Parallel complexity of logical query programs

We consider the parallel time complexity of logic programs without function symbols, called logical query programs, or Datalog programs. We give a PRAM algorithm for computing the minimum model of a logical query program, and show that for programs with the polynomial fringe property, this algorithm runs in time that is logarithmic in the input size, assuming that concurrent writes are allowed if they are consistent. As a result, the linear and piecewise linear classes of logic programs are inN C. Then we examine several nonlinear classes in which the program has a single recursive rule that is an elementary chain. We show that certain nonlinear programs are related to GSM mappings of a balanced parentheses language, and that this relationship implies the polynomial fringe property; hence such programs are inN C Finally, we describe an approach for demonstrating that certain logical query programs are log space complete forP, and apply it to both elementary single rule programs and nonelementary programs.Supported by NSF Grant IST-84-12791, a grant of IBM Corporation, and ONR contract N00014-85-C-0731.     

A 2n−2 step algorithm for routing in ann ×n array with constant-size queues

In this paper we describe a deterministic algorithm for solving any 1–1 packet-routing problem on ann ×n mesh in 2n–2 steps using constant-size queues. The time bound is optimal in the worst case. The best previous deterministic algorithm for this problem required time 2n+(n/q) using queues of size (q) for any 1qn, and the best previous randomized algorithm required time 2n+(logn) using constant-size queues.This research was supported by the Clear Center at UTD, DARPA Contracts N00014-91-J-1698 and N00014-92-J-1799, Air Force Contract F49620-92-J-0125, Army Contract DAAL-03-86-K-0171, an NSF Presidential Young Investigator Award with matching funds from AT&T and IBM, and by the Texas Advanced Research Program under Grant No. 3972. A preliminary version of this paper appeared in [5].     

Proving correctness of coroutines without history variables

We examine the question of whether history variables are necessary in formal proofs of correctness for coroutines. History variables are special variables, which are added to a program to facilitate its proof by recording the sequence of states reached by the program during a computation; after the proof has been completed the history variables may be deleted. The use of such variables in correctness proofs was first suggested by Clint [CL73] in a paper entitled Program Proving: Coroutines; subsequently, history variables have been used by Owicki [OW76a] and Howard [HO75] in verifying concurrent programs and by Apt [APT77] in verifying sequential programs. We argue that recording the entire history of a computation in a single set of variables can actually complicate a correctness proof and should be avoided if possible. We propose a modification of Clint's axiom system and a strategy for constructing proofs that eliminates the need for history variables in verifying simple coroutines. Examples (including Clint's program Histo) are given to illustrate this technique of verifying coroutines, and our axiom system is shown to be sound and relatively complete with respect to an operational semantics for coroutines. Finally, we discuss extensions of the coroutine concept for which history variables do appear to be needed; we also discuss the question of whether such variables are necessary in verifying concurrent programs.The preparation of this paper was supported by NSF Grant MCS-75-08146.     

Automated Synthesis of Recursive Programs from a ∀∃ Logical Specification

The specification of a function is often given by a logical formula, called a -formula, of the following form: xy(x,y). More precisely, a specification is given in the context of a certain theory E and is stated by the judgment E xy (x,y).In this paper, we consider the case in which E is an equational theory. It is divided into two parts. In the first part, we develop a theory for the automated proof of such judgments in the initial model ofE . The validity in the initial model means that we consider not only equational theorems but also inductive ones. From our theory we deduce an automated method for the proof of a class of such judgments. In the second part, we present an automatedmethod for program synthesis. We show how the previous proof method can be used to generate a recursive program for a function f that satisfies a judgment E x (x, f(x)).We illustrate our method with the automated synthesis of some recursive programs on domains such as integers and lists. Finally, we describe our system LEMMA, which is an implementation in Common Lisp of these new methods.     

Transformation of programs for fault-tolerance

In this paper we describe how a program constructed for afault-free system can be transformed into afault-tolerant program for execution on a system which is susceptible to failures. A program is described by a set of atomic actions which perform transformations from states to states. We assume that a fault environment is represented by a programF. Interference by the fault environmentF on the execution of a programP can then be described as afault-transformation which transformsP into a program (P). This is proved to be equivalent to the programPP _F , whereP _F is derived fromP andF, and defines the union of the sets of actions ofP andF _P . A recovery transformation transformsP into a program (P) =PR by adding a set ofrecovery actions R, called arecovery program. If the system isfailstop and faults do not affect recovery actions, we have ((P))=(P)R=PP _F R We illustrate this approach to fault-tolerant programming by considering the problem of designing a protocol that guarantees reliable communication from a sender to a receiver in spite of faults in the communication channel between them.     

From Conditional Events to Conditional Measures: A New Axiomatic Approach

Our starting point is a definition of conditional event EH which differs from many seemingly similar ones adopted in the relevant literature since 1935, starting with de Finetti. In fact, if we do not assign the same third value u (undetermined) to all conditional events, but make it depend on EH, it turns out that this function t(EH) can be taken as a general conditional uncertainty measure, and we get (through a suitable – in a sense, compulsory – choice of the relevant operations among conditional events) the natural axioms for many different (besides probability) conditional measures.     

Branching versus linear logics yet again

A brief overview is given of the temporal logics used in concurrent program verification and in database and systems specification. The properties of the underlying modal frame structures are analysed. The relative advantages of the linear and branching approaches are discussed. The state versus path formulas controversy is revisited. A meta-linear operatorL is proposed and compared with the in all trajectories operator considered in the language CTL*. The usefulness of the new operator within the context of a layered methodology for database and information systems specification and verification is illustrated. The operator is seen as a frame change operator and other interesting operators of this class are referred. Finitary and infinitary axiomatisations are given for the operatorL. The proof of the completeness of the infinitary axiomatisation is briefly outlined. This proof requires an appropriate extension of the usual Henkin methods.     

A fuzzy theoretical approach to case-based representation and inference in CISG

In a legal expert system based on CBR (Case-Based Reasoning), legal statute rules are interpreted on the basis of precedents. This interpretation, because of its vagueness and uncertainty of the interpretation cannot be handled with the means used for crisp cases. In our legal expert system, on the basis of the facts of precedents, the statute rule is interpreted as a form of case rule, the application of which involves the concepts of membership and vagueness. The case rule is stored in a data base by means of fuzzy frames. The inference based on a case rule is made by fuzzy YES and fuzzy NO, and the degree of similarity of cases. The system proposed here will be used for legal education; its main area of application is contract, especially in relation to the United Nations Convention on Contracts for the International Sale of Goods (CISG).     

Distributivity in Łℵ0 and Other Sentential Logics

Certain distributivity results for ukasiewicz's infinite-valued logic ₀ are proved axiomatically (for the first time) with the help of the automated reasoning program OTTER. In addition, nondistributivity results are established for a wide variety of positive substructural logics by the use of logical matrices discovered with the automated model-finding programs MACE and MAGIC.     

Optimal multilayer channel routing with overlap

This paper presents algorithms for multiterminal net channel routing where multiple interconnect layers are available. Major improvements are possible if wires are able to overlap, and our generalized main algorithm allows overlap, but only on everyKth (K 2) layer. Our algorithm will, for a problem with densityd onL layers,L K + 3,provably use at most three tracks more than optimal: (d + 1)/L/K + 2 tracks, compared with the lower bound of d/L/K. Our algorithm is simple, has few vias, tends to minimize wire length, and could be used if different layers have different grid sizes. Finally, we extend our algorithm in order to obtain improved results for adjacent (K = 1) overlap: (d + 2)/2L/3 + 5 forL 7.This work was supported by the Semiconductor Research Corporation under Contract 83-01-035, by a grant from the General Electric Corporation, and by a grant at the University of the Saarland.     

Fairness and the axioms of control predicates

Many recent axiomatic definitions for structured programming languages include control predicates,at(S), in(S), andafter(S), which are an abstraction of location counters. The usual axioms identify control locations so as to imply that no time (i.e., no state transition) is needed to pass from the end of one statement to the next, and in particular from the end of a loop body back to the test at the head of the loop. Here, an axiomatic framework for control predicates is examined. It is shown that if all the axioms are to be maintained with common representation mappings, there are difficult new requirements which need to be satisfied by an implementation for fair concurrent models of computation. Several approaches to resolving the difficulty are considered, and in particular it is suggested to replace some axioms of the formPQ byPeventually(Q), whereP andQ are control predicates, thereby separating control states previously identified.The North has receded, but the South has not yet arrived.-Reuven Miran, 42 Degrees in the Shade Every three lines intersect at a point, if the point is thick enough.-Folk theoremNote: A talk based on this paper was presented at the Colloquium on Temporal Logic and Specification, Altrincham, Cheshire, April 1987.C.R. Categories: D.3.1 [Programming languages] Formal definitions and theory: semantics; D..3.3 [Programming languages] Language constructs: control structures; F.3.1. [Logics and meanings of programs] Specifying and verifying and reasoning about programs.     

Y-Invalidate: A New Protocol for Implementing Weak Consistency in DSM Systems

In this work we propose and implement a new variant of the well-known write invalidate protocol called Y-invalidate. Whereas the former protocol required that every copy of a page be invalidated every time that page is updated, our variant invalidates a copy of a page at process A only at the next synchronization point which is relevant to Aand or if the copy was modified by the owner's process after the page was copied to A. We thus avoid invalidating copies of pages that were modified but never read after modification, and avoid, of course, the associated overhead. Y-Invalidate is basically a weak-consistency protocol. Its main advantage is that it implements weak consistency without the need to merge copies of a page that were updated in different machines. To the best of our knowledge, this is the first variant of weak consistency protocols which does not merge multiple copies of pages. Unlike other variants of weak consistency, Y-invalidate supports implicit synchronization points in the program by invalidating copies of shared memory pages that are referenced by while-loops. In this way, Y-invalidate approximates strict consistency. The Y-invalidate protocol was implemented in the ParC system, which is a powerful parallel extension of the C language. The ParC compiler was modified to detect some of the implicit synchronization points in the source code. Experimental results show significant improvement compared to both the traditional write-invalidate protocol and weak consistency.     

Choosing reference classes and building provisional models

A well-known problem in default logic is the ability of naive reasoners to explain bothg and ¬g from a set of observations. This problem is treated in at least two different ways within that camp.One approach is examination of the various explanations and choosing among them on the basis of various explanation comparators. A typical comparator is choosing the explanation that depends on the most specific observation, similar to the notion of narrowest reference class.Others examine default extensions of the observations and choose whatever is true in any extension, or what is true in all extensions or what is true in preferred extensions. Default extensions are sometimes thought of as acceptable models of the world that are discarded as more knowledge becomes available.We argue that the notions of specificity and extension lack clear semantics. Furthermore, we show that the problems these ideas were supposed to solve can be handled easily within a probabilistic framework.     

Low-Rank Approximation of Integral Operators by Interpolation

A central component of the analysis of panel clustering techniques for the approximation of integral operators is the so-called -admissibility condition min {diam(),diam()} 2dist(,) that ensures that the kernel function is approximated only on those parts of the domain that are far from the singularity. Typical techniques based on a Taylor expansion of the kernel function require a subdomain to be far enough from the singularity such that the parameter has to be smaller than a given constant depending on properties of the kernel function. In this paper, we demonstrate that any is sufficient if interpolation instead of Taylor expansionisused for the kernel approximation, which paves the way for grey-box panel clustering algorithms.     

Software engineering education: issues and alternatives

Postgraduate degree programs in software engineering have been in existence for some time and now undergraduate degree programs with this title are beginning to appear. A number of questions and issues of only moderate importance with respect to the postgraduate programs now become critical and of overriding importance. While one could (and did) by and large gloss over these issues earlier, this will be much more difficult, and probably impossible, in the future. These issues must be resolved in a wider context than that in which they have been dealt with before, involving engineering in the universities and professional engineering societies in the larger social context. Much of the disagreement regarding these issues can, ultimately, be traced back to differing fundamental views and definitions of the term engineering and whether software engineering should be treated as just another engineering discipline or in a significantly and fundamentally different way. After examining two different definitions and views of engineering, this paper states and discusses a number of the questions and issues which planners of new undergraduate software engineering degree programs must deal with. Some pros and cons of various alternative answers are presented and a few answers suggested. The issues discussed here begin with questions of general policy and concept (e.g., which culture – that of the traditional engineering disciplines or that of computer science – should be instilled in the students in these new degree programs), include organizational matters (e.g., the position of the new degree program in the university hierarchy) and end with selected, more detailed questions regarding the curriculum (e.g., how to deal with programming, design and management topics). It is conjectured that, although the scientific foundation for the undergraduate software engineering degree programs must and will come from computer science, their culture and orientation must come from engineering if they and their graduates are to be successful in satisfying society's needs in the long term.     

Eine bedingte Form der Integral-Ungleichung von Gronwall,leichte Verallgemeinerung eines Stabilitätssatzes von Perron und überlauffreie Skalierung von Analogrechenschaltungen

Zusammenfassung Es geht in dieser Arbeit in der Hauptsache darum, ein vorgelegtes Differentialgleichungssystem so zu skalieren, daß in der zugehörigen Analogrechnerschaltung die Spannungen an den Ausgängen der Integratoren die durch die Referenzspannung einerseits und durch das Auflösevermögen andererseits gesetzten Schranken nicht über- bzw. unterschreiten. Es werden Abschätzungssätze hergeleitet, die diese Frage im Apriori-Sinn, also ohne die Lösung des Differentialgleichungssystems zu kennen, zu lösen gestatten. Zur Abschätzung werden zunächst Normen, dannKamke-Normen verwendet. Der im Titel erwähnte Satz vonPerron ergibt sich durch spezielle Normengebung und Verzicht auf Abschätzung nach unten. Erschwert werden die Betrachtungen durch die relative Schwäche der Forderung, daß die rechte Seite des Systemsdx/dt=f(x,t) der Bedingung aus xa folgt f(x,t)v(t)x genüge (...:=Norm,a positiv reell). Dadurch scheint es bei Abschätzungen mitKamke-Normen nicht mehr möglich, von den in der Literatur über Existenzbeweise und Abschätzungssätze üblichen Methoden Gebrauch zu machen. Zur Lösung dieser Frage wird eine bedingte Form des bekannten Satzes vonGronwall (auch Satz vonBellman genannt) entwickelt.

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A conditional version of the integral inequality of gronwall, a slight generalization of a stability theorem of perron, and overflow-free scaling of analogue computer set-ups

Summary The main subject of this paper is the scaling of a given set of differential equations in such a way that the output voltages of the integrators of the associated analogue computer set-up do not exceed certain upper and lower bounds imposed by the reference voltage and the limited power of resolution of the elements of the analogue computer. The paper gives a priori bounds on the solution of the differential set. Some of these bounds work with norms, others withKamke-norms.Perron's stability theorem mentioned in the title of this paper results by inserting special norms and neglecting lower bounds. A difficulty arises by the relative weakness of the condition xa implies f(x,t)v(t)x on the right hand side of the setdx/dt=f(x,t), where ... is any norm anda is a positive real constant. As a consequence of this, it seems no longer possible to use the usual techniques known from the literature on existence theorems and bounds for the solution of differential equations. To cope with this situation, a conditional version of the well-known theorem ofGronwall (also known by the name of Lemma ofBellman) will be derived.

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Diese Arbeit ist Teil einer am Institut für Angewandte Mathematik der Technischen Hochschule München unter Anleitung von Herrn o. Prof. Dr. rer. nat. habil.J. Heinhold angefertigten Dissertation.     

The role of “craft language” in learning “Waza”

The role of craft language in the process of teaching (learning) Waza (skill) will be discussed from the perspective of human intelligence.It may be said that the ultimate goal of learning Waza in any Japanese traditional performance is not the perfect reproduction of the teaching (learning) process of Waza. In fact, a special metaphorical language (craft language) is used, which has the effect of encouraging the learner to activate his creative imagination. It is through this activity that the he learns his own habitus (Kata).It is suggested that, in considering the difference of function between natural human intelligence and artificial intelligence, attention should be paid to the imaginative activity of the learner as being an essential factor for mastering Kata.This article is a modified English version of Chapter 5 of my bookWaza kara shiru (Learning from Skill), Tokyo University Press, 1987, pp. 93–105.     

Mesh Selection for a Nearly Singular Boundary Value Problem

In this paper, we investigate the numerical solution of a model equation u _xx = exp(– ) (and several slightly more general problems) when 1 using the standard central difference scheme on nonuniform grids. In particular, we are interested in the error behaviour in two limiting cases: (i) the total mesh point number N is fixed when the regularization parameter 0, and (ii) is fixed when N. Using a formal analysis, we show that a generalized version of a special piecewise uniform mesh 12 and an adaptive grid based on the equidistribution principle share some common features. And the optimal meshes give rates of convergence bounded by |log()| as 0 and N is given, which are shown to be sharp by numerical tests.     

The risk-sensitive index and theH 2 andH ∞, norms for nonlinear systems

In this paper we study two measures of the size of systems, namely, the so-calledH ₂ and H norms. These measures are important tools for determining the influence of disturbances on performance. We show that the risk-sensitive index on an infinite time horizon contains detailed information concerning these measures, via small noise and small risk limits.The authors wish to acknowledge the funding of the activities of the Cooperative Research Centre for Robust and Adaptive Systems by the Australian Commonwealth Government under the Cooperative Research Centres Program. The first author was partially supported by AFOSR F49620-92-J-0081, ARO DAAL03-92-G-0115, and NSF DMS-9300048.     

Directions and Methodologies for Empirical Software Engineering Research

This report summarises and builds on the results of the Directions and Methodologies for Empirical Software Engineering Research group discussion. In particular, we considered the strengths, weaknesses, opportunities and threats to empirical software engineering research in light of the discussions and presentations during the workshop. The following sections describe each of these aspects of our discussion in turn. In addition, to finalise our discussion we agreed on a three-point plan for future work.