1010133
A fixpoint theory for non-monotonic parallelism
This paper studies parallel recursion. The trace specification language used in this paper incorporates sequentiality, nondeterminism, reactiveness (including infinite traces), three forms of parallelism (including conjunctive, fair-interleaving and synchronous parallelism) and general recursion. In order to use Tarski’s theorem to determine the fixpoints of recursions, we need to identify a well-founded partial order. Several orders are considered, including a new order called the lexical order, which tends to simulate the execution of a recursion in a similar manner as the Egli-Milner order. A theorem of this paper shows that no appropriate order exists for the language. Tarski’s theorem alone is not enough to determine the fixpoints of parallel recursions. Instead of using Tarski’s theorem directly, we reason about the fixpoints of terminating and nonterminating behaviours separately. Such reasoning is supported by the laws of a new composition called partition. We propose a fixpoint technique called the partitioned fixpoint, which is the least fixpoint of the nonterminating behaviours after the terminating behaviours reach their greatest fixpoint. The surprising result is that although a recursion may not be lexical-order monotonic, it must have the partitioned fixpoint, which is equal to the least lexicalorder fixpoint. Since the partitioned fixpoint is well defined in any complete lattice, the results are applicable to various semantic models. Existing fixpoint techniques simply become special cases of the partitioned fixpoint. For example, an Egli-Milnermonotonic recursion has its least Egli-Milner fixpoint, which can be shown to be the same as the partitioned fixpoint. The new technique is more general than the least Egli-Milner fixpoint in that the partitioned fixpoint can be determined even when a recursion is not Egli-Milner monotonic. Examples of non-monotonic recursions are studied. Their partitioned fixpoints are shown to be consistent with our intuition.
13475813
Compositional Reasoning for Pointer Structures
This paper studies the compositional definition and behaviour of properties that arise in pointer structures. A pointer structure is represented as a (pointer) graph. A pointer property is a set of pointer structures. A parameterised binary combinator is defined that enables important properties (like acyclicity, canonicity and reachability) to be defined in a compositional manner. The technique of parameterising a combinator derives from the definition of parallel-by-merge in ‘Unifying Theories of Programming'. It is applied here to the study of disjointness combinators that extend the separating conjunction of Separation Logic. A case study is provided to demonstrate how these ideas are used, in the form of rules of Hoare logic, to verify the correctness of an Object-Oriented program.
8852685
Generic Composition
Abstract. This paper presents a technique called generic composition to provide a uniform basis for modal operators, sequential composition, different kinds of parallel compositions and various healthiness conditions appearing in a variety of semantic theories. The weak inverse of generic composition is defined. A completeness theorem shows that any predicate can be written in terms of generic composition and its weak inverse. A number of algebraic laws that support reasoning are derived.
17662809
Hierarchical Organisation of Predicate-Semantic Models
This paper introduces techniques to organise predicate- semantic models in a hierarchical structure so that a new model can inherit the laws of the existing ones. Generic composition is used to simplify the manipulation of predicates. Necessary restrictions are imposed on the definition of each model so that the inheritance relation can be established by checking a few conditions on the healthiness conditions and the commands. Much of the checking can be supported by laws of generic composition. The techniques also help simplify the proof of well-definedness of program combinators (i.e. their closure in the semantic space) so that we no longer need to prove it (in predicate calculus) for every new model.
15862425
A Fixpoint Theory for Non-monotonic Parallelism
This paper studies parallel recursions. The trace specification language used in this paper incorporates sequentiality, nondeterminism, reactiveness (including infinite traces), conjunctive parallelism and general recursion. The language is the minimum of its kind and thus provides a context in which we can study parallel recursions in general. In order to use Tarski's theorem to determine the fixpoints of recursions, we need to identify a well-founded partial order. A theorem of this paper shows that no appropriate order exists. Tarski's theorem alone is not enough to determine the fixpoints of parallel recursions. Instead of using Tarski's theorem directly, we reason about the fixpoints of terminating and nonterminating behaviours separately. Such reasoning is supported by the laws of a new composition called partition. We propose a fixpoint technique called the partitioned fixpoint, which is the least fixpoint of the nonterminating behaviours after the terminating behaviours reach their greatest fixpoint. The surprising result is that although a recursion may not be monotonic with regard to the lexical order, it must have the partitioned fixpoint, which equals the least lexical-order fixpoint. Since the partitioned fixpoint is well defined in any complete lattice, the results are applicable to various semantic models. Major existing fixpoint techniques simply become special cases of the partitioned fixpoint. For example, an Egli-Milner-monotonic recursion has its least Egli-Milner fixpoint, which can be shown to be the same as the partitioned fixpoint. The new technique is more general than the least Egli-Milner fixpoint in that the partitioned fixpoint can be determined even when a recursion is not Egli-Milner monotonic. Examples of non-monotonic recursions with fair-interleaving parallelism are studied. Their partitioned fixpoints are shown to be consistent with our intuitions.
15321284
From Durational Specifications to TLA Designs of Timed Automata
Different temporal logics tend to emphasise different aspects of a hybrid system. In this paper, we study the predicative interpretation of Duration Calculus (DC) and Temporal Logic of Actions (TLA) and the link between them. A notation called generic composition is used to simplify the manipulation of predicates. The modalities of possibility and necessity become generic composition and its inverse of converse respectively. The transformation between different temporal logics is also characterised as such modalities. The formalism provides a framework in which human experience about hybrid system development can be formalised as refinement laws. A high-level durational specification can be decomposed to two durational specifications driven by an automaton. In such a stepwise design process, durational features are reduced while automaton features increase gradually. The application of the technique is demonstrated in the case study of the gas burner problem.
14170978
Improving Data Access Performance with Server Push Architecture
Data prefetching, where data is fetched before CPU demands for it, has been considered as an effective solution to mask data access latency. However, the current client-initiated prefetching strategies do not work well for applications with complex, non-contiguous data access patterns. While technology advances continue to enlarge the gap between computing and data access performance, trading computing power for data access delay has become a natural choice. We propose a server-based data-push approach. In this server-push architecture, a dedicated server named data push server (DPS) initiates and proactively pushes data closer to the client in time. We present the DPS architecture and study the issues such as what data to fetch, when to fetch, how to push, and data access modeling.
10107398
Yet Another Induction Algorithm
Inducing general functions from specific training examples is a central problem in the machine learning. Using sets of If-then rules is the most expressive and readable manner. To find If-then rules, many induction algorithms such as ID3, AQ, CN2 and their variants, were proposed. Sequential covering is the kernel technique of them. To avoid testing all possible selectors, Entropy gain is used to select the best attribute in ID3. Constraint of the size of star was introduced in AQ and beam search was adopted in CN2. These methods speed up their induction algorithms but many good selectors are filtered out. In this work, we introduce a new induction algorithm that is based on enumeration of all possible selectors. Contrary to the previous works, we use pruning power to reduce irrelative selectors. But we can guarantee that no good selectors are filtered out. Comparing with other techniques, the experiment results demonstrate that the rules produced by our induction algorithm have high consistency and simplicity.
1752675
Storing and Discovering Critical Workflows from Log in Scientific Exploration
This paper aims at effectively reproducing the results of previous scientific workflow executions. We first identify the information that needs to be recorded in a workflow execution log, based on which we then determine the data flow among experiments. To effectively record a workflow execution log in a relational database management system (RDBMS) when the workflow design is absent, we propose a generic relational storage schema. Then techniques have been designed to automatically discover the minimal set of experiments that must be performed in order to reproduce a scientific result by posing appropriate SQL queries. Although such SQL queries can be evaluated using an off-the-shelf database system, we investigate the unique characteristics of the workflow log data and optimization techniques for evaluating such SQL queries efficiently.
2308649
Subgoal ordering and granularity control for incremental planning
In this paper, we study strategies in incremental planning for ordering and grouping subproblems partitioned by the subgoals of a planning problem when each sub-problem is solved by a basic planner. To generate a rich set of partial orders for ordering subproblems, we propose a new ordering algorithm based on a relaxed plan built from the initial state to the goal state. The new algorithm considers both the initial and the goal states and can effectively order subgoals in such a way that greatly reduces the number of invalidations during incremental planning. We have also considered trade-offs between the granularity of the subgoal sets and the complexity of solving the overall planning problem. We show an optimal region of grain size that minimizes the total complexity of incremental planning. We propose an efficient strategy to dynamically adjust the grain size in partitioning in order to operate in this optimal region. We further evaluate a redundant-execution scheme that uses two different subgoal orders in order to improve the quality of the plans generated without greatly sacrificing run-time efficiency. Experimental results on using three basic planners (metric-FF, YAHSP, and LPG-TD-speed) show that our strategies are general for improving the time and quality of each of these planners across various benchmarks
11734040
Analyzing Security Protocols Using Association Rule Mining
Current studies to analyzing security protocols using formal methods require users to predefine authentication goals. Besides, they are unable to discover potential correlations between secure messages. This research attempts to analyze security protocols using data mining. This is done by extending the idea of association rule mining and converting the verification of protocols into computing the frequency and confidence of inconsistent secure messages. It provides a novel and efficient way to analyze security protocols and find out potential correlations between secure messages. The conducted experiments demonstrate our approaches.