1. A conjugated diene polymer obtained by reacting one end of a conjugated diene polymer having a monomer unit based on a conjugated diene and a monomer unit based on a compound represented by Formula (1) with a compound represented by Formula (2) wherein the content of the monomer unit based on the compound represented by Formula (1) is 0.01 to 20% by weight relative to 100% by weight of the total amount of the monomer unit in the conjugated diene polymer:
wherein R11 represents a hydrogen atom or a hydrocarbyl group, m is 0 or 1, R12 represents a hydrocarbylene group, and A represents a nitrogen-containing heterocyclic group,
wherein n represents an integer of 1 to 10; R21, R22 and R23 independently represent a hydrocarbyl group or a hydrocarbyloxy group, and at least one of R21, R22 and R23 is a hydrocarbyloxy group; R24 and R25 independently represent a hydrogen atom or a hydrocarbyl group that may have a nitrogen atom andor an oxygen atom, or R24 and R25 are bonded to represent a hydrocarbylene group that may have a nitrogen atom andor an oxygen atom, or R24 and R25 form one group representing a group bonded to a nitrogen atom by a double bond.
2. The conjugated diene polymer according to claim 1, wherein, in Formula (2), R21, R22 and R23 are hydrocarbyloxy groups, and R24 and R25 are hydrocarbyl groups.
3. The conjugated diene polymer according to claim 1, wherein, in Formula (1), R11 is a hydrogen atom, and A is a pyridyl group.
4. The conjugated diene polymer according to claim 1, wherein the vinyl bond content of the conjugated diene polymer is from 20% by mole to 70% by mole relative to 100% by mole of the monomer unit content based on the conjugated diene.
5. A conjugated diene polymer composition comprising the conjugated diene polymer according to claim 1 and a reinforcing agent, wherein the content of the reinforcing agent is 10 to 150 parts by weight relative to 100 parts by weight of the conjugated diene polymer.
6. The conjugated diene polymer composition according to claim 5, comprising silica and carbon black as the reinforcing agent wherein the weight ratio of the content of silica and the content of carbon black (content of silica: content of carbon black) is 2:1 to 50:1.
7. A method of manufacturing a conjugated diene polymer comprising steps A and B below:
step A: polymerizing a monomer component containing a conjugated diene and a compound represented by Formula (1) below by an alkali metal catalyst in a hydrocarbon solvent using 0.01 to 20% by weight of the compound represented by Formula (1) (relative to 100% by weight of the total amount of the monomer component used), thereby giving a polymer having the alkali metal derived from the alkali metal catalyst at least at one end of a polymer chain having a monomer unit based on the conjugated diene and a monomer unit based on the compound represented by Formula (1) below, and
step B: reacting the polymer obtained in step A and a compound represented by Formula (2) below,
wherein R11 represents a hydrogen atom or a hydrocarbyl group, m is 0 or 1, R12 represents a hydrocarbylene group, and A represents a nitrogen-containing heterocyclic group,
wherein n represents an integer of 1 to 10; R21, R22 and R23 independently represent a hydrocarbyl group or a hydrocarbyloxy group, and at least one of R21, R22 and R23 is a hydrocarbyloxy group; R24 and R25 independently represent a hydrogen atom or a hydrocarbyl group that may have a nitrogen atom andor an oxygen atom, or R24 and R25 are bonded to represent a hydrocarbylene group that may have a nitrogen atom andor an oxygen atom, or R24 and R25 form one group representing a group bonded to a nitrogen atom by a double bond.
8. The method of manufacturing a conjugated diene polymer according to claim 7, wherein, in Formula (2), R21, R22 and R23 are hydrocarbyloxy groups, and R24 and R25 are hydrocarbyl groups.
9. The method of manufacturing a conjugated diene polymer according to claim 7, wherein, in Formula (1), R11 is a hydrogen atom, and A is a pyridyl group.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A computer-implemented method of determining an abstraction for a computer program, the method comprising:
accessing within a computer a representation of the computer program, the representation comprising a directed graph; and
reducing a plurality of nodes within the directed graph to a single node, the plurality of nodes including only less than all nodes within the directed graph.
2. The method of claim 1 wherein the directed graph represents a control flow graph of the computer program.
3. The method of claim 1 wherein the nodes of the directed graph represent control points within the computer program.
4. The method of claim 1 wherein the computer program is a concurrent program.
5. The method of claim 4 wherein the abstraction comprises an abstraction of at least one of the threads of the concurrent program.
6. The method of claim 1 wherein the directed graph is a cross product of two or more directed graphs.
7. The method of claim 1 wherein the abstraction comprises a cross product of two or more directed graphs, at least one of the two or more directed graphs being an abstraction.
8. The method of claim 1 wherein the nodes of the directed graph represent program counter values for a thread of the computer program.
9. A computer-implemented method of refining an abstraction for a computer program, the method comprising:
choosing a path in the abstraction;
determining if the path is an infeasible path;
upon determining the path is infeasible, generating one or more constraints to refine the abstraction such that the refined abstraction does not comprise the infeasible path; and
determining a refined abstraction by applying the constraints to the abstraction.
10. The method of claim 9 wherein the abstraction comprises a directed graph.
11. The method of claim 9 wherein the computer program comprises a concurrent program
12. The method of claim 9 wherein the abstraction comprises the cross product of at least two threads of a concurrent program.
13. The method of claim 9 wherein the infeasible path comprises a path within a directed graph.
14. The method of claim 9 wherein at least one constraint comprises an order-based constraint.
15. The method of claim 9 wherein at least one constraint comprises a time-based constraint.
16. The method of claim 9 wherein at least one constraint comprises a predicate.
17. A computer program product comprising one or more computer-readable storage media having encoded thereon computer executable instructions which, when executed, implement a method of determining an abstraction for a computer program, the method comprising:
determining a representation of the computer program, the representation comprising a directed graph;
reducing one or more nodes within the directed graph to a single node.
choosing a path in the abstraction;
determining if the path is an infeasible path;
upon determining the path is infeasible, generating one or more constraints to refine the abstraction such that the refined abstraction does not comprise the infeasible path; and
determining a refined abstraction by applying the constraints to the abstraction.
18. The computer program product of claim 17 wherein the computer program is a concurrent program.
19. The computer program product of claim 17 wherein the directed graph is a cross product of at least two threads of a concurrent program.
20. The computer program product of claim 17 wherein at least one constraint is an order-based constraint.