Results which allow either the computatmn of symbolic solutions to first-order-linear difference equauons or the determination that solutions of a certain form do not exist are presented. Starting with a field of constants, larger fields may be constructed by the formal adjunctlon of symbols whtch behave hke solutions to first-order-linear equations (with a few restrictions) It IS in these extension fields that the difference equations may be posed and m which the solutions are requested. The principal apphcatmn of these results is In finding formulas for a broad class of finite sums or In showing the nonexistence of such formulas.

Summation in Finite Terms

The notion of dependence captures that most important properties of a program for efficient execution on parallel computers. The dependence structure of a program defines that necessary constraints of the order of execution of the program components and provides sufficient information for the exploitation of the available parallelism. Static discovery and management of the dependence structure of programs save a tremendous amount of execution time, and dynamic utilization of dependence information results in a significant performance gain on parallel computers. However, experiments with parallel computers indicate that existing multiprocessing environments are unable to deliver the desired performance over a wide range of real applications, mainly due to lack of precision of their dependence information. This calls for an effective compilation scheme capable of understanding the dependence structure of complicated application programs. This article describes a methodology for capturing analyzing program properties that are essential in the effective detection and efficient exploitation of parallelism on parallel computers. Based on this methodology, a symbolic analysis framework is developed for the Parafrase-2 parallelizing compiler. This framework extends the scope of a variety of important program analysis problems and solves them in a unified way. The attained solution space of these problems is much larger than that handled by existing compiler technology. Such a powerful approach is required for the effective compilation of a large class of application programs.

Symbolic analysis for parallelizing compilers

References 1. Bays, C. A comparison of next-fit, first-fit, and best-fit. Comm. ACM, 20, 3 (Mar. 1977), 191-192. 2. Beck, L.L. A new dynamic storage allocation technique and its performance. Tech. Rep. 14-81, Dep. Mathematical Sciences, San Diego State Univ., San Diego, Calif. (May 1981). 3. Campbell, J.A. A note on an optimal-fit method for dynamic allocation of storage. Comput. J., 14, 1 (Jan. 1971), 7-9. 4. Fenton, J.S., and Payne, D.W. Dynamic storage allocation of arbitrary sized segments. Proceedings IFIP \"74, Amsterdam, (1974), 344-348. 5. Hirschberg, D.S. A class of dynamic memory allocation algorithms. Comm. ACM, 16, 10 (Oct. 1973), 615-618. 6. Knowlton, K.C. A fast storage allocator. Comm. ACM, 8, 10 (Oct. 1965), 623-625. 7. Knuth, D.E. The Art of Computer Programming, Vol. I: Fundamental Algorithms. Addison-Wesley, Reading, Mass. (1968). 8. Margolin, B.H., Parmlee, R.P., and Schatzoff, M. Analysis of free-storage algorithms. IBM Syst. J., 10, 4 (197l), 283-304. 9. Nielsen, N.R. Dynamic memory allocation in computer simulation. Comm. A CM, 20, l 1 (Nov. 1977), 864--873. 10. Peterson, J.L., and Norman, T.A. Buddy systems. Comm. ACM, 20, 6 (June 1977), 421--431. 11. Randell, B. A note on storage fragmentation and program segmentation. Comm. ACM, 12, 7 (July 1969), 365-372. 12. Shen, K.K., and Peterson, J.L. A weighted buddy system for dynamic storage allocation. Comm. ACM, 17, 10 (Oct. 1974), 558-562. 13. Shore, J.E. Anomalous behavior of the fifty-percent rule in dynamic memory allocation. Comm. ACM, 20, 11 (Nov. 1977), 812-820. 14. Shore, J.E. On the external storage fragmentation produced by first-fit and best-fit allocation strategies. Comm. ACM, 18, 8 (Aug. 1975), 433--440. 15. Standish, T.A. Data Structure Techniques. Addison-Wesley, Reading, Mass. (1980). 16. Tadman, M. Fast-fit: A new hierarchical dynamic storage allocation technique. M.S. Thesis, Dept. Computer Science, Univ. California at Irvine (1978). 177. Weinstock, C.B. Dynamic storage allocation techniques. Ph.D. Thesis, Dept. Computer Science, Carnegie-Mellon Univ., Pittsburgh, Pa. (Apr. 1976). P r o g r a m m i n g T e c h n i q u e s

Computer-assisted microanalysis of programs

The first part of the paper shows that previous theoretical work on the semantics of probabilistic programs (Kozen) and on the correctness of performance annotated programs (Ramshaw) can be used to automate the average-case analysis of simple programs containing assignments, conditionals, and loops. A performance compiler has been developed using this theoretical foundation. The compiler is described, and it is shown that special cases of symbolic simplifications of formulas play a major role in rendering the system usable. The performance compiler generates a system of recurrence equations derived from a given program whose efficiency one wishes to analyze. This generation is always possible, but the problem of solving the resulting equations may be complex. The second part of the paper presents an original method that generalizes the previous approach and is applicable to functional programs that make use of recursion and complex data structures. Several examples are presented, including an analysis of binary tree sort. A key feature of the analysis of such programs is that distributions on complex data structures are represented using attributed probabilistic grammars.

Automating program analysis

Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of constraints expressing bounds on the resources required by the program, which are then solved, possibly applying safe approximations. In several interesting cases, these constraints take the form of recurrence relations. While techniques for solving recurrences are known and implemented in several computer algebra systems, these do not completely fulfill the needs of fully automatic complexity analysis: they only deal with a somewhat restricted class of recurrence relations, or sometimes require user intervention, or they are restricted to the computation of exact solutions that are often so complex to be unmanageable, and thus useless in practice. In this paper we briefly describe PURRS, a system and software library aimed at providing all the computer algebra services needed by applications performing or exploiting the results of worst-case complexity analyses. The capabilities of the system are illustrated by means of examples derived from the analysis of programs written in a domain-specific functional programming language for real-time embedded systems.

PURRS: Towards Computer Algebra Support for Fully Automatic Worst-Case Complexity Analysis

ABSTV, ACT. A method is presented for computing upper bounds for the speedup gamed by synchronousmultiprocessor, bottom-up, no-backtrack parsing of strings generated by a context-free grammar. First the maxunum speedup s is defined using an optimal strategy for a certain pebble game Then analyuc upper and lower bounds for s are developed These bounds are computed for parsing trees with certain propertms. The computation consists of (1) determining a subclass of strings of a language which are favorably parsed in parallel, (2) estabhshing sets of difference equations and solving them to estimate the minimum time needed to parse these strings; and (3) computing the speedup function. The method is applied to the parsing of arithmetic expressions and strings of a stmple programming language. The results presented show how maxtmum speedup gums vary with the number of processors avadable.

Upper Bounds for Speedup in Parallel Parsing

An interactive computer program which has some capability for solving systems of finite difference equations is described. Although this capability is limited to linear systems, a knowledgeable user can, with the help of the program, solve a wider class of equations. Over 100 examples, covering a variety of cases, have been solved by using the program. Some representative examples are presented. Additional features which would improve the versatility of the program are also discussed.

Symbolic Solution of Finite-Difference Equations

Automatic solution of a certain class of combinatorial problems

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Joel Katcoff

Author Tools

Chat about Author

Papers

Upper Bounds for Speedup in Parallel Parsing

Symbolic Solution of Finite-Difference Equations

Automatic solution of a certain class of combinatorial problems