SUMMARY / RELATED TOPICS

EXPTIME

In computational complexity theory, the complexity class EXPTIME is the set of all decision problems that have exponential runtime, i.e. that are solvable by a deterministic Turing machine in O time, where p is a polynomial function of n. In terms of DTIME, We know and by the time hierarchy theorem and the space hierarchy theorem, that so at least one of the first three inclusions and at least one of the last three inclusions must be proper, but it is not known which ones are. Most experts believe, it is known that if P = NP EXPTIME = NEXPTIME, the class of problems solvable in exponential time by a nondeterministic Turing machine. More EXPTIME ≠ NEXPTIME if and only if there exist sparse languages in NP that are not in P. EXPTIME can be reformulated as the space class APSPACE, the problems that can be solved by an alternating Turing machine in polynomial space; this is one way to see that PSPACE ⊆ EXPTIME, since an alternating Turing machine is at least as powerful as a deterministic Turing machine.

EXPTIME is one class in an exponential hierarchy of complexity classes with more complex oracles or quantifier alternations. The class 2-EXPTIME is defined to EXPTIME but with a doubly exponential time bound 2 2 p; this can be generalized to higher time bounds. A decision problem is EXPTIME-complete if it is in EXPTIME, every problem in EXPTIME has a polynomial-time many-one reduction to it. In other words, there is a polynomial-time algorithm that transforms instances of one to instances of the other with the same answer. Problems that are EXPTIME-complete might be thought of as the hardest problems in EXPTIME. Notice that although it is unknown whether NP is equal to P, we do know that EXPTIME-complete problems are not in P. In computability theory, one of the basic undecidable problems is the halting problem: deciding whether a deterministic Turing machine halts. One of the most fundamental EXPTIME-complete problems is a simpler version of this, which asks if a DTM halts in at most k steps.

It is in EXPTIME because a trivial simulation requires O time, the input k is encoded using O bits which causes exponential number of simulations. It is EXPTIME-complete because speaking, we can use it to determine if a machine solving an EXPTIME problem accepts in an exponential number of steps; the same problem with the number of steps written in unary is P-complete. Other examples of EXPTIME-complete problems include the problem of evaluating a position in generalized chess, checkers, or Go; these games have a chance of being EXPTIME-complete because games can last for a number of moves, exponential in the size of the board. In the Go example, the Japanese ko rule is sufficiently intractable to imply EXPTIME-completeness, but it is not known if the more tractable American or Chinese rules for the game are EXPTIME-complete. By contrast, generalized games that can last for a number of moves, polynomial in the size of the board are PSPACE-complete; the same is true of exponentially long games.

Another set of important EXPTIME-complete problems relates to succinct circuits. Succinct circuits are simple machines used to describe some graphs in exponentially less space, they accept two vertex numbers as output whether there is an edge between them. For many natural P-complete graph problems, where the graph is expressed in a natural representation such as an adjacency matrix, solving the same problem on a succinct circuit representation is EXPTIME-complete, because the input is exponentially smaller.

Percy Tuhaise

Percy Night Tuhaise, is a Ugandan lawyer and judge who, on 8 February 2018, was appointed by president Yoweri Museveni, to the Uganda Court of Appeal which doubles as the country's Constitutional Court. Prior to her current position she served on the High Court of Uganda, she graduated from the Faculty of Law of Makerere University, Uganda's largest and oldest public university, with a Bachelor of Laws, circa 1983. The following year, she was awarded a Diploma in Legal Practice by the Law Development Centre, in Kampala, Uganda's capital city, she holds a Master of Laws from Makerere University. After her admission to the Uganda Bar, she served in various roles outside public service, she was a member of the Uganda Law Reform Commission. At the time of her appointment to the Uganda High Court, she was the deputy director of the Law Development Centre, in Kampala, concurrently served as the vice-chairperson of the electricity disputes tribunal. At the High Court, Justice Tuhaise has served in the Family Division and in the International Crimes Division.

Tuhaise participated in translating of the 1995 Constitution into Runyoro/Rutooro under supervision of the Law Development Centre. She was one of the trial judges in the "Muslim Clerics’ Murder Trial", between 2016 and 2017, she is the author of several publications, in peer-reviewed fora. On 7 February 2018, president Yoweri Museveni appointed Percy Tuhaise to the Uganda Court of Appeal/Uganda Constitutional Court, pending parliamentary approval. Ministry of Justice and Constitutional Affairs Court: Bukenya has case to answer in wife grabbing case

Sant'Anna dei Palafrenieri

The Church of Saint Anne in the Vatican, known as Sant'Anna de' Parafrenieri, is a Roman Catholic parish church dedicated to Saint Anne in Vatican City. The church is the parish church of the State of Vatican City and is placed under the jurisdiction of the Vicariate of the Vatican City and is located beside the Porta Sant'Anna, an international border crossing between Vatican City State and Italy. Commissioned by the Venerabile Arciconfraternita di Sant'Anna de Parafrenieri, Giacomo Barozzi da Vignola introduced the oval plan to church design, for the first time in the churches of Sant'Andrea in Via Flaminia and Saint Anne in Vatican, pioneering a plan, to become influential to Baroque architecture. On 20 November 1565, Pope Pius IV authorized the Archconfraternity of the Pontifical Grooms to build a church dedicated to Saint Anne close to the Apostolic Palace; the construction began that same year on a design attributed to Renaissance architect Giacomo Barozzi da Vignola. It was one of the first churches in Rome with an elliptical plan.

According to David Watkin, Vignola introduced the oval plan to church design for the first time in the churches of Sant'Andrea in Via Flaminia and Saint Anne in the Vatican, pioneering a plan, to become influential to Baroque architecture. After a smooth start, the construction of the church slowed because the Archconfraternity was in financial trouble. After Vignola's death in 1573, the church was finished by his son Giacinto Barozzi, according to a payment made by the Archconfraternity; when it was consecrated in 1583 it had a temporary roof. The facade attributed to Borromini and attached to the oval church prefigured the facade of the church of Sant'Agnese in Agone in attempting to reconciled a front with five bats to two towers; the facade was completed between 1700 and 1721 by Alessandro Specchi while the dome was built in 1763 and completed in 1775. The Archconfraternity exhibited in St. Anne a pairing of the saint it commissioned in 1603 from Caravaggio. Destined for the altar of the papal Grooms in the Basilica of Saint Peter, it was painted in 1605–1606, Madonna and Child with St. Anne.

It was sold to Cardinal Scipione Borghese and now hangs in the museum of the Galleria Borghese. The church belonged to the Archconfraternity until the Lateran Treaties of 1929, which constituted the Vatican City. Pope Pius XI erected the church into a parish, with the Apostolic Constitution "Ex Lateranensi pacto" of 30 May 1929; the pastoral care of the new parish was entrusted to the Augustinian Order. In return, Pope Pius XI granted the Archconfraternity the church of Santa Caterina della Rota; the interior, built to Vignola's design, is elliptical with eight side chapels. The main entrance is located at one end of the major axis of the ellipse; the minor axis ends with two chapels. Four doors surmounted by a pediment and framed by travertine columns with Corinthian capitals are distributed between the main altar and the side chapels. Four large arches rise at the ends of the two main axes, framing the areas of entry, the altar and the two chapels; the sacred area of the main altar is a square enclosed by four arches as a clear counterpoint to the oval part of the church.

The dome itself rests on a plinth with a cornice with three strips, pierced at the base by eight windows. At the top of the dome stands the lantern, the only source of natural light onto the main altar, it is decorated with the dove of the Holy Spirit. Until the mid-18th century, the inner walls of the church were white and the columns showed the natural color of the travertine stone, typical of Renaissance churches. Influenced by the rise of the Baroque in Rome, the Archconfraternity started redecorating the church with more lavish decorations and plenty of gilt and stucco; the façade was re-decorated in the Baroque style by Alessandro Specchi who added the upper facade to Vignola's church. The dome was designed by Francesco Navole, they commissioned in 1746 the sculptor Giovan Battista de' Rossi to redecorate the church with angels holding garlands in stucco above the doors. Four windows were walled and replaced with four frescoes depicting scenes from the life of Saint Anne. Giovan Battista de' Rossi made in stucco shells with festoons decorating the frescoes.

The decorator Annibale Rotati colored the walls in blue and light gray. The doorjambs were decorated with marble stucco marbled by Giacomo de Rocchi; the gold and silver stucco was made by Pietro Ricci. Despite the Baroque decoration, the initial plan of the church is still visible. Madonna and Child with St. Anne Index of Vatican City-related articles History of early modern period domes Lewine, Milton J.. "Vignola's Church of Sant'Anna de' Palafrenieri in Rome". The Art Bulletin. College Art Association. 47: 199–229. Doi:10.2307/3048257. JSTOR 3048257 Mazza, Sandra. S. Anna dei Palafrenieri in Vaticano. Roma. Cicinelli, Aldo. Sant'Anna dei Palafrenieri in Vaticano. Le Chiese di Roma illustrate. Marietti. OCLC 3440584. Coolidge, J. ed.. La vita e le opere di Jacopo Barozzi da Vignola nel quarto centenario della morte. Cassa di Risparmio di Vignola. Fletcher, Banister. "Italy". Sir Banister Fletcher's a history of architecture. P. 895. ISBN 0-7506-2267-9. Retrieved 3 December 2010 Pope Pius XI. "Acta Apostolicae Sedis – Ex Lateranensi pacto".

Acta Apostolicae Sedis. Vatican. 21: 309–311. Ecclesiam S. Annae in paroeciam Vaticanae Civitatis erigimus.