February 1971 - Vol. 14 No. 2
Features
Pollack has proposed an algorithm for converting decision tables into flowcharts which minimize subsequent execution time when compiled into a computer program. Two modifications o this algorithm are proposed. The first relies on Shannon's noiseless coding theorem and the communications concept of entropy but does not completely test the ELSE Rule. The second modification completely tests the ELSE Rule but results in more executions than the first modification. Both modifications result in lower execution time than Pollack's algorithm. However, neither modification guarantees a globally optimal solution.
A policy-driven scheduler for a time-sharing system
The services received by a process from a time-sharing operating system can be characterized by a resource count ∑ wiRij where Rij is the number of units of service received by process j from resource i and wi is the cost per unit of the service. Each class of users can be characterized by a policy function which specifies the amount of service a user who belongs to this class should receive as a function of time. Priority changes dynamically as a function of the difference between the service promised to the user by the policy function and the service he actually receives.
A scheduling and swapping algorithm which keeps the resource count of each process above its policy function will provide the specified level of service. Overhead can be reduced by avoiding swaps of processes which have received at least this level of service. The algorithm has been implemented in a general purpose operating system, and it has provided significantly better service to interactive and to batch jobs than the previous scheduler.
An analysis of some time-sharing techniques
The effectiveness of certain time-sharing techniques such as program relocation, disk rotational delay minimization, and swap volume minimization is investigated. Summary data is presented, and the findings are discussed. The vehicle for this investigation was a SIMULA based simulation model reflecting an early framework for a planned Burroughs B6500 time-sharing system. Inasmuch as the B6500 system is based upon the use of variable sized segments and a dynamic overlay procedure, data is also presented which provides some indication of the effectiveness of this type of organization in a time-sharing environment. The design characteristics and operational capabilities of the simulation model are also described.
Experiments in automatic learning for a multipurpose hueristic program
An automatic learning capability has been developed and implemented for use with the MULTIPLE (MULTIpurpose Program that LEarns) heuristic tree-searching program, which is presently being applied to resolution theorem-proving in predicate calculus. MULTIPLE's proving program (PP) uses two evaluation functions to guide its search for a proof of whether or not a particular goal is achievable. Thirteen general features of predicate calculus clauses were created for use in the automatic learning of better evaluation functions for PP. A multiple regression program was used to produce optimal coefficients for linear polynomial functions in terms of the features. Also, automatic data-handling routines were written for passing data between the learning program and the proving program, and for analyzing and summarizing results. Data was generally collected for learning (regression analysis) from the experience of PP.
A number of experiments were performed to test the effectiveness and generality of the learning program. Results showed that the learning produced dramatic improvements in the solutions to problems which were in the same domain as those used for collecting learning data. Learning was also shown to generalize successfully to domains other than those used for data collection. Another experiment demonstrated that the learning program could simultaneously improve performance on problems in a specific domain and on problems in a variety of domains. Some variations of the learning program were also tested.
On the probability distribution of the values of binary trees
An integral equation is derived for the generating function for binary tree values, the values reflecting sorting effort. The analysis does not assume uniformly distributed branching ratios, and therefore is applicable to a family of sorting algorithms discussed by Hoare, Singleton, and van Emden. The solution to the integral equation indicates that using more advanced algorithms in the family makes only minor reductions in the expected sorting efforts, but substantially reduces the variance in sorting effort.
Statistical tests of the values of several thousand trees containing up to 10,000 points have given first, second, and third moments of the value distribution function in satisfactory agreement with the moments computed from the generating function. The empirical tests, as well as the analytical results, are in agreement with previously pubished results for the first moment in the cases of uniform and nonuniform distribution of branching ratio, and for the second moment in the case of uniform distribution of branching ratio.
Application of game tree searching techniques to sequential pattern recognition
A sequential pattern recognition (SPR) procedure does not test all the features of a pattern at once. Instead, it selects a feature to be tested. After receiving the result of that test, the procedure either classifies the unknown pattern or selects another feature to be tested, etc. Medical diagnosis is an example of SPR. In this paper the authors suggest that SPR be viewed as a one-person game played against nature (chance). Virtually all the powerful techniques developed for searching two-person, strictly competitive game trees can easily be incorporated either directly or by analogy into SPR procedures. In particular, one can incorporate the “miniaverage backing-up procedure” and the “gamma procedure,” which are the analogues of the “minimax backing-up procedure” and the “alpha-beta procedure,” respectively. Some computer simulated experiments in character recognition are presented. The results indicate that the approach is promising.
Complex interval arithmetic is defined using real interval arithmetic. Complex interval division is defined so as to assure smallest possible resulting intervals.
Algorithm 405: roots of matrix pencils: the generalized eigenvalue problem [F2]
* This work was supported by the US National Aeronautics and Space Administration, by the National Science Foundation under Grant GS-2703 to the University of Chicago, and by the US Office of Naval Research under Grant NONR 760(24) NR 047-048 to Carnegie-Mellon University. Computations were done on the University of Chicago's Maniac III computer and were supported by the US Atomic Energy Commission under grants AT (11-1)-614 and AT (11-1)-2094.
