Boxing is a combat sport in which two people wearing protective gloves, throw punches at each other for a predetermined amount of time in a boxing ring. Amateur boxing is both an Olympic and Commonwealth Games sport and is a standard fixture in most international games—it has its own World Championships. Boxing is overseen by a referee over a series of one- to three-minute intervals called rounds. A winner can be resolved before the completion of the rounds when a referee deems an opponent incapable of continuing, disqualification of an opponent, or resignation of an opponent; when the fight reaches the end of its final round with both opponents still standing, the judges' scorecards determine the victor. In the event that both fighters gain equal scores from the judges, professional bouts are considered a draw. In Olympic boxing, because a winner must be declared, judges award the contest to one fighter on technical criteria. While humans have fought in hand-to-hand combat since the dawn of human history, the earliest evidence of fist-fighting sporting contests date back to the ancient Near East in the 3rd and 2nd millennia BC.

The earliest evidence of boxing rules date back to Ancient Greece, where boxing was established as an Olympic game in 688 BC. Boxing evolved from 16th- and 18th-century prizefights in Great Britain, to the forerunner of modern boxing in the mid-19th century with the 1867 introduction of the Marquess of Queensberry Rules; the earliest known depiction of boxing comes from a Sumerian relief in Iraq from the 3rd millennium BC. Depictions from the 2nd millennium BC are found in reliefs from the Mesopotamian nations of Assyria and Babylonia, in Hittite art from Asia Minor. A relief sculpture from Egyptian Thebes shows both spectators; these early Middle-Eastern and Egyptian depictions showed contests where fighters were either bare-fisted or had a band supporting the wrist. The earliest evidence of fist fighting with the use of gloves can be found on Minoan Crete. Various types of boxing existed in ancient India; the earliest references to musti-yuddha come from classical Vedic epics such as the Ramayana and Rig Veda.

The Mahabharata describes two combatants boxing with clenched fists and fighting with kicks, finger strikes, knee strikes and headbutts. Duels were fought to the death. During the period of the Western Satraps, the ruler Rudradaman - in addition to being well-versed in "the great sciences" which included Indian classical music, Sanskrit grammar, logic - was said to be an excellent horseman, elephant rider and boxer; the Gurbilas Shemi, an 18th-century Sikh text, gives numerous references to musti-yuddha. In Ancient Greece boxing was enjoyed consistent popularity. In Olympic terms, it was first introduced in the 23rd Olympiad, 688 BC; the boxers would wind leather thongs around their hands. There were no boxers fought until one of them acknowledged defeat or could not continue. Weight categories were not used; the style of boxing practiced featured an advanced left leg stance, with the left arm semi-extended as a guard, in addition to being used for striking, with the right arm drawn back ready to strike.

It was the head of the opponent, targeted, there is little evidence to suggest that targeting the body was common. Boxing was a popular spectator sport in Ancient Rome. In order for the fighters to protect themselves against their opponents they wrapped leather thongs around their fists. Harder leather was used and the thong soon became a weapon; the Romans introduced metal studs to the thongs to make the cestus. Fighting events were held at Roman Amphitheatres; the Roman form of boxing was a fight until death to please the spectators who gathered at such events. However in times, purchased slaves and trained combat performers were valuable commodities, their lives were not given up without due consideration. Slaves were used against one another in a circle marked on the floor; this is. In AD 393, during the Roman gladiator period, boxing was abolished due to excessive brutality, it was not until the late 16th century. Records of Classical boxing activity disappeared after the fall of the Western Roman Empire when the wearing of weapons became common once again and interest in fighting with the fists waned.

However, there are detailed records of various fist-fighting sports that were maintained in different cities and provinces of Italy between the 12th and 17th centuries. There was a sport in ancient Rus called Kulachniy Boy or "Fist Fighting"; as the wearing of swords became less common, there was renewed interest in fencing with the fists. The sport would resurface in England during the early 16th century in the form of bare-knuckle boxing sometimes referred to as prizefighting; the first documented account of a bare-knuckle fight in England appeared in 1681 in the London Protestant Mercury, the first English bare-knuckle champion was James Figg in 1719. This is the time when the word "boxing" first came to be used; this earliest form of modern boxing was different. Contests in Mr. Figg's time, in addition to fist fighting contained fencing and cudgeling. On 6 January 1681, the first recorded boxing match took place in Britain when Christopher Monck, 2nd Duke of Albemarle engineered a bout between his butler and his butcher with the latter winning the prize.

Early fighting had no written rules. There were no weight divisions or round limits, no referee. In general, it was chaotic. An ear

Mount Cameroon Race of Hope

The Mount Cameroon Race of Hope is an annual, televised footrace held at Mount Cameroon in the Southwest Region of Cameroon in January or February. The 20th edition of the Guinness mount Cameroon race of hope was scheduled for February 14, 2015; the information was made public in a joint press conference granted by the president of the Cameroon Athletics federation, Emmanuel Motomby Mbome and the General manager of Guinness Cameroun, Baker Magunda. During the Press Conference it was made known that the mode of registration and price remain the same but there will be several innovations this year notably the Olympic flame that would go round the country prior to the race; the flame of hope will visit every qualifier race notably in Ngaoundere move to Batie, Yaounde and Buea. On each lap of the tour, Guinness Cameroon will carry out some activities of general interest such as constructing water catchments and hospitals; the event follows a path up Mount Cameroon and back. Participants are divided into men's and women's divisions and further subdivided into professionals and casual runners.

Each winner in the men's and women's professional divisions will receive 10,000,000 francs CFA in 2011. Teams may compete in the relay division; the first Race of Hope was in 1995. Since participation has increased; as of 2010, the winners since the race's inception had all been Cameroonians. Sarah Etonge has won the women's division for four straight years; the first race took place in 1973. For many years, the race was organised and sponsored by Guinness under the name Guinness Mount Cameroon Race. In 2005, control of the event was taken by 12 local committees in Buea and representatives of the national Cameroon Athletics Federation and the Ministry of Sports and Physical Education; the budget in 2007 was 130 million francs CFA, the bulk of, provided by the Ministry of Sports and Physical Education. The change to public control was controversial: In 2005, Mayor Charles Mbella Moki of the Buea Rural Council accused the organisers of mismanagement and proposed that Guinness to be given back full control.

In 2006, the CAF cut the prize money to the winners by 25% without warning to cover their membership fees in the organisation. About 5,000 visitors come to Buea each year to view the race. Cultural and sporting events take place in Buea; these include artists, choral groups, dancers. Local authorities sanction the event through the paramount chief of Buea, who climbs Mount Cameroon to petition the gods for their blessing; the 2007 documentary film Volcanic Sprint is about the race. The 2019 race saw marginal attendance due to the ongoing Anglophone Crisis. Constantine N. Mbufung view my profile. Benly Anchunda'2015 MOUNT CAMEROON RACE OF HOPE SCHEDULED FOR 14TH FEBRUARY'. CRTV News 06/12/2014 Efande, Peter. "Ange Sama:'We've Increased The Financial Package For Winners'". Cameroon Tribune. Accessed 20 February 2007. Jones, Emma. "Mount Cameroon Race of Hope Marathon", Pilot Destination Guide. Accessed 1 August 2008. Mbonwoh, Nkeze. "All Set for Sunday's Race of Hope". Cameroon Tribune. Accessed 20 February 2007.

Mbonwoh, Nkeze. "Modification of Race of Hope - Decision Suspended". "". Accessed 11 February 2010. Mbous, Jacques Sebastien. "16eme Edition de la Course de l'Espoir." Official Note from Cameroon Athletic Federation, 6 January 2011. Nana, Walter Wilson. "Buea Wants Guinness To Manage Race Of Hope - Mayor". The Post Online. Accessed 21 February 2007. Nana, Walter Wilson. "Race Of Hope Winner To Bag FCFA 3 Million". The Post Online. Accessed 21 February 2007. Nana, Walter Wilson, Innocent Mbunwe. "2006 Mount Cameroon Race Of Hoope: Winners Angry With 25% Prize Slash". The Post Online. Accessed 21 February 2007. Nana, Walter Wilson, Innocent Mbunwe. "Race Of Hope: Teacher Is New Champion, Etonge Confirms'Queen Of The Mountain' Supremacy". The Post Online. Accessed 21 February 2007. Vubem, Fred. "Mt. Cameroon Race Mixed Commission Evaluates Preparations". Cameroon Tribune. Accessed 20 February 2007. ----- "Volcanic Sprint". Accessed 11 February 2007

Myhill–Nerode theorem

In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1958. Given a language L, a pair of strings x and y, define a distinguishing extension to be a string z such that one of the two strings xz and yz belongs to L. Define a relation RL on strings by the rule that x RL y if there is no distinguishing extension for x and y, it is easy to show that RL is an equivalence relation on strings, thus it divides the set of all strings into equivalence classes. The Myhill–Nerode theorem states that L is regular if and only if RL has a finite number of equivalence classes, moreover that the number of states in the smallest deterministic finite automaton recognizing L is equal to the number of equivalence classes in RL. In particular, this implies. If L is a regular language by definition there is a DFA A that recognizes it, with only finitely many states.

If there are n states partition the set of all finite strings into n subsets, where subset Si is the set of strings that, when given as input to automaton A, cause it to end in state i. For every two strings x and y that belong to the same subset, for every choice of a third string z, automaton A reaches the same state on input xz as it reaches on input yz, therefore must either accept both of the inputs xz and yz or reject both of them. Therefore, no string z can be a distinguishing extension for x and y, so they must be related by RL. Thus, Si is a subset of an equivalence class of RL. Combining this fact with the fact that every member of one of these equivalence classes belongs to one of the sets Si, this gives a many-to-one relation from states of A to equivalence classes, implying that the number of equivalence classes is finite and at most n. In the other direction, suppose that RL has finitely many equivalence classes. In this case, it is possible to design a deterministic finite automaton that has one state for each equivalence class.

The start state of the automaton corresponds to the equivalence class containing the empty string, the transition function from a state X on input symbol y takes the automaton to a new state, the state corresponding to the equivalence class containing string xy, where x is an arbitrarily chosen string in the equivalence class for X. The definition of the Myhill–Nerode relation implies that the transition function is well-defined: no matter which representative string x is chosen for state X, the same transition function value will result. A state of this automaton is accepting if the corresponding equivalence class contains a string in L. Thus, the existence of a finite automaton recognizing L implies that the Myhill–Nerode relation has a finite number of equivalence classes, at most equal to the number of states of the automaton, the existence of a finite number of equivalence classes implies the existence of an automaton with that many states; the Myhill–Nerode theorem may be used to show that a language L is regular by proving that the number of equivalence classes of RL is finite.

This may be done by an exhaustive case analysis in which, beginning from the empty string, distinguishing extensions are used to find additional equivalence classes until no more can be found. For example, the language consisting of binary representations of numbers that can be divided by 3 is regular. Given the empty string, 00, 01 and 10 are distinguishing extensions resulting in the three classes, but after this step there is no distinguishing extension anymore; the minimal automaton accepting our language would have three states corresponding to these three equivalence classes. Another immediate corollary of the theorem is that if a language defines an infinite set of equivalence classes, it is not regular, it is this corollary, used to prove that a language is not regular. The Myhill–Nerode theorem can be generalized to trees. See tree automaton. Pumping lemma for regular languages, an alternative method for proving that a language is not regular; the pumping lemma may not always be able to prove.

Hopcroft, John E.. "Chapter 3", Introduction to Automata Theory and Computation, Massachusetts: Addison-Wesley Publishing, ISBN 0-201-02988-X. Nerode, Anil, "Linear Automaton Transformations", Proceedings of the AMS, 9, JSTOR 2033204. Regan, Notes on the Myhill-Nerode Theorem, retrieved 2016-03-22. Bakhadyr Khoussainov. Automata Theory and its Applications. Springer Science & Business Media. ISBN 978-1-4612-0171-7