A New Implementation of Automath

This paper presents aut, a modern Automath checker. It is a straightforward re-implementation of the Zandleven Automath checker from the seventies. It was implemented about five years ago, in the programming language C. It accepts both the AUT-68 and AUT-QE dialects of Automath. This program was written to restore a damaged version of Jutting's translation of Landau's Grundlagen. Some notable features: It is fast. On a 1 GHz machine it will check the full Jutting formalization (736 K of nonwhitespace Automath source) in 0.6 seconds. Its implementation of -terms does not use named variables or de Bruijn indices (the two common approaches) but instead uses a graph representation. In this representation variables are represented by pointers to a binder. The program can compile an Automath text into one big Automath single line-style -term. It outputs such a term using de Bruijn indices. (These -terms cannot be checked by modern systems like Coq or Agda, because the -typed -calculi of de Bruijn are different from the -typed -calculi of modern type theory.)The source of aut is freely available on the Web at the address .     

External Rewriting for Skeptical Proof Assistants

This paper presents the design, the implementation, and experiments of the integration of syntactic, conditional possibly associative-commutative term rewriting into proof assistants based on constructive type theory. Our approach is called external because it consists in performing term rewriting in a specific and efficient environment and checking the computations later in a proof assistant. Two typical systems are considered in this work: ELAN, based on the rewriting calculus, as the term rewriting-based environment, and Coq, based on the calculus of inductive constructions as the proof assistant. We first formalize the proof terms for deduction by rewriting and strategies in ELAN using the rewriting calculus with explicit substitutions. We then show how these proof terms can soundly be translated into Coq syntax where they can be directly type checked. For the method to be applicable for rewriting modulo associativity and commutativity, we provide an effective method to prove equalities modulo these axioms in Coq using ELAN. These results have been integrated into an ELAN-based rewriting tactic in Coq.     

Automated Proof Construction in Type Theory Using Resolution

We provide techniques to integrate resolution logic with equality in type theory. The results may be rendered as follows. A clausification procedure in type theory, equipped with a correctness proof, all encoded using higher-order primitive recursion. A novel representation of clauses in minimal logic such that the -representation of resolution steps is linear in the size of the premisses. A translation of resolution proofs into lambda terms, yielding a verification procedure for those proofs. Availability of the power of resolution theorem provers in interactive proof construction systems based on type theory.     

Lower Bounds for the Weak Pigeonhole Principle and Random Formulas beyond Resolution

We work with an extension of Resolution, called Res(2), that allows clauses with conjunctions of two literals. In this system there are rules to introduce and eliminate such conjunctions. We prove that the weak pigeonhole principle PHP^cn_n and random unsatisfiable CNF formulas require exponential-size proofs in this system. This is the strongest system beyond Resolution for which such lower bounds are known. As a consequence to the result about the weak pigeonhole principle, Res(log) is exponentially more powerful than Res(2). Also we prove that Resolution cannot polynomially simulate Res(2) and that Res(2) does not have feasible monotone interpolation solving an open problem posed by Krají ek.     

ACJT群签名方案中成员撤消的高效实现

成员撤消问题是设计群签名方案中的一个难题,到目前为止尚无满意的解决办法.在ACJT群签名方案的基础上,提出了新的成员撤消方法.在新方案中,管理员在撤消一个成员时仅需要一次乘法运算来更新群公钥,签名和验证算法的计算量均独立于目前群成员个数和被撤消的成员个数,因而算法是高效的.以前的具有撤消成员功能的群签名方案,签名和验证算法的计算量要么依赖当前的群成员个数,要么依赖被撤消的群成员个数,而且群公钥的更新或者成员密钥的更新往往需要多次指数运算.     

不可满足公式的同态证明系统

合取范式(CNF)公式H到F的同态φ是一个从H的文字集合到F的文字集合的映射,并保持补运算和子句映到子句.同态映射保持一个公式的不可满足性.一个公式是极小不可满足的是指该公式本身不可满足,而且从中删去任意一个子句后得到的公式可满足.MU(1)是子句数与变元数的差等于1的极小不可满足公式类.一个三元组(H,φ,F)称为的一个来自H的同态证明,如果φ是一个从H到F的同态.利用基础矩阵的方法证明了:一个不可满足公式F的树消解证明,可以在多项式时间内转换成一个来自MU(1)中公式的同态证明.从而,由MU(1)中的公式构成的同态证明系统是完备的,并且由MU(1)中的公式构成的同态证明系统与树消解证明系统之间是多项式等价的.     

配电所微机自动化系统防雷概述

配电所微机综合自动化保护系统为电力系统安全可靠运行、故障快速处理提供了保障,为铁路通信、信号等设施的安全用电奠定了坚实基础,但雷击事件以其极高的电压幅值和不可预测性成为微机自动化系统的天敌,有效防止雷击,减少雷电干扰,成为影响配电所自动化系统安全运行的关键,本文对此进行了讨论。     

我国举证时限制度的立法现状及几点建议

举证时限制度是最高人民法院《关于民事诉讼证据的若干规定》中重点解决的问题之一,这一制度的确立,标志着我国举证责任制度从证据随时提出主义到证据适时提出主义的转变。章对举证时限制度的含义、立法目的、立法现状及完善等进行了探讨。     

可公开认证的密钥共享

文章基于椭圆曲线上离散对数的难解问题提出了一种公开认证协议，设计了公开可认证的密钥共享方案，任何人对参与者和管理者的数据都能进行认证。该方案可防欺诈，在现代网络通信中有较高的应用价值。     

A modal proof theory for final polynomial coalgebras

An infinitary proof theory is developed for modal logics whose models are coalgebras of polynomial functors on the category of sets. The canonical model method from modal logic is adapted to construct a final coalgebra for any polynomial functor. The states of this final coalgebra are certain “maximal” sets of formulas that have natural syntactic closure properties.

The syntax of these logics extends that of previously developed modal languages for polynomial coalgebras by adding formulas that express the “termination” of certain functions induced by transition paths. A completeness theorem is proven for the logic of functors which have the Lindenbaum property that every consistent set of formulas has a maximal extension. This property is shown to hold if the deducibility relation is generated by countably many inference rules.

A counter-example to completeness is also given. This is a polynomial functor that is not Lindenbaum: it has an uncountable set of formulas that is deductively consistent but has no maximal extension and is unsatisfiable, even though all of its countable subsets are satisfiable.