Controllability of predicates and languages in discrete-event systems

In discrete-event systems, two control techniques, called supervisory control and state feedback logic, are applicable if control specifications are given in terms of predicates on the set of states. The concepts of controllability for both techniques has been proposed for the analysis and design of these techniques. First it is shown that controllability of the legal language for a given predicate is equivalent to that for the corresponding reachability set. Next we deal with the relationship between the supremal controllable subpredicate of the predicate and the supremal controllable sublanguage of the corresponding legal language     

Controllability and control-invariance in discrete-event systems

Recently, for discrete-event systems modelled by automata, Ramadge and Wonham (1987 a, b) have proposed two control techniques called ‘supervisory control’ and ‘state feedback logic’. If control specifications are given in terms of predicates on the set of states, both techniques are applicable. This paper discusses the relationship between these techniques. It is shown that the language accepted by the discrete-event system with maximally permissive feedback is equal to the supremal controllable language if the predicate is control invariant. Moreover, it is shown that the predicate is control invariant if there exists a controllable language with a certain condition on the set of reachable states, but the converse does not hold in general     

Efficient Detection of Channel Predicates in Distributed Systems

This paper discusses efficient detection of global predicates in a distributed program. Previous work in this area required predicates to be specified as a conjunction of predicates defined on individual processes. Many properties in distributed systems, however, use the state of channels, such as “the channel is empty,” or “there is a token in the channel.” In this paper, we introduce the concept of alinearchannel predicate and provide efficient centralized and distributed algorithms to detect any conjunction of local and linear channel predicates. The class of linear predicates is fairly broad. For example, classic problems such as detection of termination and computation of global virtual time are instances of conjunctions of linear channel predicates. Linear predicates can be functions of the number of messages in the channel, or can be based upon the actual contents of the messages. The main application of our results are in debugging and testing of distributed programs. For these applications it is important to detect thefirststate where some predicate is true. We show that this first state is uniquely defined if and only if linear predicates are used.     

Predicate-transformer semantics of general recursion

Summary We develop the semantics of a language with arbitrary atomic statements, unbounded nondeterminacy, and mutual recursion. The semantics is expressed in weakest preconditions and weakest liberal preconditions. Individual states are not mentioned. The predicates on the state space are treated as elements of a distributive lattice. The semantics of recursion is constructed by means of the theorem of Knaster-Tarski. It is proved that the law of the excluded miracle can be preserved, if that is wanted. The universal conjunctivity of the weakest liberal precondition, and the connection between the weakest precondition and the weakest liberal precondition are proved to remain valid. Finally we treat Hoare-triple methods for proving correctness and conditional correctness of programs.     

Detection of weak unstable predicates in distributed programs

This paper discusses detection of global predicates in a distributed program. Earlier algorithms for detection of global predicates proposed by Chandy and Lamport (1985) work only for stable predicates. A predicate is stable if it does not turn false once it becomes true. Our algorithms detect even unstable predicates, without excessive overhead. In the past, such predicates have been regarded as too difficult to detect. The predicates are specified by using a logic described formally in this paper. We discuss detection of weak conjunctive predicates that are formed by conjunction of predicates local to processes in the system. Our detection methods will detect whether such a predicate is true for any interleaving of events in the system, regardless of whether the predicate is stable. Also, any predicate that can be reduced to a set of weak conjunctive predicates is detectable. This class of predicates captures many global predicates that are of interest to a programmer. The message complexity of our algorithm is bounded by the number of messages used by the program. The main applications of our results are in debugging and testing of distributed programs. Our algorithms have been incorporated in a distributed debugger that runs on a network of Sun workstations in UNIX     

On the Approximation Resistance of a Random Predicate

A predicate is called approximation resistant if it is NP-hard to approximate the corresponding constraint satisfaction problem significantly better than what is achieved by the naive algorithm that picks an assignment uniformly at random. In this paper we study predicates of Boolean inputs where the width of the predicate is allowed to grow. Samorodnitsky and Trevisan proved that, assuming the Unique Games Conjecture, there is a family of very sparse predicates that are approximation resistant. We prove that, under the same conjecture, any predicate implied by their predicate remains approximation resistant and that, with high probability, this condition applies to a randomly chosen predicate.     

Control synthesis of timed discrete event systems based onpredicate invariance

In this paper, arc-timed Petri nets are used to model controlled real-time discrete event systems, and the control synthesis problem that designs a controller for a system to satisfy its given closed-loop behavior specification is addressed. For the problem with the closed-loop behavior specified by a state predicate, real-time control-invariant predicates are introduced, and a fixpoint algorithm to compute the unique extremal control-invariant subpredicate of a given predicate, key to the control synthesis, is presented. For the problem with the behavior specified by a labeled arc-timed Petri net, it is shown that the control synthesis problem can be transformed into one that synthesizes a controller for an induced arc-timed Petri net with a state predicate specification. The problem can then be solved by using the fixpoint algorithm as well. The algorithm involves conjunction and disjunction operations of polyhedral sets and can be algorithmically implemented, making automatic synthesis of controllers for real-time discrete event systems possible.     

A method for the modular synthesis of controllers for timed discrete-event systems

A method for the modular supervisory control of timed discrete-event systems (TDES) is presented. The modular synthesis method is an extension of the centralized synthesis method proposed in our earlier work. We consider a state predicate specification as a conjunction of several state subpredicate specifications. The control problem is to synthesize a modular controller, the conjunction of all individual controllers, in such a way that the closed-loop behaviour of TDES satisfies the state predicate specification. Our modular synthesis method is developed based on the concept of state space of TDES, the notion of control-invariant state predicates for the TDES and a fixed point algorithm to calculate a control-invariant state subpredicate of a given state predicate. In addition, for the development of our modular synthesis method, we introduce the notion of control-invariance non-conflict among control-invariant state predicates, and the notion of forcing-non-conflict among controllers synthesized based on control-invariant state predicates which are control-invariance non-conflicting. The modular synthesis method in general offers better design flexibility and may require fewer computations than the centralized one. As in our centralized synthesis method, the proposed modular synthesis method does not require the construction and examination of complete sequences of event trajectories of the system. It is suggested that the computation of our proposed method of yielding solutions for a class of synthesis problems in TDES can be economical.     

Question-guided stubborn set methods for state properties

This paper presents two stubborn set methods for alleviating the state explosion problem when reasoning about state properties. The first method makes it possible to determine whether a state of the system is reachable in which a given state predicate holds. The second method makes it possible to determine if from all reachable states it is possible to reach a state where a given state predicate holds. The novelty of the two methods is that they rely on so-called up sets and down sets rather than the notion of visible transitions which causes earlier methods to give only limited reduction of the state space, especially when considering state predicates referring to many of the state variables of the system. The suggested stubborn set methods have been implemented in the LoLA tool, and we report on some experimental results obtained with this computer tool together with some general guidance for applying the two question-guided stubborn set methods and their different implementations in verification. The two methods are presented in the context of Petri Nets, but are applicable also to other state and action oriented modelling formalisms for which the basic stubborn set theory is applicable.

Efficient distributed detection of conjunctions of local predicates

Global predicate detection is a fundamental problem in distributed systems and finds applications in many domains such as testing and debugging distributed programs. This paper presents an efficient distributed algorithm to detect conjunctive-form global predicates in distributed systems. The algorithm detects the first consistent global state that satisfies the predicate even if the predicate is unstable. Unlike previously proposed run-time predicate detection algorithms, our algorithm does not require the exchange of control messages during the normal computation. All the necessary information to detect predicates is piggybacked on computation messages of application programs. The algorithm is distributed because the predicate detection efforts as well as the necessary information are equally distributed among the processes. We prove the correctness of the algorithm and compare its performance with respect to message, storage and computational complexities with that of the previously proposed run-time predicate detection algorithms     

众包环境下多谓词查询优化

近年来,众包查询优化得到了数据库领域的广泛关注。主要研究了众包多谓词选择查询问题--借助于人力找到满足多谓词查询条件的对象。一种简单的方法是枚举数据集中的对象,对于每个对象判断是否满足每条谓词。它产生的代价是[|R|?n],其中[|R|]为数据集中对象的数量,[n]为谓词的数量。很显然,当处理大数据集或者查询包含较多谓词的时候,简单方法的代价是非常昂贵的。由于不同的谓词具有不同的选择性,如果首先验证高选择性的谓词,那么在验证剩余谓词的时候,就可以避免验证不满足高选择性谓词的对象。因此,采用一个好的谓词顺序实现众包选择查询可以显著减少人工代价。然而,实际中很难获得最佳的谓词序列。针对该问题,提出了一种基于采样的框架来获得高质量的查询序列。为了控制查询序列生成的成本,设计了基于随机序列的最优选择方法,该方法通过随机选择序列获得最终的谓词顺序。由于基于随机序列的选择方法可能产生较大的代价,为了减少开销,提出了一种基于过滤的序列选择方法。通过在众包平台上使用真实数据集评测了提出的方法,实验结果表明,该方法能够显著减少查询序列生成的代价,同时获得高质量的查询序列。     

A Pattern-Weight Formulation of Search Knowledge

Pattern-weight pairs (PWs) are a new form of search and planning knowledge. PWs are predicates over states coupled with a least upper bound on the distance from any state satisfying that predicate to any goal state. The relationship of PWs to more traditional forms of search knowledge is explored with emphasis on macros and subgoals. It is shown how PWs may be used to overcome some of the difficulties associated with macro-tables and lead to shorter solution paths without replanning. An algorithm is given for converting a macro-table to a more powerful PW set. Superiority over the Squeeze algorithm is demonstrated. It is also shown how PWs provide a mechanism for achieving dynamic subgoaling through the combination of knowledge from multiple alternative subgoal sequences. The flexibility and execution time reasoning provided by PWs may have significant use in reactive domains. The main cost associated with PWs is the cost of applying them at execution time. An associative retrieval algorithm is given that expedites this matching-evaluation process. Empirical results are provided which demonstrate asymptotically improving performance with problem size of the PW technique over macro-tables.     

An efficient distributed online algorithm to detect strong conjunctive predicates

Detecting strong conjunctive predicates is a fundamental problem in debugging and testing distributed programs. A strong conjunctive predicate is a logical statement to represent the desired event of the system. Therefore, if the predicate is not true, an error may occur because the desired event does not happen. Recently, several reported detection algorithms reveal the problem of unbounded state queue growth since the system may generate a huge number of execution states in a very short time. In order to solve this problem, this paper introduces the notion of removable states which can be disregarded in the sense that detection results still remain correct. A fully distributed algorithm is developed in this paper to perform the detection in an online manner. Based on the notion of removable states, the time complexity of the detection algorithm is improved as the number of states to be evaluated is reduced.     

Predicate control: synchronization in distributed computations with look-ahead

The predicate control problem involves synchronizing a distributed computation to maintain a given global predicate. In contrast with many popular distributed synchronization problems such as mutual exclusion, readers writers, and dining philosophers, predicate control assumes a look-ahead, so that the computation is an off-line rather than an on-line input. Predicate control is targeted towards applications such as rollback recovery, debugging, and optimistic computing, in which such computation look-ahead is natural.We define predicate control formally and show that, in its full generality, the problem is NP-complete. We find efficient solutions for some important classes of predicates including “disjunctive predicates”, “mutual exclusion predicates”, and “readers writers predicates”. For each class of predicates, we determine the necessary and sufficient conditions for solving predicate control and describe an efficient algorithm for determining a synchronization strategy. In the case of “independent mutual exclusion predicates”, we determine that predicate control is NP-complete and describe an efficient algorithm that finds a solution under certain constraints.     

基于谓词切片的字符串测试数据自动生成

字符串谓词使用相当普遍，如何实现字符串测试数据的自动生成是一个有待解决的问题，针对字符串谓词，讨论了路径Path上给定谓词的谓词切片的动态生成算法，以及基于谓词切片的字符串测试数据自动生成方法，并给出了字符串间距离的定义，利用程序DUC（Definithon-Use-Control)表达式，构造谓词的谓词切片，对任意的输入，通过执行谓词切片，获取谓词中变量的当前值，进而对谓词中变量的每一字符进行分支函数极小化，动态生成给定字符串谓词边界的ON－OFF测试点，实验表明，该方法是行之有效的。     

Alternating states for dual nondeterminism in imperative programming

The refinement calculus of Back, Morgan, Morris, and others is based on monotone predicate transformers (weakest preconditions) where conjunctions stand for demonic choices between commands and disjunctions for angelic choices. Arbitrary monotone predicate transformers cannot be modelled by relational semantics but can be modelled by so-called multirelations. Results of Morris indicate, however, that the natural domain for the combination of demonic and angelic choice is the free distributive completion (FDC) of the state space.The present paper provides a new axiomatization and more explicit construction of the FDC of an arbitrary ordered set. The FDC concept is self-dual, but the construction is not. We therefore determine the duality function from the FDC to the dual of the FDC of the dual ordered set. The elements of the FDC are classified according to their conjunctivity and disjunctivity. The theory is applied to imperative programming with operators for sequential composition and demonic and angelic choice. The theory based on the FDC is shown to be equivalent to a weakest precondition theory for up-closed predicates. If the order is discrete (i.e., the equality relation), the FDC turns out to be the domain of the choice semantics of Back and von Wright, whereas up-closed multirelations are functions towards this domain.     

Domain semantics of possibility computations

The purpose of this paper is to introduce a kind of computational model, called possibility computation, to deal with non-determinism. Both its denotational and logical semantics in the framework of domain theory are established and their equivalence is verified. In this approach, the denotational semantics will be set up by assigning to programs possibility state transformers, i.e., Scott-continuous functions from the domain of input states to the possibility powerdomain of the codomain of final states. This possibility powerdomain of a dcpo will consist of all possibility valuations, ordered pointwise, of this dcpo. The logical semantics will be given by fuzzy predicate transformers introduced by the first author and Jung following Dijkstra’s predicate transformers. Two semantics equivalence will be verified in terms of the integration of fuzzy predicates with respect to possibility valuations. The categorical monad of the possibility powerdomain will be investigated.     

Intractability results in predicate detection

It has been shown that global predicate detection in a distributed computation is an NP-complete problem in general. However, efficient predicate detection algorithms exist for some subclasses of predicates, such as stable predicates, observer-independent predicates, conjunctions of local predicates, channel predicates, etc. We show here that the problem of deciding whether a given predicate is a member of any of these tractable subclasses is NP-hard in general.We also explore the tractability of linear and regular predicates. In particular, we show that, unless RP=NP, there is no polynomial-time algorithm to detect for linear and regular predicates B.     

基于与状态无关的激活集的包含派生谓词的规划问题求解

派生谓词是PDDL2．2语言的新特性之一。在2004年的规划大赛IPC-4上,许多规划系统都无法求解包含派生谓词的两个标准竞赛问题。在经典规划中,派生谓词是指不受领域动作直接影响的谓词,它们在当前状态下的真值是在封闭世界假设中由某些基本谓词通过领域公理推导出来的。本文提出一种新的方法来求解包含派生谓词的规划问题,即用与状态无关的激活集来取代派生谓词用于放宽式规划中。     

基于STRIPS的领域知识提取策略

提出了谓词之间的一种相似关系,并用该相似关系得到可实现某谓词的动作集.利用该动作集中所有动作的公共前提谓词和公共效果谓词,提取出隐含在动作描述中的领域知识,并给出了描述领域知识的一种形式化方法.最后,对具体的规划问题,可利用领域知识判断出初始状态或目标状态中存在的矛盾.该领域知识的提取策略已应用于智能规划器StepByStep之中,所获取的领域知识对选择待实现的谓词提供了必要的理论依据.