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Theory of computation

In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: automata theory and languages, computability theory, computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?". In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several models in use, but the most examined is the Turing machine. Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, because it represents what many consider the most powerful possible "reasonable" model of computation, it might seem that the infinite memory capacity is an unrealizable attribute, but any decidable problem solved by a Turing machine will always require only a finite amount of memory.

So in principle, any problem that can be solved by a Turing machine can be solved by a computer that has a finite amount of memory. The theory of computation can be considered the creation of models of all kinds in the field of computer science; therefore and logic are used. In the last century it was separated from mathematics; some pioneers of the theory of computation were Ramon Llull, Alonzo Church, Kurt Gödel, Alan Turing, Stephen Kleene, Rózsa Péter, John von Neumann and Claude Shannon. Automata theory is the study of abstract machines and the computational problems that can be solved using these machines; these abstract machines are called automata. Automata comes from the Greek word. Automata theory is closely related to formal language theory, as the automata are classified by the class of formal languages they are able to recognize. An automaton can be a finite representation of a formal language. Automata are used as theoretical models for computing machines, are used for proofs about computability.

Language theory is a branch of mathematics concerned with describing languages as a set of operations over an alphabet. It is linked with automata theory, as automata are used to generate and recognize formal languages. There are several classes of formal languages, each allowing more complex language specification than the one before it, i.e. Chomsky hierarchy, each corresponding to a class of automata which recognizes it; because automata are used as models for computation, formal languages are the preferred mode of specification for any problem that must be computed. Computability theory deals with the question of the extent to which a problem is solvable on a computer; the statement that the halting problem cannot be solved by a Turing machine is one of the most important results in computability theory, as it is an example of a concrete problem, both easy to formulate and impossible to solve using a Turing machine. Much of computability theory builds on the halting problem result. Another important step in computability theory was Rice's theorem, which states that for all non-trivial properties of partial functions, it is undecidable whether a Turing machine computes a partial function with that property.

Computability theory is related to the branch of mathematical logic called recursion theory, which removes the restriction of studying only models of computation which are reducible to the Turing model. Many mathematicians and computational theorists who study recursion theory will refer to it as computability theory. Complexity theory considers not only whether a problem can be solved at all on a computer, but how efficiently the problem can be solved. Two major aspects are considered: time complexity and space complexity, which are how many steps does it take to perform a computation, how much memory is required to perform that computation. In order to analyze how much time and space a given algorithm requires, computer scientists express the time or space required to solve the problem as a function of the size of the input problem. For example, finding a particular number in a long list of numbers becomes harder as the list of numbers grows larger. If we say there are n numbers in the list if the list is not sorted or indexed in any way we may have to look at every number in order to find the number we're seeking.

We thus say that in order to solve this problem, the computer needs to perform a number of steps that grows linearly in the size of the problem. To simplify this problem, computer scientists have adopted Big O notation, which allows functions to be compared in a way that ensures that particular aspects of a machine's construction do not need to be considered, but rather only the asymptotic behavior as problems become large. So in our previous example we might say; the most important open problem in all of computer science is the question of whether a certain broad class of problems denoted NP can be solved efficiently. This is discussed further at Complexity classes P and NP, P versus NP problem is one of the seven Millennium Prize Problems stated by the Clay Mathematics Institute in 2000; the Official Problem Description was given by Turing Award winner Stephen Cook. Aside from a Turing machine, other equivalent models of computation are in use. Lambda calculus A computation consists of an initi

Cottage Inn Pizza

Cottage Inn Pizza is an American international franchise pizza delivery corporation headquartered in Ann Arbor, Michigan. The original Cottage Inn restaurant opened in Ann Arbor in 1948 and remains the company's flagship today. There are over 50 franchised stores in Michigan and Ohio in the United States, as well as in China. Cottage Inn provides a variety of pizza most well known for their specialty gourmet pizzas, along with various crust styles and toppings; the original Cottage Inn restaurant, opened in 1948, still stands in its original location at 512 East William, Ann Arbor. Although it started as a coffee shop, pizza was introduced in 1948, it has the distinction of being the first restaurant in Ann Arbor to serve pizza. The current owner acquired the building in 1961; the restaurant went through renovations in 1975, 1980, 1987. In 1993, the restaurant expanded again to banquet room facilities. Due to its proximity to the University of Michigan campus, the original Cottage Inn is frequented by students and visitors.

The restaurant has an established relationship with the Ann Arbor community, participating in community service events such as feeding the homeless on Thanksgiving. In early 2014, Cottage Inn announced a plan to expand nationally using a franchising business model; the company is accepting applications from potential franchisees through their franchising website. By 1978, Cottage Inn's continued growth required the formation of a second company to devote to delivery services; as a result, Cottage Inn Carryout & Delivery, Inc. was established. The first Cottage Inn store under this new company was founded at Packard and Hill streets in Ann Arbor. In June 1986, the first franchise opened in Ypsilanti. In 2003, the new corporate headquarters and distribution center opened in Ann Arbor. In 2017, Cottage Inn opened a franchise location in China. In 2012, Cottage Inn partnered with the Michigan International Speedway to become the official pizza vendor on NASCAR weekends. Although the original plan was for Cottage Inn to provide 24-hour delivery service to customers in the campsites and staffing issues required the company to scale back its services.

Cottage Inn serves as a pizza vendor for other events held at the Michigan International Speedway, including the Faster Horses Festival


KTHI is a commercial radio station located in Caldwell, broadcasting to the Boise, area. KTHI airs a classic hits music format; the call letters KTHI were used for a television station in Fargo, North Dakota, now known as KVLY-TV. Journal Communications and the E. W. Scripps Company announced on July 30, 2014 that the two companies would merge to create a new broadcast company under the E. W. Scripps Company name that will own the two companies' broadcast properties, including KTHI; the transaction is slated to be completed in 2015, pending shareholder and regulatory approvals. In January 2018, Scripps announced. In August 2018, Lotus Communications announced that it would acquire Scripps' Boise & Tucson clusters for $8 million; the sale was completed on December 12. KTHI official website Query the FCC's FM station database for KTHI Radio-Locator information on KTHI Query Nielsen Audio's FM station database for KTHI

Mary McGarry Morris

Mary McGarry Morris is an American novelist, short story author and playwright from New England. She uses its towns as settings for her works. In 1991, Michiko Kakutani of The New York Times described Morris as "one of the most skillful new writers at work in America today", she has been most compared to John Steinbeck and Carson McCullers. Although her writing style is different, Morris has been compared to William Faulkner for her character-driven storytelling, she was a finalist for the National Book PEN/Faulkner Award for Fiction. As of 2011, Morris has published eight novels, some of which were best-sellers, numerous short stories, she has written a play about the insanity trial of Mary Todd Lincoln. Vanished, Her first novel, was written over 10-year period, it was rejected by numerous publishers and agents before agent Jean Naggar helped her sell it to Viking Press. It was published in 1988 to favorable reviews and was a finalist for the National Book Award and the PEN/Faulkner Award for Fiction.

Her 1991 novel A Dangerous Woman was named by Time as one of its Five Best Novels of the Year and as one of the best books of the year by American Library Association Library Journal. Based on A Dangerous Woman, Morris won the Noble Discover Great New Writers Award; the novel was adapted for a 1993 movie of the same name, which starred Debra Winger, Gabriel Byrne, David Strathairn, Barbara Hershey, Maggie Gyllenhaal and Jake Gyllenhaal. Her 1995 novel Songs in Ordinary Time, sold one and one-half million copies, was a New York Times Bestseller, a selection of Oprah's Book Club, it was adapted as a CBS television movie starring Beau Bridges. Her fourth novel, Fiona Range, was published to critical acclaim. A reviewer for The New York Times Book Review stated Morris can "bring the ordinary to life with the sheer clarity of vision, she knows how a house with children in it sounds at night, what the heat and bustle in a kitchen feel like before a family dinner and how indiscretions arise in a dining room when everyone is flushed with wine."Morris' fifth novel was entitled A Hole in the Universe and tells the story of a man returning to his community after having served 25 years in prison for murder.

The Washington Post wrote: "Morris is a master at sympathetic portraits of those clinging to the peripheries of society. And nowhere is her talent more evident than in her extraordinary new novel, A Hole in the Universe. Morris a superb storyteller...and undeniable compassion for and intuitive understanding of her characters' lives make us know and care about these people, too." Her sixth novel, The Lost Mother was written from the perspective of a 12-year-old boy. He recounts his life after his mother leaves him, his sister and his father in the midst of the Great Depression; the Boston Globe described the book as "wonderful and absorbing", The Washington Post wrote "The Lost Mother is the quietest, subtlest novel that kept me up into the small hours of the night, unable to look away." Morris has said of The Lost Mother:"Inspiration was easy because it was during those same years that my grandmother abandoned her husband and three children. The day she left, she brought her four-year-old daughter and youngest child, my mother, to a friend's house dressed in her best clothes, my grandmother climbed into a taxi and rode away forever.

The image of that little girl watching from the window as her mother deserted her would come to me whenever there was sorrow in my mother's life. Forgiving by nature, my mother tried to understand what had happened, but because she felt such love and fierce loyalty to her own children, her mother's actions remained a painful, troubling mystery. Growing up, I was keenly aware of the loss my mother felt as well as the great love and admiration she had for her father, a quiet country man who raised his three children alone in those desperate times working day and night to support them." Morris published The Last Secret. The Last Secret depicts the unraveling of the life of an accomplished suburban mother, who discovers her husband's betrayal, known by others, at the time a shameful secret surfaces from her own past. Morris' eighth novel was Light from a Distant Star, it drew comparisons to Harper Lee's To Kill a Mockingbird. It tells of a brutal family love. At the center of the novel is 13-year-old Nellie Peck, a girl who wrestles with the meanings of loyalty and truth.

Finalist, National Book Award, 1988 Finalist, PEN/Faulkner Award for Fiction, 1989 Five Best Books of 1991, Time Best Books of 1991, American Library Association Library Journal Barnes and Noble Discover Great New Writers Award, 1991 Oprah Book Club Selection, 1997 Morris was born in Meriden and raised in Rutland, Vermont. She resides in Massachusetts with her husband Michael W. Morris, they have twelve grandchildren. Her first novel, was nominated for high awards, it was the first. Before writing full-time, Morris had worked as a social worker for the Massachusetts Department of Public Welfare in Lawrence, Massachusetts. A number of her novels are set in fictional towns in Vermont while parts of Vanished, A Hole in the Universe and The Lost Mother are set in Massachusetts. Vanished, 1988, Viking Press A Dangerous Woman]

Human (Dodie EP)

Human is the third extended play by English singer-songwriter Dodie Clark, known mononymously as Dodie. The album was self-released by Clark on 18 January 2019, it peaked at number 5 on the UK Official Albums Chart, Clark's highest charting album to date in her home country and her third consecutive entry in the top 40. Human is composed of seven tracks, four of which had premiered on Clark's successful YouTube channel in the past. "She," an acoustic love song about her love for another woman, was uploaded on 27 September 2014 when Clark was 19. The title track "Human" was uploaded on 23 July 2016 featuring Jon Cozart. "Burned Out" was uploaded on 1 December 2017. "Not What I Meant" was uploaded as a duet with Dom Fera called "Bitter Content" on 25 January 2018. In a video uploaded on 22 January 2019 Clark revealed that throughout the past nine months she had been hiding a "secret song" in her videos by peppering her videos with spontaneous singing of one word or phrase; when all the clips are put together it reveals the album opening track "Arms Unfolding" The album title track "Human" was released as the lead single on 21 September 2018 alongside the album pre-order and an accompanying music video directed by Hazel Hayes."If I'm Being Honest" was released as the second single from the album on 2 November 2018 with a live session music video directed by Sammy Paul.

A full length science fiction inspired video directed by Dom Fera was released on 30 November 2018. "If I'm Being Honest" was nominated for the 2019 Independent Music Award for Best Song – Folk/Singer-Songwriter. A music video for "Monster" directed by PJ Liguori was released on 21 January 2019. To promote the album, Clark embarked on the Human Tour across the UK, North America throughout 2019. All songs written by Clark. Credits sourced from Spotify

Hamdan Azhar

Hamdan Azhar is an American data scientist and activist. He is a founding member of the Bitcoin Center, a former data scientist at Facebook, a visiting professor of data science at the City University of New York. Azhar is best known for his work in emoji data science, or using emoji data to inform sentiment analysis of popular reaction to current events in politics and society, he is an inventor on Facebook's patent application for "Determining and utilizing contextual meaning of digital standardized image characters", published in June 2017, along with Thomas Dimson, Bogdan State, Shankar Kalyanaraman. Hamdan Azhar was raised in an immigrant family in the Marine Park neighborhood of Brooklyn, he attended the Bronx High School of Science, earned his bachelor's in economics from Pennsylvania State University, his master's in biostatistics from the University of Michigan School of Public Health. From 2011-2012, Azhar was a research assistant at the Center for Decision Sciences at Columbia Business School