5851955
Vacillatory Learning of Nearly Minimal Size Grammars
In Gold's influential language learning paradigm a learning machine converges in the limit to one correct grammar. In an attempt to generalize Gold's paradigm, Case considered the question whether people might converge to vacillating between up to (some integer) n > 1 distinct, but equivalent, correct grammars. He showed that larger classes of languages can be algorithmically learned (in the limit) by converging to up to n + 1 rather than up to n correct grammars. He also argued that, for ''small'' n>1, it is plausible that people might sometimes converge to vacillating between up to n grammars. The insistence on small n was motivated by the consideration that, for ''large'' n, at least one of n grammars would be too large to fit in people's heads. Of course, even for Gold's n = 1 case, the single grammar converged to in the limit may be infeasibly large. An interesting complexity restriction to make, then, on the final grammar(s) converged to in the limit is that they all have small size. In this paper we study some of the trade-offs in learning power involved in making a well-defined version of this restriction. We show and exploit as a tool the desirable property that the learning power under our size-restricted criteria (for successful learning) is independent of the underlying acceptable programming systems. We characterize the power of our size-restricted criteria and use this characterization to prove that some classes of languages, which can be learned by converging in the limit to up to n + 1 nearly minimal size correct grammars, cannot be learned by converging to up to n unrestricted grammars even if these latter grammars are allowed to have a finite number of anomalies (i.e., mistakes) per grammar. We also show that there is no loss of learning power in demanding that the final grammars be nearly minimal size iff one is willing to tolerate an unbounded, finite number of anomalies in the final grammars and there is a constant bound on the number of different grammars converged to in the limit. Hence, if we allow an unbounded, finite number of anomalies in the final grammars and the number of different grammars converged to in the limit is unbounded but finite (or if there is a constant bound on the number of anomalies allowed in the final grammars), then there is a loss of learning power in requiring that the final grammars be nearly minimal size. These results do not always match what might be expected from the cases, previously examined by Freivalds, Kinber, and Chen, of learning nearly minimal size programs for functions.
39847140
Team Learning of Recursive Languages
A team of learning machines is a multiset of learning machines. A team is said to successfully learn a concept just in case each member of some nonempty subset, of predetermined size, of the team learns the concept. Team learning of languages turns out to be a suitable theoretical model for studying computational limits on multi-agent machine learning. Team learning of recursively enumerable languages has been extensively studied. However, it may be argued that from a practical point of view all languages of interest are recursive. 
 
This paper gives theoretical results about team learnability of recursive languages. These results are mainly about two issues: redundancy and aggregation. The issue of redundancy deals with the impact of increasing the size of a team and increasing the number of machines required to be successful. The issue of aggregation deals with conditions under which a team may be replaced by a single machine without any loss in learning ability. The learning scenarios considered are: (a) Identification in the limit of accepting grammars for recursive languages. (b) Identification in the limit of decision procedures for recursive languages. (c) Identification in the limit of accepting grammars for indexed families of recursive languages. (d) Identification in the limit of accepting grammars for indexed families with enumerable class of grammars for the family as the hypothesis space. Scenarios which can be modeled by team learning are also presented.
39763724
Branch and bound on the network model
Abstract Karp and Zhang developed a general randomized parallel algorithm for solving branch and bound problems. They showed that with high probability their algorithm attained optimal speedup within a constant factor (for p⩽ n/( log n) c , where p is the number of processors, n is the “size” of the problem, and c is a constant). Ranade later simplified the analysis and obtained a better processor bound. Karp and Zhang's algorithm works on models of computation where communication cost is constant. The present paper considers the Branch and Bound problem on networks where the communication cost is high. Suppose sending a message in a p processor network takes G = O ( log p) time and node expansion (defined below) takes unit time (other operations being free). Then a simple randomized algorithm is presented which is, asymptotically, nearly optimal for p = O (2 log c n ) , where c is any constant and n is the number of nodes in the input tree with cost no greater than the cost of the optimal leaf in the tree.
10962196
Absolute versus probabilistic classification in a logical setting
Suppose we are given a set W of logical structures, or possible worlds, a set of logical formulas called possible data and a logical formula @f. We then consider the classification problem of determining in the limit and almost always correctly whether a possible world M satisfies @f, from a complete enumeration of the possible data that are true in M. One interpretation of almost always correctly is that the classification might be wrong on a set of possible worlds of measure 0, with respect to some natural probability distribution over the set of possible worlds. Another interpretation is that the classifier is only required to classify a set W^' of possible worlds of measure 1, without having to produce any claim in the limit on the truth of @f for the members of the complement of W^' in W. We compare these notions with absolute classification of W with respect to a formula that is almost always equivalent to @f in W, hence we investigate whether the set of possible worlds on which the classification is correct is definable. We mainly work with the probability distribution that corresponds to the standard measure on the Cantor space, but we also consider an alternative probability distribution proposed by Solomonoff and contrast it with the former. Finally, in the spirit of the kind of computations considered in Logic programming, we address the issue of computing almost correctly in the limit witnesses to leading existentially quantified variables in existential formulas.
18622476
Learning in the Presence of Partial Explanations
Abstract The effect of a partial explanation as additional information in the learning process is investigated. A scientist performs experiments to gather experimental data about some phenomenon, and then tries to construct an explanation (or theory) for the phenomenon. A plausible model for the practice of science is an inductive inference machine (scientist) learning a program (explanation) from a graph (set of experiments) of a recursive function (phenomenon). It is argued that this model of science is not an adequate one, as scientists, in addition to performing experiments, make use of some approximate partial explanation based on the “state of the art” knowledge about that phenomenon. An attempt has been made to model this partial explanation as additional information in the scientific process. It is shown that the inference capability of machines is improved in the presence of such a partial explanation. The quality of this additional information is modeled using certain “density” notions. It is shown that additional information about a “better” quality partial explanation enhances the inference capability of learning machines as scientists more than a “not so good” partial explanation. Similar enhancements to inference of approximations, a more sophisticated model of science, are demonstrated. Inadequacies in Gold's paradigm of language learning are investigated. It is argued that Gold's model fails to incorporate certain additional information that children get from their environment. Children are sometimes told about some grammatical rule that enumerates elements of the language. It is argued that these rules are a kind of additional information. They enable children to see in advance elements that are yet to appear in their environments. Also, children are being given some information about what is not in the language. Sometimes, they are rebuked for making incorrect utterances, or are told of a rule that enumerates certain non-elements of the language. An attempt has been made to extend Gold's model to incorporate both the above types of additional information. It is shown that either type of additional information enhances the learning capability of formal language learning devices.
7521284
On learning to coordinate: random bits help, insightful normal forms, and competency isomorphisms
A mere bounded number of random bits judiciously employed by a probabilistically correct algorithmic coordinator is shown to increase the power of learning to coordinate compared to deterministic algorithmic coordinators. Furthermore, these probabilistic algorithmic coordinators are provably not characterized in power by teams of deterministic ones. An insightful, enumeration technique based, normal form characterization of the classes that are learnable by total computable coordinators is given. These normal forms are for insight only since it is shown that the complexity of the normal form of a total computable coordinator can be infeasible compared to the original coordinator. Montagna and Osherson showed that the competence class of a total coordinator cannot be strictly improved by another total coordinator. It is shown in the present paper that the competencies of any two total coordinators are the same modulo isomorphism. Furthermore, a completely effective, index set version of this competency isomorphism result is given, where all the coordinators are total computable. We also investigate the competence classes of total coordinators from the points of view of topology and descriptive set theory.
1156882
Analytic evaluation of the expectation and variance of different performance measures of a schedule on a single machine under processing time variability
Abstract
In this paper, we present closed-form expressions, wherever possible, or devise algorithms otherwise, to determine the expectation and variance of a given schedule on a single machine. We consider a variety of completion time and due date-based objectives. The randomness in the scheduling process is due to variable processing times with known means and variances of jobs and, in some cases, a known underlying processing time distribution. The results that we present in this paper can enable evaluation of a schedule in terms of both the expectation and variance of a performance measure considered, and thereby, aid in obtaining a stable schedule. Additionally, the expressions and algorithms that are presented, can be incorporated in existing scheduling algorithms in order to determine expectation-variance efficient schedules.

112103084
Using simulation generators for modeling flexible manufacturing systems
7194511
A Concept Prototype for Integrated Gaming and Simulation for Incident Management
This paper describes a prototype that has been developed to demonstrate the concept of integrated gaming and simulation for incident management. An architecture for the purpose was developed and presented at the last conference. A hypothetical emergency incident scenario has been developed for demonstrating the applicability of integrated simulation and gaming. A number of simulation and gaming modules have been utilized to model the major aspects of the hypothetical scenario. The modules demonstrate the value of utilizing simulation for incident management applications. They can be used to highlight the value of simulation and gaming for training applications in particular. Two of the simulation modules have been integrated using a modified implementation of the high level architecture to give an idea of the advantages. Technical issues in integration are identified
17397415
Analyzing the supply chain for a large logistics operation using simulation
This paper presents a case study of using simulation for analyzing the impact of proposed changes in the supply chain processes for a large logistics operation. The major changes explored include business process changes, and use of new supply chain software. The results of the analysis indicate that the changes in forecast accuracy provide much larger savings compared to process automation changes. A number of insights are drawn from the results of the analyses.
15127807
Pricing of Information Products on Online Servers: Issues, Models, and Analysis
Online information servers that provide access to diverse databases where users can search for, browse through, and download the information they need have been rapidly increasing in number in the past few years. Online vendors have traditionally charged users for information on the based on the length of the time they were connected to the databases. With hardware and software advances, many online servers have recently started changing their pricing strategies to search-based and/or subscription-fee pricing. This paper examines the various issues involved in pricing these information products, and presents an economic approach to analyze conditions under which the various pricing schemes may prove optimal for the online servers. Our results show that the variation in consumer expertise and valuation of information affects the choice of a pricing strategy by the server. We present general conditions under which subscription-fee pricing is optimal even when consumer demand is inelastic. We also find that, given the cost structures characterizing the market, undifferentiated online servers can compete and coexist in the market each making positive profits. We show that in a competitive setting an increase in costs of online servers can sometimes benefit them by enabling them to differentiate themselves. Our results offer insights into the trends in pricing strategies and may provide an explanation as to why many servers may persist with connect-time strategies.