Nondeterministic Turing machine

In theoretical computer science, a nondeterministic Turing machine is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next action is not determined by its state and the current symbol it sees. NTMs are sometimes used in thought experiments to examine the abilities and limitations of computers. One of the most important open problems in theoretical computer science is the P vs. NP problem, which concerns the question of how difficult it is to simulate nondeterministic computation with a deterministic computer. In essence, a Turing machine is imagined to be a simple computer that reads and writes symbols one at a time on an endless tape by following a set of rules, it determines what action it should perform next according to its internal state and what symbol it sees. An example of one of a Turing Machine's rules might thus be: "If you are in state 2 and you see an'A', change it to'B', move left, change to state 3."

In a deterministic Turing machine, the set of rules prescribes at most one action to be performed for any given situation. A deterministic Turing machine has a transition function that, for a given state and symbol under the tape head, specifies three things: the symbol to be written to the tape, the direction in which the head should move, the subsequent state of the finite control. For example, an X on the tape in state 3 might make the DTM write a Y on the tape, move the head one position to the right, switch to state 5. By contrast, in a nondeterministic Turing machine, the set of rules may prescribe more than one action to be performed for any given situation. For example, an X on the tape in state 3 might allow the NTM to: Write a Y, move right, switch to state 5or Write an X, move left, stay in state 3. How does the NTM "know" which of these actions it should take? There are two ways of looking at it. One is to say that the machine is the "luckiest possible guesser"; the other is to imagine that the machine "branches" into many copies, each of which follows one of the possible transitions.

Whereas a DTM has a single "computation path" that it follows, an NTM has a "computation tree". If at least one branch of the tree halts with an "accept" condition, we say that the NTM accepts the input. A nondeterministic Turing machine can be formally defined as a 6-tuple M =, where Q is a finite set of states Σ is a finite set of symbols ι ∈ Q is the initial state ⊔ ∈ Σ is the blank symbol A ⊆ Q is the set of accepting states δ ⊆ × is a relation on states and symbols called the transition relation. L is the movement to the left, S is no movement, R is the movement to the right; the difference with a standard Turing machine is that for those, the transition relation is a function. Configurations and the yields relation on configurations, which describes the possible actions of the Turing machine given any possible contents of the tape, are as for standard Turing machines, except that the yields relation is no longer single-valued; the input for an NTM is provided in the same manner as for a deterministic Turing machine: the machine is started in the configuration in which the tape head is on the first character of the string, the tape is all blank otherwise.

An NTM accepts an input string if and only if at least one of the possible computational paths starting from that string puts the machine into an accepting state. When simulating the many branching paths of an NTM on a deterministic machine, we can stop the entire simulation as soon as any branch reaches an accepting state; as a mathematical construction used in proofs, there are a variety of minor variations on the definition of an NTM, but these variations all accept equivalent languages. The head movement in the output of the transition relation is encoded numerically instead of using letters to represent moving the head Left and Right, it is common to omit the stationary output, instead insert the transitive closure of any desired stationary transitions. Some authors add an explicit reject state, which causes the NTM

Ajita Suchitra Veera

Ajita Suchitra Veera is an Indian film director, illustrator and film producer. Veera is best known for a visual, epic, cinematic style, with unconventional narrative structures breaking form, blending reality and imagination, dreams, philosophical and humanistic ideas, her upcoming feature film "Ballad of Rustom" was in Oscar contention for Best Picture 86th Academy Awards 2014. Her earlier short film "Notes on Her" was an official entry to the Oscars in 2003, her First Feature Film "Ballad of Rustom" which she wrote and produced and did production design, collaborated on film editing, sound design and music, was described as a "powerful cinematographic poem and faustian" by The 61st International Film Festival Mannheim, Germany. Veera was born in Southern India, her father Anjan Babu, is an illustrator, graphic designer and photo-journalist. Her mother Usha Rani, is a journalist turned banker. At the age of three Veera started learning to sketch from her father, an illustrator, she did her schooling from Nasr School and was the only child to parents who were both working and much of her early childhood was spent sketching, watching movies and printing photographs with her father in their small private photo studio.

Veera's father introduced her to a range of cameras in their studio and she dabbled in making pinhole cameras and other scientific devices, which fascinated her as a child. This would on influence her distinct visual style. An introvert, shy kid in her childhood, she was raised as a special and individualistic child by her parents. Both parents loved watching Hollywood classics and Indian Art House. Veera was taken to watch movies by her father in the local cinemas playing Hollywood films, this was a significant influence in her childhood. David Lean's Doctor Zhivago and the grand epic narratives and adventure films like "Butch Cassidy and Sundance kid" coupled with detective stories and science fiction, which she read avidly, fascinated her immensely. In high school Veera was introduced to the Indian master Satyajit Ray – his films and short stories, which would affect her in her cinematic development, she started watching lot of the World Cinema directors specially French New Wave directors – François Truffaut, Jean-Luc Godard, Robert Bresson and Hollywood directors – Alfred Hitchcock, Sidney Pollack, by renting videos and going to small theatres and film clubs in Hyderabad while graduating from college, was enamored by directors like Hitchcock, Kurosawa and Luis Buñuel.

She graduated in Science and was a bright student, she decided to discontinue her education in science and pursue her ultimate passion for cinema. After a brief stint in M. A Theatre Arts, Central University Hyderabad and acting in plays she joined the Film and Television Institute of India, the prestigious national film institute in India, she graduated in Film Direction. The short film "Notes on Her" 2003 which she directed was an Oscar entry and critically acclaimed for its unconventional style, it marks the beginning of her cinematic journey, her graduate film "The Solitary Sandpiper", blending dream and reality and fantastic visual landscapes, where she worked innovatively to create a distinct color palette with special processing techniques on negative, such as "Bleach bypass" to create desaturated, high contrast images, would be the hallmark of her feature film "Ballad of Rustom" again in 2013 and define her keen interest in image making in cinema. Documentary "CHAOS" which explores the interrelationship of science and art juxtaposing mathematics and music was a significant step in her filmmaking which mark her distinct craftsmanship.

Veera free lanced as a director working on corporate videos and small promotionals before starting her own film company called Imaginem Cinema in 2009 which she started to create the necessary space for imaginative and interesting new cinema from India. Her first feature film Ballad of Rustom, slated for a worldwide release in 2014, which she wrote and produced under her company Imaginem Cinema, on which Veera is the production designer, extensively collaborated on sound design, film editing and music, won the "Best Director" at the 12th Osian Cinefan in India in 2012 and Veera was awarded the Indibor Bose Award for Excellence in Cinema, instituted by Cine Central one of the oldest film societies, founded by the legendary master Satyajit Ray in Calcutta; this is the first award instituted in 45 years since the formation of this society for a Film Director. "Ballad of Rustom" had unveiled its trailer at the Cannes Marche du Film and opened at the 61st International Film Festival Mannheim, Heidelberg, in international competition in November 2012, the oldest film festival parallel to Cannes and went to screen in International Film Festival Prague, Czech Republic.

Ajita Suchitra Veera is the first Indian director to be invited to this European festival in its 20 long years which has seen World Cinema masters such as Wim Wenders, Roman Polanski, Krystoff Zanussi. "Ballad of Rustom" was screened at the 17th International Film Festival Kerala, & International Film Festival Hague and the 12th Osian Cinefan, New Delhi. 2003: "Notes on Her" -Short Film 2012: Ballad of Rustom 2013: Ballad of Rustom 2014: Ballad of Rustom "A Character's Real and Imaginary Journey Drive Ballad of Rustom." Motion.ko

Sunni Revival

The Sunni Revival was a period in Islamic history marked by the revival of the political fortunes of Sunni Islam, a renewed interest in Sunni law and theology and the spread of new styles in art and architecture. Conventionally, the revival lasted from 1055 until 1258. Richard Bulliet has proposed that the term "recentering" better describes the period than "revival" or "renaissance"; the period is characterized as much by developments within Sunnism as by Sunni relations with Shia Islam. In particular, it was a period homogenization of Sunnism as scholars and leaders strove for ijmāʿ; some scholars have argued that the Sunni Revival led to the decline of scientific output in the Islamic world. The Sunni Revival followed a period of Shia ascendancy, sometimes called the "Shia Century", under the Fatimid dynasty in Africa and parts of Arabia. During this period, Shia polities controlled most of the Islamic world, including its core areas; the Abbasid Caliph, the supreme Sunni leader, was under the control of the Buyids, who governed Baghdad, while the Sharif of Mecca was under the authority of the Fatimids.

The revival began when the Sunni Seljuk Turks conquered Baghdad from the Buyids in 1055. The period of Seljuk domination lasted a century, until about 1150, they were definitively ousted from Baghdad in 1157. Thereafter a period of Abbasid resurgence and ecumenism followed until the Mongols sacked Baghdad in 1258; the chief architect of the political and legal Sunni revival was Nizam al-Mulk, grand vizier of the Seljuk Empire. He founded the school which took the Nizamiyya of Baghdad; the chief architect of the theological revival, al-Ghazali, taught at Nizam's school in Baghdad. This was not the first madrasa, but it was by far the most influential and nizamiyya fashioned after were founded wherever the Sunni revival spread, they were a major factor in the homogenization of Sunnism during the revival. The figure most associated with the Sunni Revival in Syria is Nur ad-Din, who built twenty madrasas in Damascus. In 1171, Saladin brought Egypt into the Sunni fold, his Ayyubid dynasty vigorously strengthened Sunnism in Syria and Egypt