Dependent type systems are the basis of many proof development environments. In Aspinalland Compagnoni's paper, a system λP≤ is proposed as a subtyping extension of the first orderdependent type system λP (also...Dependent type systems are the basis of many proof development environments. In Aspinalland Compagnoni's paper, a system λP≤ is proposed as a subtyping extension of the first orderdependent type system λP (also called An). λP≤ has nice meta-theoretic properties includingsubject reduction and decidability. In this article, v,e give a reformulation of λP≤ t called λII≤.The advantages of λII< include: type level transitivity elimination property and pretypesbasedsubtyping system. These features considerably faCilitate the met-theoretical study and furtherextensions of this system.展开更多
We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional ...We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional γ slack cells without quotas. For any given and , in our Model I we determine the waiting time until at least frequency cells and at least run cells reach their quotas. For any given τ ≤ α + β, in our Model II we determine the waiting time until τ cells reach their quotas. Computer algorithms are developed to calculate the distributions, expectations and standard deviations of the waiting time random variables of the two models. Numerical results demonstrate the efficiency of the algorithms.展开更多
文摘Dependent type systems are the basis of many proof development environments. In Aspinalland Compagnoni's paper, a system λP≤ is proposed as a subtyping extension of the first orderdependent type system λP (also called An). λP≤ has nice meta-theoretic properties includingsubject reduction and decidability. In this article, v,e give a reformulation of λP≤ t called λII≤.The advantages of λII< include: type level transitivity elimination property and pretypesbasedsubtyping system. These features considerably faCilitate the met-theoretical study and furtherextensions of this system.
文摘We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional γ slack cells without quotas. For any given and , in our Model I we determine the waiting time until at least frequency cells and at least run cells reach their quotas. For any given τ ≤ α + β, in our Model II we determine the waiting time until τ cells reach their quotas. Computer algorithms are developed to calculate the distributions, expectations and standard deviations of the waiting time random variables of the two models. Numerical results demonstrate the efficiency of the algorithms.
