Research and Advances

Analyses of deterministic parsing algorithms

This paper describes an approach for determining the minimum, maximum, and average times to parse sentences acceptable by a deterministic parser. These quantities are presented in the form of symbolic formulas, called time-formulas. The variables in these formulas represent not only the length of the input string but also the time to perform elementary operations such as pushing, popping, subscripting, iterating, etc. By binding to the variables actual numerical values corresponding to a given compiler-machine configuration, one can determine the execution time for that configuration. Time-formulas are derived by examining the grammar rules and the program representing the algorithm one wishes to analyze. The approach is described by using a specific grammar that defines simple arithmetic expressions. Two deterministic parsers are analyzed: a top-down recursive descent LL(1) parser, and a bottom-up SLR(1) parser. The paper provides estimates for the relative efficiencies of the two parsers. The estimates applicable to a specific machine, the PDP-10, are presented and substantiated by benchmarks. Finally, the paper illustrates the proposed approach by applying it to the analyses of parsers for a simple programming language.
Research and Advances

Two languages for estimating program efficiency

Two languages enabling their users to estimate the efficiency of computer programs are presented. The program whose efficiency one wishes to estimate is written in the first language, a go-to-less programming language which includes most of the features of Algol 60. The second language consists of interactive commands enabling its users to provide additional information about the program written in the first language and to output results estimating its efficiency. Processors for the two languages are also described. The first processor is a syntax-directed translator which compiles a program into a symbolic formula representing the execution time for that program. The second processor is a set of procedures for algebraic manipulation which can be called by the user to operate on the formula produced by the first processor. Examples of the usage of the two languages are included. The limitations of the present system, its relation to Knuth's work on the analysis of algorithms, and some of the directions for further research are also discussed.

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