No abstract

The programming of a proof procedure is discussed in connection with trial runs and possible improvements.

An algorithm for the generation of feasible schedules and the computation of the completion times of the job operations of feasible schedule is presented. Using this algorithm, the distribution of schedule times over the set of feasible schedule--or a subset of feasible schedules--was determined for technological orderings that could occur in a general machine shop. These distributions are found to be approximately normal. Biasing techniques corresponding to "first come first serve," random choice of jobs ready at each machine and combinations of these two extremes were used to compute distributions of schedule times. In all the experiments "first come first serve" appears the best in the sense that convergence to the minimum is fastest and the smallest. The work presented in this paper is supported by the AEC Computing and Applied Mathematics Center, Institute of Mathematical Sciences, New York University, under Contract AT(30-l)-1480 with the U.S. Atomic Energy Commission.

Computer engineers and language designers have built us a Tower of Babel: the engineers add a room each time they design a new machine; the language designs construct a whole story when they unveil a new operating system.There are many reasons for such proliferation: a basic cause is the fact that today there are many computers, each with its own machine language. Likewise, many compiler languages have been developed. At first compiler languages (such as Fortran and Cobol) were developed to overcome the tedium and pitfalls of machine language programming.In addition to being more convenient, compiler languages were soon found to be an ideal means for communication. What better way to describe an algorithm, i.e., a definite computing procedure with no unforeseen contingencies, than to present the computer program that does the algorithm. Hence Algol was born, to provide both a publication language and a practical language for actual use.Most of the compiler languages were developed to handle programs involving numerical computation: they allow little if any manipulation of alphabetic quantities or strings of symbols. Hence in parallel with compiler language designers, workers in specialized fields developed symbol-manipulating languages for processing literary texts, or manipulating [acts opposed to numbers. Notably we have COMIT, developed at MIT for linguistic studies leading to machine translation of human languages; more lately SNOBOL was invented at Bell Laboratories. A variety of information-processing languages have been invented, in which facts are held in lists or more general structures such as trees (resembling sentence diagrams) or graphs (something like airline charts or road maps showing the connections between cities). Such languages that handle lists, graphs, and trees are called list-processing languages; examples are IPL-V, SLIP, NUSPEAK, LISP, as well as SNOBOL and COMIT. More recently, at NYU we have developed SYMAN, a system of subroutines adding to Fortran simply the facility to manipulate strings of symbols and lists of strings.A severe criticism of compiler languages and list-processing languages is that they do not make maximum use of the capacity of the machine. For example, a Fortran program might take even up to fifty percent longer to run to completion than would a machine-language coded version of the same program. In the old days (about ten years ago) running time was measured in hours, so that a loss in efficiency was