Abstract: A method for recovering natural gas from a group of subterranean zones containing natural gas, including injecting an amount of a displacing gas into a first subterranean zone, producing a first produced gas from the first subterranean zone, collecting an amount of the first produced gas wherein the quality of the collected first produced gas is higher than or equal to a threshold production quality for the first produced gas, injecting an amount of the first produced gas into a second subterranean zone wherein the quality of the injected first produced gas is higher than or equal to a threshold injection quality for the first produced gas, producing a second produced gas from the second subterranean zone, and collecting an amount of the second produced gas wherein the quality of the collected second produced gas is higher than or equal to a threshold production quality for the second produced gas.

Abstract: A method for recovering natural gas from a group of subterranean zones containing natural gas, including injecting an amount of a displacing gas into a first subterranean zone, producing a first produced gas from the first subterranean zone, collecting an amount of the first produced gas wherein the quality of the collected first produced gas is higher than or equal to a threshold production quality for the first produced gas, injecting an amount of the first produced gas into a second subterranean zone wherein the quality of the injected first produced gas is higher than or equal to a threshold injection quality for the first produced gas, producing a second produced gas from the second subterranean zone, and collecting an amount of the second produced gas wherein the quality of the collected second produced gas is higher than or equal to a threshold production quality for the second produced gas.

Abstract: An invariant checking method and apparatus using binary decision diagrams (BDDs) in combination with constraint solvers for determining whether a system property is an invariant of a system description. The invariant checking method receives system descriptions and system properties and transforms them into a model formula. Specific variables are eliminated from the model formula and a corresponding output formula is generated. The output formula is transformed into a logic formula by substituting a new logic variable for each integer constraint in the output formula. A constrained BDD is constructed from the logic formula. The constrained BDD uses a heuristic algorithm to order the logic variables in the paths leading to true or false. A constraint solver is applied to the integer constraints that correspond to the occurrences of logic variables in the BDD paths, which determines whether the system property is or is not an invariant of the system description.

Abstract: A method for generating test cases for software and a test case generator comprising a simulator that drives software under test from one input state to the next. The simulator is constrained by predetermined criteria to visit states that meet the criteria thus preserving computer resources. The states reached by the simulator are tested.

Abstract: An accessory for modifying the decay pattern of vibrations set up in an implement to which the accessory is attached, and the combination of a decay pattern modifying accessory and an implement. Methods of manufacturing decay pattern modifying accessories are also disclosed.

Abstract: An invariant checking method and apparatus using binary decision diagrams (BDDs) in combination with constraint solvers for determining whether a system property is an invariant of a system description. The invariant checking method receives system descriptions and system properties and transforms them into a model formula. Specific variables are eliminated from the model formula and a corresponding output formula is generated. The output formula is transformed into a logic formula by substituting a new logic variable for each integer constraint in the output formula. A constrained BDD is constructed from the logic formula. The constrained BDD uses a heuristic algorithm to order the logic variables in the paths leading to true or false. A constraint solver is applied to the integer constraints that correspond to the occurrences of logic variables in the BDD paths, which determines whether the system property is or is not an invariant of the system description.

Abstract: An accessory for modifying the decay pattern of vibrations set up in an implement to which the accessory is attached, and the combination of a decay pattern modifying accessory and an implement. Methods of manufacturing decay pattern modifying accessories are also disclosed.