Continuation-based control in the implementation of parallel logic programs

Continuations are used to define the flow of messages between low level tasks in a parallel logic programming language. A combination of compiler and runtime operations reduces message traffic by up to 50% when success continuations are passed as parameters in messages that start new processes. Continuations are also the key to fast task switching, a critical operation in this fine grain parallel system. Data from sample programs shows the effectiveness of continuations in reducing message traffic and the speed with which task switches are performed on a typical host architecture.Supported by NSF Grant CCR-8707177 and grants from Motorola, Inc, and Hewlett-Packard Corp.     

A garbage collection algorithm for shared memory parallel processors

This paper describes a technique for adapting the Morris sliding garbage collection algorithm to execute on parallel machines with shared memory. The algorithm is described within the framework of an implementation of the parallel logic language Parlog. However, the algorithm is a general one and can easily be adapted to parallel Prolog systems and to other languages. The performance of the algorithm executing a few simple Parlog benchmarks is analyzed. Finally, it is shown how the technique for parallelizing the sequential algorithm can be adapted for a semi-space copying algorithm.     

Memory requirements for parallel programs

Parallel execution is normally used to decrease the amount of time required to run a program. However, the parallel execution may require far more space than that required by the sequential execution. Worse yet, the parallel space requirement may be very much more difficult to predict than the sequential space requirement because there are more factors to consider. These include essentially nondeterministic factors that can influence scheduling, which in turn may dramatically influence space requirements. We survey some scheduling algorithms that attempt to place bounds on the amount of time and space used during parallel execution. We also outline a direction for future research. This direction takes us into the area of functional programming, where the declarative nature of the languages can help the programmer to produce correct parallel programs, a feat that can be difficult with procedural languages. Currently the high-level nature of functional languages can make it difficult for the programmer to understand the operational behavior of the program. We look at some of the problems in this area, with the goal of achieving a programming environment that supports correct, efficient parallel programs.     

An experiment for truly parallel logic programming

A truly parallel logic programming system is proposed. The system is based on the commercially available parallel logic programming language STRAND, which has been extended in order to overcome the inherent limitations of such systems, like AND-type of parallelism, lack of backtracking, limited unification, etc. The system has been tested using an example from the area of natural language processing.     

On computing logic programs

In this paper we present and compare some classical problem-solving methods for computing the stable models of logic programs with negation. Using a graph theoretic representation of logic programs and their stable models, we discuss and compare linear programming, propositional satisfiability, constraint satisfaction, and graph methods.     

Adaptive execution techniques of parallel programs for multiprocessors

In simultaneous multithreading (SMT) multiprocessors, using all the available threads (logical processors) to run a parallel loop is not always beneficial due to the interference between threads and parallel execution overhead. To maximize the performance of a parallel loop on an SMT multiprocessor, it is important to find an appropriate number of threads for executing the parallel loop. This article presents adaptive execution techniques that find a proper execution mode for each parallel loop in a conventional loop-level parallel program on SMT multiprocessors. A compiler preprocessor generates code that, based on dynamic feedbacks, automatically determines at run time the optimal number of threads for each parallel loop in the parallel application. We evaluate our technique using a set of standard numerical applications and running them on a real SMT multiprocessor machine with 8 hardware contexts. Our approach is general enough to work well with other SMT multiprocessor or multicore systems.     

Scaling parallel programs for multiprocessors: methodology andexamples

Models for the constraints under which an application should be scaled, including constant problem-size scaling, memory-constrained scaling, and time-constrained scaling, are reviewed. A realistic method is described that scales all relevant parameters under considerations imposed by the application domain. This method leads to different conclusions about the effectiveness and design of large multiprocessors than the naive practice of scaling only the data set size. The primary example application is a simulation of galaxies using the Barnes-Hut hierarchical N-body method     

ALLPAD: approximate learning of logic programs with annotated disjunctions

Logic Programs with Annotated Disjunctions (LPADs) provide a simple and elegant framework for representing probabilistic knowledge in logic programming. In this paper we consider the problem of learning ground LPADs starting from a set of interpretations annotated with their probability. We present the system ALLPAD for solving this problem. ALLPAD modifies the previous system LLPAD in order to tackle real world learning problems more effectively. This is achieved by looking for an approximate solution rather than a perfect one. A number of experiments have been performed on real and artificial data for evaluating ALLPAD, showing the feasibility of the approach. Editors: Stephen Muggleton, Ramon Otero, Simon Colton.     

Compiling bottom-up and mixed derivations into top-down executable logic programs

We present a technique for the compilation of bottom-up and mixed logic derivations into PROLOG-programs. It is obtained as an extension of a program transformation technique called Compiling Control. We illustrate its applications in three different domains: solving numerical problems, integrity checking in deductive databases and theorem proving. The aim is to obtain efficient PROLOG programs for problems in which a non-top-down control is most appropriate.Work partly supported by ESPRIT BRA COMPULOG (project 3012).Supported by the Belgian I.W.O.N.L.-I.R.S.I.A. under contract number 5203. Author for correspondence.Supported by the Belgian National Fund for Scientific Research.     

Randomized parallel list ranking for distributed memory multiprocessors

We present a randomized parallel list ranking algorithm for distributed memory multiprocessors, using a BSP type model. We first describe a simple version which requires, with high probability, log(3p)+log ln(n)=Õ(logp+log logn) communication rounds (h-relations withh=Õ(n/p)) andÕ(n/p)) local computation. We then outline an improved version that requires high probability, onlyr?(4k+6) log(2/3p)+8=Õ(k logp) communication rounds wherek=min{i?0 |ln(i+1)n?(2/3p)²ⁱ⁺¹}. Notekn) is an extremely small number. Forn andp?4, the value ofk is at most 2. Hence, for a given number of processors,p, the number of communication rounds required is, for all practical purposes, independent ofn. Forn?1, 500,000 and 4?p?2048, the number of communication rounds in our algorithm is bounded, with high probability, by 78, but the actual number of communication rounds observed so far is 25 in the worst case. Forn?10010100 and 4?p?2048, the number of communication rounds in our algorithm is bounded, with high probability, by 118; and we conjecture that the actual number of communication rounds required will not exceed 50. Our algorithm has a considerably smaller member of communication rounds than the list ranking algorithm used in Reid-Miller’s empirical study of parallel list ranking on the Cray C-90.⁽¹⁾ To our knowledge, Reid-Miller’s algorithm⁽¹⁾ was the fastest list ranking implementation so far. Therefore, we expect that our result will have considerable practical relevance.     

A characterization of answer sets for logic programs

Checking if a program has an answer set, and if so, compute its answer sets are just some of the important problems in answer set logic programming. Solving these problems using Gelfond and Lifschitz's original definition of answer sets is not an easy task. Alternative characterizations of answer sets for nested logic pro- grams by Erdem and Lifschitz, Lee and Lifschitz, and You et al. are based on the completion semantics and various notions of tightness. However, the notion of tightness is a local notion in the sense that for different answer sets there are, in general, different level mappings capturing their tightness. This makes it hard to be used in the design of algorithms for computing answer sets. This paper proposes a characterization of answer sets based on sets of generating rules. From this char- acterization new algorithms are derived for computing answer sets and for per- forming some other reasoning tasks. As an application of the characterization a sufficient and necessary condition for the equivalence between answer set seman- tics and completion semantics has been proven, and a basic theorem is shown on computing answer sets for nested logic programs based on an extended notion of loop formulas. These results on tightness and loop formulas are more general than that in You and Lin's work.     

Strong equivalence of logic programs under the infinite-valued semantics

We consider the notion of strong equivalence [V. Lifschitz, D. Pearce, A. Valverde, Strongly equivalent logic programs, ACM Transactions on Computational Logic 2 (4) (2001) 526-541] of normal propositional logic programs under the infinite-valued semantics [P. Rondogiannis, W.W. Wadge, Minimum model semantics for logic programs with negation-as-failure, ACM Transactions on Computational Logic 6 (2) (2005) 441-467] (which is a purely model-theoretic semantics that is compatible with the well-founded one). We demonstrate that two such programs are strongly equivalent under the infinite-valued semantics if and only if they are logically equivalent in the corresponding infinite-valued logic. In particular, we show that strong equivalence of normal propositional logic programs is decidable, and more specifically coNP-complete. Our results have a direct implication for the well-founded semantics since, as we demonstrate, if two programs are strongly equivalent under the infinite-valued semantics, then they are also strongly equivalent under the well-founded semantics.     

Synchronised execution on shared memory multiprocessors

Threads provides a mechanism for simulating the execution of parallel algorithms on a simplified model of a shared-memory multiprocessor. The algorithms can be expressed in a high-level block-structured language, which supports multiple threads of execution within a common body of program code. Results show an ability to achieve good speedup for small problems using algorithms derived by simple modifications of sequential algorithms. As well, a sibling thread synchronisation feature provides the basis for the synchronous execution of threads. k-parallel algorithms tailored to the machine size and implemented as synchronously executing iterations, can provide near linear speedup as the problem size is increased. The techniques described in this paper seem to promise an effective synchronous execution mode for shared-memory MIMD architectures.     

Beyond multi-adjoint logic programming

In ‘multi-adjoint logic programming’, MALP in brief, each fuzzy logic program is associated with its own ‘multi-adjoint lattice’ for modelling truth degrees beyond the simpler case of true and false, where a large set of fuzzy connectives can be defined. On this wide repertoire, it is crucial to connect each implication symbol with a proper conjunction thus conforming constructs of the form (←_i, &_i) called ‘adjoint pairs’, whose use directly affects both declarative and operational semantics of the MALP framework. In this work, we firstly show how the strong dependence of adjoint pairs can be largely weakened for an interesting ‘sub-class’ of MALP programs. Then, we reason in a similar way till conceiving a ‘super-class’ of fuzzy logic programs beyond MALP, which definitively drops out the need for using adjoint pairs, since the new semantics behaviour relies on much more relaxed lattices than multi-adjoint ones.     

Most specific logic programs

More specific versions of definite logic programs are introduced. These are versions of a program in which each clause is further instantiated or removed and which have an equivalent set of successful derivations to those of the original program, but a possibly increased set of finitely failed goals. They are better than the original program because failure in a non-successful derivation may be detected more quickly. Furthermore, information about allowed variable bindings which is hidden in the original program may be made explicit in a more specific version of it. This allows better static analysis of the program's properties and may reveal errors in the original program. A program may have several more specific versions but there is always a most specific version which is unique up to variable renaming. Methods to calculate more specific versions are given and it is characterized when they give the most specific version.     

The strong semantics for logic programs

Recently, the well-founded semantics of a logic programP has been strengthened to the well-founded semantics-by-case (WF_C) and this in turn has been strengthened to the extended well-founded semantics (WF_E). Both WF_C(P) and WF_E(P) have thelogical consequence property, namely, if an atomAj is true in the theory Th(P), thenAj is true in the semantics as well. However, neither WF_C nor WF_E has the GCWA property, i.e., if an atomAj is false in all minimal models ofP,Aj may not be false in WF_C(P) (resp. WF_E(P)). We extend the ideas in WF_C and WF_E to define a strong well-founded semantics WF_S which has the GCWA property. The strong semantics WF_S(P) is defined by combining GCWA with the notion ofderived rules. Here we use a new Type-III derived rules in addition to those used in WF_C and WF_E. The relationship between WF_S and WF_C is also clarified.     

Tableaux for logic programming

We present a logic programming language, which we call Proflog, with an operational semantics based on tableaux and a denotational semantics based on supervaluations. We show the two agree. Negation is well behaved, and semantic noncomputability issues do not arise. This is accomplished essentially by dropping a domain closure requirement. The cost is that intuitions developed through the use of classical logic may need modification, though the system is still classical at a level once removed. Implementation problems are discussed very briefly; the thrust of the paper is primarily theoretical.Research partly supported by NSF Grant CCR-9104015.     

Proving pointer programs in higher-order logic

Building on the work of Burstall, this paper develops sound modelling and reasoning methods for imperative programs with pointers: heaps are modelled as mappings from addresses to values, and pointer structures are mapped to higher-level data types for verification. The programming language is embedded in higher-order logic. Its Hoare logic is derived. The whole development is purely definitional and thus sound. Apart from some smaller examples, the viability of this approach is demonstrated with a non-trivial case study. We show the correctness of the Schorr–Waite graph marking algorithm and present part of its readable proof in Isabelle/HOL.