Modern multiprocessors deploy a variety of weak memory models(WMMs).Total Store Order(TSO)is a widely-used weak memory model in SPARC implementations and x86 architecture.It omits the store-load constraint by allowing...Modern multiprocessors deploy a variety of weak memory models(WMMs).Total Store Order(TSO)is a widely-used weak memory model in SPARC implementations and x86 architecture.It omits the store-load constraint by allowing each core to employ a write buffer.In this paper,we apply Unifying Theories of Programming(abbreviated as UTP)in investigating the trace semantics for TSO,acting in the denotational semantics style.A trace is expressed as a sequence of snapshots,which records the changes in registers,write buffers and the shared memory.All the valid execution results containing reorderings can be described after kicking out those that do not satisfy program order and modification order.This paper also presents a set of algebraic laws for TSO.We study the concept of head normal form,and every program can be expressed in the head normal form of the guarded choice which is able to model the execution of a program with reorderings.Then the linearizability of the TSO model is supported.Furthermore,we consider the linking between trace semantics and algebraic semantics.The linking is achieved through deriving trace semantics from algebraic semantics,and the derivation strategy under the TSO model is provided.展开更多
ZooKeeper Atomic Broadcast (Zab) is an atomic broadcast protocol specially designed for ZooKeeper, which supports additional crash recovery. This protocol actually has been widely adopted by famous Internet companies,...ZooKeeper Atomic Broadcast (Zab) is an atomic broadcast protocol specially designed for ZooKeeper, which supports additional crash recovery. This protocol actually has been widely adopted by famous Internet companies, but there are few studies on the correctness and credibility of the Zab protocol, and thus we utilize formal methods to study the correctness. In this paper, Zab, Paxos and Raft are all analyzed and compared to help better understand the Zab protocol. Then we model the Zab protocol with TLA+ and verify three properties abstracted from the specification by the model checker TLC, including two liveness properties and one safety property. The final experimental results can prove that the design of the protocol conforms to the original requirements. This paper makes up for the analysis of formal methods in the Zab protocol.展开更多
基金supported by the National Key Research and Development Program of China under Grant No.2018YFB2101300the National Natural Science Foundation of China under Grant Nos.61872145 and 62032024Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213.
文摘Modern multiprocessors deploy a variety of weak memory models(WMMs).Total Store Order(TSO)is a widely-used weak memory model in SPARC implementations and x86 architecture.It omits the store-load constraint by allowing each core to employ a write buffer.In this paper,we apply Unifying Theories of Programming(abbreviated as UTP)in investigating the trace semantics for TSO,acting in the denotational semantics style.A trace is expressed as a sequence of snapshots,which records the changes in registers,write buffers and the shared memory.All the valid execution results containing reorderings can be described after kicking out those that do not satisfy program order and modification order.This paper also presents a set of algebraic laws for TSO.We study the concept of head normal form,and every program can be expressed in the head normal form of the guarded choice which is able to model the execution of a program with reorderings.Then the linearizability of the TSO model is supported.Furthermore,we consider the linking between trace semantics and algebraic semantics.The linking is achieved through deriving trace semantics from algebraic semantics,and the derivation strategy under the TSO model is provided.
基金This work was partly supported by the National Key Research and Development Program of China under Grant No.2018YFB2101300the National Natural Science Foundation of China under Grant No.61872145+1 种基金Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213the Fundamental Research Funds for the Central Universities of China.
文摘ZooKeeper Atomic Broadcast (Zab) is an atomic broadcast protocol specially designed for ZooKeeper, which supports additional crash recovery. This protocol actually has been widely adopted by famous Internet companies, but there are few studies on the correctness and credibility of the Zab protocol, and thus we utilize formal methods to study the correctness. In this paper, Zab, Paxos and Raft are all analyzed and compared to help better understand the Zab protocol. Then we model the Zab protocol with TLA+ and verify three properties abstracted from the specification by the model checker TLC, including two liveness properties and one safety property. The final experimental results can prove that the design of the protocol conforms to the original requirements. This paper makes up for the analysis of formal methods in the Zab protocol.
