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A fast and usually linear algorithm for global flow analysis (abstract only)
ible graphs is presented. The algorithm is shown to treat a very general class of function spaces. For a graph of e edges, the algorithm has a worst case time bound of O(e log e) function operations. It is also shown that in programming terms, the number of operations is proportional to e plus the number of exits from program loops. Consequently a restriction to one-entry one-exit control structures guarantees linearity. The algorithm can be extended to yet larger classes of function spaces and graphs by relaxing the time bound. Examples are given of code improvement problems which can be solved using the algorithm.
Reduction: a method of proving properties of parallel programs
When proving that a parallel program has a given property it is often convenient to assume that a statement is indivisible, i.e. that the statement cannot be interleaved with the rest of the program. Here sufficient conditions are obtained to show that the assumption that a statement is indivisible can be relaxed and still preserve properties such as halting. Thus correctness proofs of a parallel system can often be greatly simplified.
Programming languages, natural languages, and mathematics
Some social aspects of pro gramming are illuminated through analogies with similar aspects of mathematics and natural languages. The split between pure and applied mathematics is found similarly in programming. The development of natural languages toward flexionless, word-order based language types speaks for programming language design based on general, abstract constructs. By analogy with incidents of the history of artificial, auxiliary languages it is suggested that Fortran and Cobol will remain dominant for a long time to come. The most promising avenues for further work of wide influence are seen to be high quality program literature (i.e. programs) of general utility and studies of questions related to program style.
On the complexity of LR(k) testing
The problem of determining whether an arbitrary context-free grammar is a member of some easily parsed subclass of grammars such as the LR(k) grammars is considered. The time complexity of this problem is analyzed both when k is considered to be a fixed integer and when k is considered to be a parameter of the test. In the first case, it is shown that for every k there exists an O(nk+2) algorithm for testing the LR(k) property, where n is the size of the grammar in question. On the other hand, if both k and the subject grammar are problem parameters, then the complexity of the problem depends very strongly on the representation chosen for k. More specifically, it is shown that this problem is NP-complete when k is expressed in unary. When k is expressed in binary the problem is complete for nondeterministic exponential time. These results carry over to many other parameterized classes of grammars, such as the LL(k), strong LL(k), SLR(k), LC(k), and strong LC(k) grammars.
Exception handling: issues and a proposed notation
This paper defines exception conditions, discusses the requirements exception handling language features must satisfy, and proposes some new language features for dealing with exceptions in an orderly and reliable way. The proposed language features serve to highlight exception handling issues by showing how deficiencies in current approaches can be remedied.
Automatic data structure choice in a language of very high level
SETL is a set-theoretically oriented language of very high level whose repertoire of semantic objects includes finite sets, ordered n-tuples, and sets of ordered n-tuples usable as mappings. This paper describes the structure of an optimizer for this language. Among other methods of interest, the optimizer uses techniques which allow relations of inclusion and membership to be established, the domains and ranges of (tabulated) mappings to be estimated from above and below, and the single-valuedness of (tabulated) mappings to be proved. Once facts of this kind have been established, automatic choice of data structures becomes possible. The methods employed are based upon, and extend, known techniques of data flow analysis.
Backtrack programming techniques
The purpose of this paper is twofold. First, a brief exposition of the general backtrack technique and its history is given. Second, it is shown how the use of macros can considerably shorten the computation time in many cases. In particular, this technique has allowed the solution of two previously open combinatorial problems, the computation of new terms in a well-known series, and the substantial reduction in computation time for the solution to another combinatorial problem.
Specifying queries as relational expressions: the SQUARE data sublanguage
This paper presents a data sublanguage called SQUARE, intended for use in ad hoc, interactive problem solving by non-computer specialists. SQUARE is based on the relational model of data, and is shown to be relationally complete; however, it avoids the quantifiers and bound variables required by languages based on the relational calculus. Facilities for query, insertion, deletion, and update on tabular data bases are described. A syntax is given, and suggestions are made for alternative syntaxes, including a syntax based on English key words for users with limited mathematical background.
A genealogy of control structures
The issue of program control structures has had a history of heated controversy. To put this issue on a solid footing, this paper reviews numerous theoretical results on control structures and explores their practical implications.
The classic result of Böhm and Jacopini on the theoretical completeness of if-then-else and while-do is discussed. Several recent ideas on control structures are then explored. These include a review of various other control structures, results on time/space limitations, and theorems relating the relative power of control structures under several notions of equivalence.
In conclusion, the impact of theoretical results on the practicing programmer and the importance of one-in, one-out control structures as operational abstractions are discussed. It is argued further that there is insufficient evidence to warrant more than if-then-else, while-do, and their variants.
Practical syntactic error recovery
This paper describes a recovery scheme for syntax errors which provides automatically-generated high quality recovery with good diagnostic information at relatively low cost. Previous recovery techniques are summarized and empirical comparisons are made. Suggestions for further research on this topic conclude the paper.
Merging with parallel processors
Consider two linearly ordered sets A, B, | A | = m, | B | = n, m ≤ n, and p, p ≤ m, parallel processors working synchronously. The paper presents an algorithm for merging A and B with the p parallel processors, which requires at most 2⌈log2(2m + 1)⌉ + ⌊3m/p⌋ + [m/p][log2(n/m)] steps. If n = 2&bgr;m (&bgr; an integer), the algorithm requires at most 2[log2(m + 1)] + [m/p](2 + &bgr;) steps. In the case where m and n are of the same order of magnitude, i.e. n = km with k being a constant, the algorithm requires 2[log2(m + 1)] + [m/p](3 + k) steps. These performances compare very favorably with the previous best parallel merging algorithm, Batcher's algorithm, which requires n/p + ((m + n)/2p)log2m steps in the general case and km/p + ((k + 1)/2)(m/p)log2m in the special case where n = km.
Optimizing the performance of a relational algebra database interface
An approach for implementing a “smart” interface to support a relational view of data is proposed. The basic idea is to employ automatic programming techniques so that the interface analyzes and efficiently refines the high level query specification supplied by the user. A relational algebra interface, called SQUIRAL, which was designed using this approach, is described in detail. SQUIRAL seeks to minimize query response time and space utilization by: (1) performing global query optimization, (2) exploiting disjoint and pipelined concurrency, (3) coordinating sort orders in temporary relations, (4) employing directory analysis, and (5) maintaining locality in page references. Algorithms for implementing the operators of E. F. Codd's relational algebra are presented, and a methodology for composing them to optimize the performance of a particular user query is described.
CONVERT: a high level translation definition language for data conversion
This paper describes a high level and nonprocedural translation definition language, CONVERT, which provides very powerful and highly flexible data restructuring capabilities. Its design is based on the simple underlying concept of a form which enables the users to visualize the translation processes, and thus makes data translation a much simpler task.
“CONVERT” has been chosen for conveying the purpose of the language and should not be confused with any other language or program bearing the same name.
Implementation of a structured English query language
The relational model of data, the XRM Relational Memory System, and the SEQUEL language have been covered in previous papers and are reviewed. SEQUEL is a relational data sublanguage intended for ad hoc interactive problem solving by non-computer specialists. A version of SEQUEL that has been implemented in a prototype interpreter is described. The interpreter is designed to minimize the data accessing operations required to respond to an arbitrary query. The optimization algorithms designed for this purpose are described.
A preliminary system for the design of DBTG data structures
The functional approach to database design is introduced. In this approach the goal of design is to derive a data structure which is capable of supporting a set of anticipated queries rather than a structure which “models the business” in some other way. An operational computer program is described which utilizes the functional approach to design data structures conforming to the Data Base Task Group specifications. The automatic programming technology utilized by this program, although typically used to generate procedure, is here used to generate declaratives.
Optimal balancing of I/O requests to disks
Determining a policy for efficient allocation and utilization of a set of disk drives with differing operational characteristics is examined using analytical techniques. Using standard queueing theory, each disk drive is characterized by a queueing model with service time of a disk drive represented by the probability density function of the sum of two uniform distributions. Total response time of the set of disk models is then minimized under varying load conditions. The results indicate that faster devices should have higher utilization factors and that the number of different device types utilized tends to decrease with decreasing load. Specific examples using 2314 and 3330 combinations are examined.
Multiprocessing compactifying garbage collection
Algorithms for a multiprocessing compactifying garbage collector are presented and discussed. The simple case of two processors, one performing LISP-like list operations and the other performing garbage collection continuously, is thoroughly examined. The necessary capabilities of each processor are defined, as well as interprocessor communication and interlocks. Complete procedures for garbage collection and for standard list processing primitives are presented and thoroughly explained. Particular attention is given to the problems of marking and relocating list cells while another processor may be operating on them. The primary aim throughout is to allow the list processor to run unimpeded while the other processor reclaims list storage The more complex case involving several list processors and one or more garbage collection processors are also briefly discussed.
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