be efficiently solved on a parallel computer.

This is. It is not known whether NC = P. In other words, it is not known whether there are any tractable problems that are inherently sequential. Just as it is suspected that P does not equal NP, so it is suspected that NC does not equal P. Similarly, the class L contains all problems that can be solved by a sequential computer in logarithmic space; such machines run in polynomial time. It is suspected that L ≠ P. To the use of NP-complete problems to analyze the P = NP question, the P-complete problems, viewed as the "probably not parallelizable" or "probably inherently sequential" problems, serves in a similar manner to study the NC = P question. Finding an efficient way to parallelize the solution to some P-complete problem would show that NC = P, it can be thought of as the "problems requiring superlogarithmic space". The logic behind this is analogous to the logic that a polynomial-time solution to an NP-complete problem would prove P = NP: if we have a NC reduction from any problem in P to a problem A, an NC solution for A NC = P. Similarly, if we have a log-space reduction from any problem in P to a problem A, a log-space solution for A L = P.

The most basic P-complete problem is this: given a Turing machine, an input for that machine, a number T, does that machine halt on that input within the first T steps? It is clear that this problem is P-complete: if we can parallelize a general simulation of a sequential computer we will be able to parallelize any program that runs on that computer. If this problem is in NC so is every other problem in P. If the number of steps is written in binary, the problem is EXPTIME-complete; this problem illustrates a common trick in the theory of P-completeness. We aren't interested in whether a problem can be solved on a parallel machine. We're just interested in whether a parallel machine solves it much more than a sequential machine. Therefore, we have to reword the problem so that the sequential version is in P; that is. If a number T is written as a binary number the obvious sequential algorithm can take time 2n. On the other hand, if T is written as a unary number it only takes time n. By writing T in unary rather than binary, we have reduced the obvious sequential algorithm from exponential time to linear time.

That puts the sequential problem in P. Then, it will be in NC. Many other problems have been proved to be P-complete, therefore are believed to be inherently sequential; these include the following problems, either as given, or in a decision-problem form: Circuit Value Problem - Given a circuit, the inputs to the circuit, one gate in the circuit, calculate the output of that gate Restricted Case of CVP - Like CVP, except each gate has two inputs and two outputs, every other layer is just AND gates, the rest are OR gates, the inputs of a gate come from the preceding layer Linear programming - Maximize a linear function subject to linear inequality constraints Lexicographically First Depth First Search Ordering - Given a graph with fixed ordered adjacency lists, nodes u and v, is vertex u visited before vertex v in a depth-first search induced by the order of the adjacency lists? Context Free Grammar Membership - Given a context-free grammar and a string, can that string be generated by that grammar?

Horn-satisfiability: given a set of Horn clauses, is there a variable assignment which satisfies them? This is P's version of the boolean satisfiability problem. Game of Life - Given an initial configuration of Conway's Game of Life, a particular cell, a time T, is that cell alive after T steps? LZW Data Compression - given strings s and t, will compressing s with an LZ78 method add t to the dictionary? Type inference for partial types - Given an untyped term from the lambda calculus, determine whether this term has a partial type. In order to prove that a give

Treasure Hunting

Treasure Hunting is a Manhwa series by Kang Gyung-Hyo. The series has sold more than 13 million copies worldwide; the series introduces South Korean readers to different countries around the world, their history and culture, through the eponymous treasure hunt for a lost, hidden or stolen artifact, culturally or significant to the particular country. It mentions any historical ties between South Korea and the country being visited. In translations for different countries, this introduction is changed accordingly for the target readers; the primary character of the series is the young but precocious Pang-Yi who accompanied his uncle, the Professor Gu-Bon, on various foreign trips for archaeology or historical studies. They encounter a clue to some legendary lost, the hunt would take them across the country, bringing them to sights and experiences significant to the country. Pang-Yi's rival is a child prodigy, though they are willing to work together occasionally. Ji Pang-yi: The protagonist of the main series.

He is a precocious boy with amazing knowledge of power of observation. Pang-Yi was able to visit numerous or archaeologically important sites and fell into adventures recovering lost treasures. A running joke in the earlier series had him matched with a pretty girl from each country visited. Professor Ji Gu-bon: Famous archaeologist, invited overseas for conferences or expert advice, he is portrayed as a fat gourmand with a brilliant mind. Once, he lost a lot of weight and he became to be a quite handsome man. Yi Eun-ju: Man-crazy Research Assistant to Professor Gu-Bon, she holds a crush on Dr. Mark, despite them being the antagonists. Do To-ri: Pang-Yi's rival, but he is caring about Pang-yi, his IQ is 180. But he has no luck with girls, untalented in mathematics, suffers from acrophobia. Dotori's mentor is Dr. Dotoran. Dr. Do To-ran: Academic rival to Professor Gu-Bon. While Prof Gu-Bon was based in Korea, Dr. To-ran worked extensively for long periods overseas and appeared more cosmopolitan, his IQ is higher than his son, To-ri.

Do Re-mi: Do To-ri's younger sister. She is less intelligent than friendlier towards Pang-Yi, she is interested in art. Dr. Bong Pal-yi: One of main antagonist of the main series, the protagonist in the prequel series. In the main series, he use his handsome looks to fool many females into helping him to steal treasures. Bong Ja-ba: One of main antagonist of the main series, she is Pal-yi's cousin. She uses her abilities to fight. Despite this, she was arrested. Mark Youngman: One of main antagonists of the main series, he is a member of the Treasure Master's. Like Pal-yi, he made Eun-ju fall in love with him. Unlike the other antagonists in this series, he escapes Interpol and he is never arrested by any police, his real nationality is unknown. Wanda Kim: Pal-ri's mother, she supports her son in his effort to steal treasures. • Ko & Kai: They are Dr. Bong Pal-Yi’s henchmen. Ko is fat but Kai is thin, they met Dr. Pal-Yi. • Katherine/Sophie: First appears in France. She is a rich girl who acts like a spoiled brat and she likes Pangyi and Dotori.

Her name is as same as Katherine of Medici. • Nuree: First appears in Turkey. He likes Dotori, But like Reyna, the girl in Israel, he is Muslim. • Reyna: First appears in Israel. She wants to choose her own religion, but she wants to be Jewish proudly just like her parents. • Nguen Bun Hong: First appears in Vietnam. He loves to cook Pho, he is the third generation of chef after his grandpa. • Windy: First appears in Iraq. She is Pangyi’s friend, she is a member of UNESCO. • Shun Li: First appears in China. She is a Chinese fighter, her hair looks like a Chinese snack. • Maria: First appears in Brazil. She is a Brazilian natural explorer, she is Professor Ji Gubon’s friend and he likes her too. • Mr. Hudson: First appears in Egypt, he is an Egyptian oil millionaire. He wants Dotori team to help him hunting treasure in pyramid that he discovered. Yi Eun Ju has a crush on him. • Raffi: First appears in New Zealand. He is a Maori warrior, he likes to play Rugby. His favourite Rugby team is All black team. • Kena: First appears in New Zealand.

He is Maori tribal chief. He used to be a Maori warrior, he wants his grandson Raffi to be a Maori warrior just like him. • Mrs. Misra: First appears in India, she is a beautiful Indian woman. She is Tandoori’s mom. Professor Ji Gubon has a crush on her. • Tandoori: First appears in India. He is a boy, his religion is Sikh. • Professor Will: He is an old English man. He is Professor Do Toran's teacher. • Vice Professor Albert: First appears in UK. He is a rich English man, he is Professor Will’s rival. He has a treasure of his own and he likes to make a competition for Pangyi vs Bong Palyi team, he wants them to battle to get his treasure. • Jose: First appears in Cuba. He is a Cuban baseball player. • Amelia: First appears in Cuba. She is Jose’s aunt, she is a Cuban doctor. Professor Ji Gubon has a crush on her. • Anna: First appears in Cuba. She is a pirate, she wants to steal all the treasure in the ocean. She is a relative of Davy Jones. • Pepper: First appears in Mozambique. He is a Mozambican solider, he can fight good.

He wants to own AK-47 gun of Mozambique. • Tom: First appears in UK. Student Council President receive message from 008, his parents were dead and adopted by Dr. Bong Palyi. • Vivika: First appears in Austria. She is an adopted child of Preside

Marc Levine

Marc Levine is an American politician serving as the California State Assemblyman for the 10th district since 2012. A member of the Democratic Party, his district encompasses the North San Francisco Bay Area. Levine is the current Chairman the California Legislative Jewish Caucus. Prior to being elected to the State Assembly in 2012, he was a member of the San Rafael City Council. Marc Levine served on the San Rafael City Council and gained a reputation for innovative environmental policies and pragmatic solutions. Levine's election to the California State Assembly in 2012 was an upset, in which he prevailed despite being outspent five-to-one by a fellow Democrat, Assemblyman Michael Allen. Levine was reelected to in 2014 by nearly a three-to-one margin and received more votes than any other member of the State Assembly. Levine is Jewish, he lives in Marin County with their two children. Levine has stated: "Immigrants are welcome and we will do everything we can to help them achieve legal status."

In 2015, he took action by authoring two immigration bills— both of which were signed by Governor Brown. AB 899 safeguards the privacy of immigrant children by requiring federal immigration officials to obtain a court order before accessing juvenile records. AB 900 helps unaccompanied minor immigrants who are escaping violence and exploitation to receive humanitarian relief through the Special Immigrant Juvenile Status visa process. In 2014, when more than 60,000 unaccompanied refugee children from poverty-stricken and violence-torn areas of Guatemala, El Salvador and Honduras arrived to the United States, more than 4,000 children came to California. Levine worked with legislative leaders and Governor Brown to pass legislation providing $3 million in legal aid for those immigrants. Official website Campaign website