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In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics^{[citation needed]}.

Usage[link]

Formal verification can be helpful in proving the correctness of systems such as: cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code.

The verification of these systems is done by providing a formal proof on an abstract mathematical model of the system, the correspondence between the mathematical model and the nature of the system being otherwise known by construction. Examples of mathematical objects often used to model systems are: finite state machines, labelled transition systems, Petri nets, timed automata, hybrid automata, process algebra, formal semantics of programming languages such as operational semantics, denotational semantics, axiomatic semantics and Hoare logic.^{[citation needed]}

Approaches to formal verification[link]

One approach and formation is model checking, which consists of a systematically exhaustive exploration of the mathematical model (this is possible for finite models, but also for some infinite models where infinite sets of states can be effectively represented finitely using abstraction). Usually this consists of exploring all states and transitions in the model, by using smart and domain-specific abstraction techniques to consider whole groups of states in a single operation and reduce computing time. Implementation techniques include state space enumeration, symbolic state space enumeration, abstract interpretation, symbolic simulation, abstraction refinement. The properties to be verified are often described in temporal logics, such as linear temporal logic (LTL) or computational tree logic (CTL).

Another approach is logical inference. It consists of using a formal version of mathematical reasoning about the system, usually using theorem proving software such as a HOL theorem prover, the ACL2, Isabelle, or Coq theorem provers. This is usually only partially automated and is driven by the user's understanding of the system to validate. Recent tools such as Perfect Developer and Escher C Verifier attempt to automate the proof process fully.

"Non-classical" logics such as linear logic and temporal logics can also be used in logical inference, not just in model checking.

Formal verification for software[link]

Logical inference for the formal verification of software can be further divided into:

• the more traditional 1970s approach in which code is first written in the usual way, and subsequently proven correct in a separate step;
• dependently typed programming, in which the types of functions include (at least part of) those functions' specifications, and type-checking the code establishes its correctness against those specifications. Fully featured dependently typed languages support the first approach as a special case.

A slightly different (and complementary) approach is program derivation, in which efficient code is produced from functional specifications by a series of correctness-preserving steps. An example of this approach is the Bird-Meertens Formalism, and this approach can be seen as another form of correctness by construction.

Verification and validation[link]

Verification is one aspect of testing a product's fitness for purpose. Validation is the complementary aspect. Often one refers to the overall checking process as V & V.

• Validation: "Are we trying to make the right thing?", i.e., is the product specified to the user's actual needs?
• Verification: "Have we made what we were trying to make?", i.e., does the product conform to the specifications?

The verification process consists of static/structural and dynamic/behavioral aspects. E.g., for a software product one can inspect the source code (static) and run against specific test cases (dynamic). Validation usually can be done only dynamically, i.e., the product is tested by putting it through typical and atypical usages ("Does it satisfactorily meet all use cases?").

Industry use[link]

The growth in complexity of designs increases the importance of formal verification techniques in the hardware industry.^[2][3] At present, formal verification is used by most or all^{[citation needed]} leading hardware companies, but its use in the software industry is still languishing.^{[citation needed]} This could be attributed to the greater need in the hardware industry, where errors have greater commercial significance.^{[citation needed]} Because of the potential subtle interactions between components, it is increasingly difficult to exercise a realistic set of possibilities by simulation. Important aspects of hardware design are amenable to automated proof methods, making formal verification easier to introduce and more productive.^[4]

As of 2011^[update], several operating systems have been formally verified: NICTA's Secure Embedded L4 microkernel, sold commercially as seL4 by OK Labs;^{[citation needed]} OSEK/VDX based real-time operating system ORIENTAIS by East China Normal University;^{[citation needed]} Green Hills Software's Integrity operating system;^{[citation needed]} and SYSGO's PikeOS.^[5][6]

See also[link]

Software Testing portal

Look up verifiability in Wiktionary, the free dictionary.

• Automated theorem proving
• Formal equivalence checking
• LURCH
• Proof checker
• Property Specification Language
• Selected formal verification bibliography
• Static code analysis
• Temporal logic in finite-state verification
• Post silicon validation
• Intelligent verification
• Runtime verification

References[link]

This biographical article needs additional citations for verification. Please help by adding reliable sources. Contentious material about living persons that is unsourced or poorly sourced must be removed immediately, especially if potentially libelous or harmful. (January 2011)

John Part
Personal information
Nickname	Darth Maple
Born	(1966-06-29) June 29, 1966 (age 45) Toronto, Ontario, Canada
Home town	Oshawa, Ontario Canada
Darts information
Playing darts since	1987
Darts	23g Cosmo Darts
Laterality	Right-handed
Walk-on music	The Imperial March (Darth Vader's theme from Star Wars)
Organisation (see split in darts)
BDO	1991 - 1997
PDC	1997 - present
Current world ranking	24
BDO majors - best performances
World Ch'ship	Winner 1994
World Masters	Last 16 1995, 1997
PDC premier events - best performances
World Ch'ship	Winner 2003, 2008
World Matchplay	Runner-up 2002, 2005
World Grand Prix	Runner-up 2002, 2003
Grand Slam	Quarter-final 2007
Premier League	6th 2005, 2009
Desert Classic	Winner 2006
European Ch'ship	First round 2008, 2011
UK Open	Runner-up 2004
US Open/WSoD	Semi-final 2007
Players Ch'ship Finals	Second round 2009
Other tournament wins
Tournament	Years
Blueberry Hill Canada National Championships Canadian Open Cleveland Darts Extraveganza Golden Harvest North American Cup Ireland Open Autumn Classic Ireland Open Spring Classic North American Darts Championship PDC Eastbourne Open PDC Nations Cup Singles PDC Northern Ireland Open Players Ch'ship (AUT) Players Ch'ship (CAN) Players Ch'ship (DER) Players Ch'ship (GIB) Players Ch'ship (HAY) Shanghai International Darts Open Soft Tip Bullshooter World Championship UK Open South West Regional Final Vauxhall Autumn Open Vauxhall Spring Open WDF World Cup Pairs West Tyrone Open Windy City Open	2001, 2002 1995, 2001, 2002, 2004, 2007 1995, 2001, 2004 2002 2004 2002 2002 2010 2000 2002 2002 2011 2011 2011 2008 2007 2009 2008 2003 2003 2002, 2003 1993 2002, 2003 2002, 2003
Other achievements
PDC World Number 1 January to June 2003 Member of Oshawa Sports Hall of Fame

John Part (born June 29, 1966 in Toronto, Ontario) is a Canadian professional darts player, who is nicknamed Darth Maple. Part is a three-times World Champion, having triumphed in the BDO World Championship in 1994 and the PDC World Championship in 2003 and 2008. His 2006 Las Vegas Desert Classic title and a host of other tournament wins make him statistically North America's greatest darts player ever.^[1]

Career[link]

Early career[link]

Part was given a dartboard by his parents as a Christmas present in 1987^[2] which gave him the bug to take up the game. He became a professional darts player in 1991. He won several championships, principally in Canada from 1991 to 1995. But his greatest success in the BDO was his 1994 World championship win. He won the final by 6 sets to 0 against Bobby George. In 1997, he decided to leave the BDO to play in the PDC.

PDC Success[link]

He entered the PDC in 1997, but didn't make an impact until 2001 when he reached his first World Championship final, where he was whitewashed by Phil Taylor 0-7 who comprehensively averaged 108 to Part's 92. He reached the final of the World Matchplay in 2002 and was again beaten by Taylor in a much closer final, by 16 legs to 18. He also lost to his fierce rival in the 2002 World Grand Prix.

Part exacted his revenge on Taylor in the 2003 World Championship by winning his first PDC World Championship crown. He managed to beat Cliff Lazarenko, Jamie Harvey, Chris Mason and Kevin Painter to play Taylor yet again in the final. Part led 3-0 and 4-1 in sets, but Taylor bounced back to win four sets in-a-row to lead 5-4. Part did not let the shift in momentum affect him as he won the next two sets to lead 6-5, before Taylor leveled to take the game to a deciding set. Part broke Taylor's throw to win the set by 3-1 in legs and to win the title by 7-6. He became world number one from January to June afterwards. The remainder of the season also proved successful for Part as he played Taylor for the second successive year in the World Grand Prix final and lost again, this time 3–7. He also reached the final of the 2003 Las Vegas Desert Classic where he was beaten by Peter Manley, 12–16 (legs).

Part could not defend his World Championship crown in 2004 as he crashed out in the third round to Mark Dudbridge 3–4. The rest of 2004 was not as good as previous years as he only reached the final of the UK Open where he was defeated by Roland Scholten 6–11.

He lost to Dudbridge again in the 2005 World Championship this time in the fourth round and by a 2–4 scoreline. He subsequently dropped down the world rankings somewhat in 2005 and 2006, but still enjoyed a major championship success in August 2005 when he reached the World Matchplay final. He beat Phil Taylor in the semi-finals 16-11 before losing to Colin Lloyd 12-18. In July 2006, he added the Las Vegas Desert Classic trophy to his haul of championship wins, beating Raymond van Barneveld, 6 sets to 3 in the final.^{[citation needed]}

In 2007, he returned to some of his best form. Starting from 19th in the rankings, he managed to reach the semi-finals of the inaugural US Open, the World Grand Prix and the Las Vegas Desert Classic. These consistent performances meant he entered the 2008 World Championship as the 11th seed. He managed to win the tournament by coming through a tight quarter-final match against James Wade 5–4 and then beating Kevin Painter in the semi-final to set up a final with the rank outsider, Kirk Shepherd who was a qualifier for the event. Part's greater experience shone through as he stormed into a 4–0 lead and eventually closed out the match 7–2. Victory ensured he joined Taylor, van Barneveld, Eric Bristow and John Lowe as the only players then to have won a World Championship more than two times.^[3] With this win he also became only one of two players to have won the PDC World Championship more than once, the other player being Taylor. He also became the first player to win the World Championship in three different venues – having won the 1994 BDO at the Lakeside, the 2003 PDC at Circus Tavern and now the 2008 PDC at Alexandra Palace. This has since been equalled by Taylor.

Despite winning the World Championship, Part had an indifferent 2008. He finished bottom of the Premier League and suffered early exits in the US Open, Desert Classic and the inaugural European Championship. He did however reach the quarter-finals of the World Grand Prix.

Part was defeated in the first round of the 2009 World Championship, losing 3-0 to American Bill Davis - the second time in which Part has lost his first match in the World Championship, having won the title the previous year (he was knocked out by Mark Dudbridge in 2004 having won the title in 2003). Part was defeated by Kirk Shepherd in the second round of the 2010 World Championship in a repeat of the 2008 final, only recording a 76 average in a 4-1 loss. This result meant Part droped down the rankings and did not appear in the 2010 Premier League.

In June 2010, Part came through a large field of players to win the PDC North American Darts Championship in Las Vegas. However, he was whitewashed 0–3 by Danish qualifier Per Laursen in the 2011 World Championship.

He won his first players championship since 2007 in February 2011 in Derby convincingly beating Mark Walsh 6-0 with 104.86 average. On the previous day he narrowly missed double 12 for a 9 dart finish. Part stated "he had nothing to lose" and that illness had stopped him reaching where he wanted to be at the World Championships. Part's form continued when he won another players championship in May 2011 in Austria by thrashing Denis Ovens 6-0 in the final, having earlier overcoming Phil Taylor 6-2. The win granted him qualification for all the major televised tournaments in 2011, something which he failed to do in 2010 except for the UK Open.

During the first round of the 2011 World Matchplay, John hit a 9 Darter against Mark Webster and came from 7-1 down to within one leg at 9-8. He subsequently lost the match but hit a milestone in his darting career with his first ever televised perfect game.

He qualified for the World Grand Prix, in which he won his first round match against reigning World Champion Adrian Lewis. He lost in the last 16 against eventual finalist Brendan Dolan, 1-3.

At the 2012 World Championship he made it to the quarter-finals for the first time since his 2008 title. He dropped just three sets on his way to the last 8 by defeating John Henderson, Richie Burnett and Kevin Painter.^[4][5] He was involved in one of the greatest matches ever seen at the World Championships against James Wade. Wade opened up a 3-1 set lead, before his form started to dip to coincide with Part scoring heavier and hitting more doubles to win 3 sets in a row. The players broke each others throws twice in the deciding set to require a sudden-death leg, which Wade managed to win. Part said afterwards that it was "the greatest game I've ever lost!".^[6]

Part represented Canada with Ken MacNeil in the 2012 PDC World Cup of Darts and together they were beaten 2-3 by England in the second round, having lost a sudden death leg.^[7]

Television Commentary[link]

In June 1994, BBC commentator Sid Waddell decided to leave the BBC to join Sky Television. This left just Tony Green as the only commentator on the event. Part is considered to be one of the games's best "counters" or "spotters" (the ability to work out scoring shots or where the next dart may be thrown). This knowledge is essential to a darts commentator and contributed to Part being chosen by the BBC to join Green in the commentary box during the latter stages of the 1995 Embassy World Championships.^{[citation needed]}

Tournament finals[link]

This biographical section of an article needs additional citations for verification. Please help by adding reliable sources. Contentious material about living persons that is unsourced or poorly sourced must be removed immediately, especially if potentially libelous or harmful. (January 2012)

PDC premier event finals: 10 (3 titles, 7 runner-ups)[link]

Legend World Championship (2–1) World Matchplay (0–2) Premier League (0–0) Other (1–4) Outcome No. Year Championship Opponent in the final Score[N 1] Runner-up 1. 2001 World Darts Championship Taylor, PhilPhil Taylor 0–7 (s) Runner-up 2. 2002 World Matchplay Phil Taylor 16–18 (l) Runner-up 3. 2002 World Grand Prix Phil Taylor 3–7 (s) Winner 1. 2003 World Darts Championship Phil Taylor 7–6 (s) Runner-up 4. 2003 Las Vegas Desert Classic Manley, PeterPeter Manley 12–16 (l) Runner-up 5. 2003 World Grand Prix Phil Taylor 2–7 (s) Runner-up 6. 2004 UK Open Scholten, RolandRoland Scholten 6–11 (l)[citation needed] Runner-up 7. 2005 World Matchplay Lloyd, ColinColin Lloyd 12–18 (l)[citation needed] Winner 2. 2006 Las Vegas Desert Classic van Barneveld, RaymondRaymond van Barneveld 6–3 (s)[citation needed] Winner 3. 2008 World Darts Championship (2) Shepherd, KirkKirk Shepherd 7–2 (s)[citation needed] ^ (l) = score in legs, (s) = score in sets. World Championship Performances[link] 1994 (BDO) - Winner beat Bobby George 6-0 1995 (BDO) - Round 2 lost to Paul Williams 2-3 1996 (BDO) - Round 2 lost to Steve Beaton 0-3 1997 (BDO) - Round 2 lost to Roger Carter 1-3 1998 (PDC) - Round 1 lost to Paul Lim 1-3 1999 (PDC) - Round 1 lost to Alan Warriner-Little 0-3 2000 (PDC) - Round 2 lost to Dennis Smith 0-3 2001 (PDC) - Runner Up lost to Phil Taylor 0-6 2002 (PDC) - Quarter-finals lost to Phil Taylor 0-6 2003 (PDC) - Winner beat Phil Taylor 7-6 2004 (PDC) - Round 3 lost to Mark Dudbridge 3-4 2005 (PDC) - Round 4 lost to Mark Dudbridge 2-4 2006 (PDC) - Round 3 lost to Wayne Mardle 2-4 2007 (PDC) - Round 2 lost to Chris Mason 2-4 2008 (PDC) - Winner beat Kirk Shepherd 7-2 2009 (PDC) - Round 1 lost to Bill Davis 0-3 2010 (PDC) - Round 2 lost to Kirk Shepherd 1-4 2011 (PDC) - Round 1 lost to Per Laursen 0-3 2012 (PDC) - Quarter-finals lost to James Wade 4-5 References[link] ^ "John Part Player Profile". Professional Darts Corporation. http://www.pdc.tv/page/PlayerProfile/0,,10180~1451654,00.html. Retrieved January 20, 2012.  ^ Biography from Part's web site ^ Superb Part storms to PDC title BBC News, 1 January 2008 ^ "2012 PDC World Championship Results". Darts Database. http://www.dartsdatabase.co.uk/FixtureList.aspx?EventKey=3069. Retrieved December 30, 2011.  ^ "Part puts out Painter". Sky Sports. http://www.skysports.com/darts/pdc/story/0,25061,15623_7400730,00.html. Retrieved December 29, 2011.  ^ "World Championship Quarter-Finals". PDC. December 30, 2011. http://www.pdc.tv/page/NewsdeskDetail/0,,10180~2561291,00.html. Retrieved December 30, 2011.  ^ "Cash Converters World Cup Round Two Doubles Round-Up". PDC. 4 February 2012. http://www.pdc.tv/page/NewsdeskDetail/0,,10180~2600417,00.html. Retrieved 4 February 2012.  External links[link] John Part's official web site John Part's Profile and Stats on Darts Database John Part's helpful darting series offering advice on how to play and practice the sport Preceded by John Lowe BDO World Champion 1994 Succeeded by Richie Burnett Preceded by Phil Taylor PDC World Champion 2003 Succeeded by Phil Taylor Preceded by Raymond van Barneveld PDC World Champion 2008 Succeeded by Phil Taylor Persondata Name Part, John Alternative names Short description Date of birth 1966-06-29 Place of birth Toronto, Ontario, Canada Date of death Place of death