Hydrogen spectral series

In computer science, partial order reduction is a technique for reducing the size of the state-space to be searched by a model checking algorithm. It exploits the commutativity of concurrently executed transitions, which result in the same state when executed in different orders.

In explicit state space exploration, partial order reduction usually refers to the specific technique of expanding a representative subset of all enabled transitions. This technique has also been described as model checking with representatives Template:Harv. There are various versions of the method, the so-called stubborn set method Template:Harv, ample set method Template:Harv, and persistent set method Template:Harv.

Ample sets

Ample sets are an example of model checking with representatives. Their formulation relies on a separate notion of dependency. Two transitions are considered independent only if whenever they are mutually enabled, they cannot disable another and the execution of both results in a unique state regardless of the order in which they are executed. Transitions that are not independent, are dependent. In practice dependency is approximated using static analysis.

Ample sets for different purposes can be defined by giving conditions as to when a set of transitions is "ample" in a given state.

C0 ${ample(s)=\emptyset }\iff {enabled(s)=\emptyset }$

C1 If a transition $\alpha$ depends on some transition relation in ample(s), this transition cannot be invoked until some transition in the ample set executed.

Conditions C0 and C1 are sufficient for preserving all the deadlocks in the state space. Further restrictions are needed in order to preserve more nuanced properties. For instance, in order to preserve properties of linear temporal logic, the following two conditions are needed:

C2 If $enabled(s)\neq ample(s)$, each transition in the ample set is invisible

C3 A cycle is not allowed if it contains a state in which some transition $\alpha$ is enabled, but is never included in ample(s) for any states s on the cycle.

These conditions are sufficient for an ample set, but not necessary conditions Template:Harv.

Stubborn sets

Stubborn sets make no use of an explicit independence relation. Instead they are defined solely through commutativity over sequences of actions. A set $T(s)$ is (weakly) stubborn at s, if the following hold.

D0 $\forall a\in T(s)\forall b_{1},...,b_{n}\notin T(s)$, if execution of the sequence $b_{1},...,b_{n},a$ is possible and leads to the state $s'$, then execution of the sequence $a,b_{1},...,b_{n}$ is possible and will lead to state $s'$

D1 Either $s$ is a deadlock, or $\exists a\in T(s)$ such that $\forall b_{1},...,b_{n}\notin T(s)$, the execution of $b_{1},...,b_{n},a$ is possible.

These conditions are sufficient for preserving all deadlocks, just like C0 and C1 are in the ample set method. They are, however, somewhat weaker, and as such may lead to smaller sets. The conditions C2 and C3 can also be further weakened from what they are in the ample set method, but the stubborn set method is compatible with C2 and C3.

Others

There are also other notations for partial order reduction. One of the commonly used is the persistent set/sleep set algorithm. Detailed information can be found in Patrice Godefroid's thesis Template:Harv.

In symbolic model checking, partial order reduction can be achieved by adding more constraints (guard strengthening).

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534