Batched evaluation of linear tabled logic programs

Logic programming languages, such as Prolog, provide a high-level, declarative approach to programming. Logic Programming offers great potential for implicit parallelism, thus allowing parallel systems to often reduce a program's execution time without programmer intervention. We believe that for complex applications that take several hours, if not days, to return an answer, even limited speedups from parallel execution can directly translate to very significant productivity gains. It has been argued that Prolog's evaluation strategy – SLD resolution – often limits the potential of the logic programming paradigm. The past years have therefore seen widening efforts at increasing Prolog's declarativeness and expressiveness. Tabling has proved to be a viable technique to efficiently overcome SLD's susceptibility to infinite loops and redundant subcomputations. Our research demonstrates that implicit or-parallelism is a natural fit for logic programs with tabling. To substantiate this belief, we have designed and implemented an or-parallel tabling engine – OPTYap – and we used a shared-memory parallel machine to evaluate its performance. To the best of our knowledge, OPTYap is the first implementation of a parallel tabling engine for logic programming systems. OPTYap builds on Yap's efficient sequential Prolog engine. Its execution model is based on the SLG-WAM for tabling, and on the environment copying for or-parallelism. Preliminary results indicate that the mechanisms proposed to parallelize search in the context of SLD resolution can indeed be effectively and naturally generalized to parallelize tabled computations, and that the resulting systems can achieve good performance on shared-memory parallel machines. More importantly, it emphasizes our belief that through applying or-parallelism and tabling to logic programs the range of applications for Logic Programming can be increased.

This article presents some basic aspects of the proof theory of first order logic programming. We start off from general resolution, unit resolution, input resolution and SLD resolution. Then we turn to the sequent calculus and its relationship to resolution and present deductive systems for logic programs (with negation). After discussing partiality in logic programming, this article ends with the introduction of inductive extensions of logic programs, which provide a powerful proof-theoretic framework for logic programming.

We show how the language Constraint Handling Rules (CHR), a high-level logic language for the implementation of constraint solvers, can be slightly extended to become a general-purpose logic programming language with an expressive power subsuming the expressive ower of Horn clause programs with SLD resolution. The extended language, called “CHR∀”, retains however the extra features of CHR, e.g., committed choice and matching, which axe important for other purposes, especially for efficiently solving constraints. CHR∀ turns out to be a very flexible query language in the sense that it supports several (constraint) logic programming paradigms and allows to mix them in a single program. In particular, it supports top-down query evaluation and also bottom-up evaluation as it is frequently used in (disjunctive) deductive databases.

SLD resolution with negation as finite failure (SLDNF) reflects the procedural interpretation of predicate calculus as a programming language and forms the computational basis for Prolog systems. Despite its advantages for stack-based memory management, SLDNF is often not appropriate for query evaluation for three reasons: (a) it may not terminate due to infinite positive recursion; (b) it may be terminate due to infinite recursion through negation; and (c) it may repeatedly evaluate the same literal in a rule body, leading to unacceptable performance.We address all three problems for goal-oriented query evaluation of general logic programs by presenting tabled evaluation with delaying, called SLG resolution. It has three distinctive features:(i) SLG resolution is a partial deduction procedure, consisting of seven fundamental transformations. A query is transformed step by step into a set of answers. The use of transformations separates logical issues of query evaluation from procedural ones. SLG allows an arbitrary computation rule for selecting a literal from a rule body and an arbitrary control strategy for selecting transformations to apply.(ii) SLG resolution is sound and search space complete with respect to the well-founded partial model for all non-floundering queries, and preserves all three-valued stable models. To evaluate a query under differenc three-valued stable models, SLG resolution can be enhanced by further processing of the answers of subgoals relevant to a query.(iii) SLG resolution avoids both positive and negative loops and always terminates for programs with the bounded-term-size property. It has a polynomial time data complexity for well-founded negation of function-free programs. Through a delaying mechanism for handling ground negative literals involved in loops, SLG resolution avoids the repetition of any of its derivation steps.Restricted forms of SLG resolution are identified for definite, locally stratified, and modularly stratified programs, shedding light on the role each transformation plays.

This paper proposes a novel class of wavelength scheduling algorithms in optical burst switching networks. The proposed wavelength scheduling algorithms process a batch of data bursts together instead of processing them one by one. When a control burst with a reservation request arrives to a batch scheduler, the scheduler waits for a small amount of time, called the acceptance delay, before deciding to accept or reject the reservation request. After the acceptance delay has passed, the scheduler processes all the reservation requests that have arrived during the acceptance delay, then it accepts the requests that will maximize the utilization of the wavelength channels. We describe an optimal batch scheduler that serves as an upper bound on the performance of batch scheduling algorithms. Furthermore, we introduce four novel heuristic batch scheduling algorithms. The bursts of the proposed algorithms is evaluated using a discrete-event simulation model. Simulation results suggest that batch schedulers could decrease the blocking probability by 25% compared the best previously known wavelength scheduling algorithm.

Previously proposed wavelength scheduling algorithms in optical burst switching networks process each reservation request individually and in a greedy manner. In this paper we propose a new family of wavelength scheduling algorithms that process a batch of reservation requests together instead of processing them one by one. When a control burst with a reservation request arrives to a free batch scheduler, the scheduler waits for a small amount of time, called the acceptance delay, before deciding to accept or reject the reservation request. After the acceptance delay has passed, the scheduler processes all the reservation requests that have arrived during the acceptance delay, then it accepts the requests that will maximize the utilization of the wavelength channels. We describe an optimal batch scheduler that serves as an upper bound on the performance of batch scheduling algorithms. Furthermore, we introduce two heuristic batch scheduling algorithms. The performance of the proposed algorithms is evaluated using a discrete-event simulation model. Simulation results suggest that batch schedulers could decrease the blocking probability by 25% compared to the best previously known wavelength scheduling algorithm.

Tableau-based proof systems can be elegantly speci ed and directly executed by a tabled Logic Programming (LP) system. Our experience with the XMC model checker shows that such an encoding can be used to search for the existence of a proof very eAEciently. However, the users of a tableau system are often interested in getting suAEcient evidence (in terms of the tableau proof rules) on why a proof does or does not exist. In this paper, we address the problem of constructing such an evidence without introducing any additional computational overhead to the proof search. A tabled LP system maintains a memo table of \lemmas that were tried and possibly proved during query evaluation. We propose the concept of justi er for extracting suAEcient evidence for the truth or falsehood of literals in a logic program, by post-processing the memo tables created during query evaluation. Based on this logic program justi er, we show how to construct evidence for the presence/absence of tableau in a tableau-based proof system. We provide experimental results showing the e ectiveness of the justi er in constructing succinct evidence of the evaluation performed by the XMC model checker. Finally we discuss the role of the justi er as a programming abstraction for encoding efcient algorithms as tabled logic programs.

In typical optical burst switching (OBS) networks a reservation request is either accepted or rejected as soon as it is presented to the employed wavelength scheduling algorithm. This paper proposes a class of wavelength scheduling algorithms that process a batch of data bursts together instead of processing them one by one. When a control burst with a reservation request arrives to a free batch scheduler, the scheduler waits for a small amount of time, called the acceptance delay, before deciding to accept or reject the reservation request. After the acceptance delay has passed, the scheduler processes all the reservation requests that have arrived during the acceptance delay period, then it accepts the requests that maximizes the utilization of the wavelength channels. We describe an optimal batch scheduler that serves as an upper bound on the performance of batch scheduling algorithms. Furthermore, we introduce two novel heuristic batch scheduling algorithms. Simulation results suggest that batch schedulers could decrease the blocking probability by 25% compared to the best previously known wavelength scheduling algorithm

Grid enables resource sharing and dynamic allocation of computational resources. It is a great challenge to make numerous resources available on-demand to guarantee the Quality-of-Service for jobs. This paper presents a two-stage optimization model for resource allocation in grid. Job constraints are classified into mandatory constraints and negotiated constraints. In the first stage, a preprocessing procedure such as resource discovery deals with the mandatory constraints. This has been fulfilled as our previous work. In the second stage, negotiated constraints are treated as Knapsack Problem-based optimization problem. Centralized scheduling and decentralized scheduling have been considered in this paper. This work is fulfilled as part of the Constellation Model for grid resource management. We formulate centralized scheduling as Multi-Constraint Multiple Knapsack Problem (MCMKP). In centralized scheduling, jobs are submitted to a global job queue. A global scheduler assigns each job to a proper grid site according to the scheduling strategy. The scheduling is done periodically (e.g. daily or weekly). We formulate decentralized scheduling as Multi-Dimensional Knapsack Problem (MDKP). In decentralized scheduling, jobs are submitted to local job queues. Allocation decisions are made by local schedulers individually. Jobs that can not be executed immediately are sent to a global waiting queue. When local scheduling is initialized, a local scheduler can select jobs from both the local job queue and the global waiting queue. Objectives of both centralized scheduling and decentralized scheduling are to optimize the utility defined by a grid economy approach. The defined utility makes the trade-offs between user-concerned metrics and system-concerned metrics. Heuristic algorithms such as Very Large-Scale Neighborhood Search proposed by R. K. Ahuja and C. B. Cunha [2005] can be used to solve the combinatorial optimization problem. We implemented a prototype of the Constellation Model. Genetic algorithms for constrained optimization which is proposed by S. Venkatraman and G. G. Yen [2005] have been implemented to solve the above optimization problems. Experimental results show that, performance metrics such as gained utility, response rate, and resource utilization are improved and resources are allocated in an optimal way.

In hard real-time systems, the importance of meeting a task execution deadline is a central issue for correctness and reliability of such systems. The focus of this research is to design and implement a real-time system which utilizes a set of mobile robots that are performing individual and common critical tasks. Specifically, a scheduling scheme consists of local and global schedulers is developed to schedule critical tasks using a transputer-based machine. To guarantee execution of critical tasks within the requested time frame, each task is provided with a Safety Time Factor (STF) based on its worst-case computation time. This STF can be added to the execution time of a newly arrived task if its deadline and the status of scheduled tasks allow. The local scheduler takes the advantages of accumulated safety times and provides alternatives for scheduling sporadic critical tasks. The performance of the model is evaluated in terms of the number of critical tasks that are guaranteed and executed by local processors. >

In this paper, we conduct an in-depth evaluation of a broad spectrum of scheduling alternatives for clusters. These include the widely used batch scheduling, local scheduling, gang scheduling, all prior communication-driven coscheduling algorithms (Dynamic Coscheduling (DCS), Spin Block (SB), Periodic Boost (PB), and Co-ordinated Coscheduling (CC)) and a newly proposed HYBRID coscheduling algorithm on a 16-node, Myrinet-connected Linux cluster. Performance and energy measurements using several NAS, LLNL and ANL benchmarks on the Linux cluster provide several interesting conclusions. First, although batch scheduling is currently used in most clusters, all blocking-based coscheduling techniques such as SB, CC and HYBRID and the gang scheduling can provide much better performance even in a dedicated cluster platform. Second, in contrast to some of the prior studies, we observe that blocking-based schemes like SB and HYBRID can provide better performance than spin-based techniques like PB on a Linux platform. Third, the proposed HYBRID scheduling provides the best performance-energy behavior and can be implemented on any cluster with little effort. All these results suggest that blocking-based coscheduling techniques are viable candidates to be used in clusters for significant performance-energy benefits.

Nominal logic is a variant of first-order logic with special facilities for reasoning about names and binding based on the underlying concepts of swapping and freshness. It serves as the basis of logic programming and term rewriting techniques that provide similar advantages to, but remain simpler than, higher-order logic programming or term rewriting systems. Previous work on nominal rewriting and logic programming has relied on nominal unification, that is, unification up to equality in nominal logic. However, because of nominal logic's equivariance property, these applications require a stronger form of unification, which we call equivariant unification. Unfortunately, equivariant unification and matching are NP-hard decision problems. This paper presents an algorithm for equivariant unification that produces a complete set of finitely many solutions, as well as NP decision procedure and a version that enumerates solutions one at a time. In addition, we present a polynomial time algorithm for swapping-free equivariant matching, that is, for matching problems in which the swapping operation does not appear.

Guest Editorial: Situational awareness of integrated energy systems

Enhanced wireless communication improves the connectivity of vehicular networks in which vehicles are utilized as infrastructures for communication and computation. Thus, a new concept “Vehicular Edge Computing (VEC)” is formed. As VEC utilizes a collaborative multitude of near-user edge resources (i.e. vehicles) in the Internet of Vehicles, the capability of these joint resources becomes heterogeneous especially in their movements. Therefore, one critical problem is how to efficiently schedule each task under such mobile environments. For the reason, we propose a hybrid dynamic scheduling scheme (HDSS) that has the ability to optimize the task scheduling dynamically based on the changeable system environments. HDSS provides a decision function (DF) to select a better-performed scheduling algorithm from two provided candidates: the queue-based dynamic scheduling (QDS) algorithm and the time-based dynamic scheduling (TDS). QDS coincides with the Join-the-Shortest Queue scheme, which decides the scheduling by sorting out a server with the shortest queue-length; nevertheless, TDS is novel scheme that is designed to implement task allocation by estimating the waiting time of each server in order to select a server with the fastest response. Finally, this research generates formal models of each scheduling algorithm and the hybrid scheduling scheme to conduct performance evaluation with a fluid flow approximation technique. The analysis results in a superior performance of HDSS in the unstable VEC environments.

ARM-FPGA coupled platforms allow accelerating the computation of specific algorithms by executing them in the FPGA fabric. Several computation steps of our case study for a stereo vision application have been accelerated by hardware implementations. Dynamic Partial Reconfiguration places these hardware tasks in the programmable logic at appropriate times. For an efficient scheduling, it needs to be decided when and where to execute a task. Although there already exist hardware/software scheduling strategies and algorithms, none exploit all possible optimization techniques: re-use, prefetching, parallelization, and pipelining of hardware tasks. The scheduling algorithm proposed in this paper takes this into account and optimizes for the objectives latency/throughput and power/energy.