145211
Computational Limits on Team Identification of Languages
A team of learning machines is a multiset of learning machines. A team is said to successfully identify a concept just in case each member of some nonempty subset, of predetermined size, of the team identifies the concept. Team identification of programs for computable functions from their graphs has been investigated by Smith. Pitt showed that this notion is essentially equivalent to function identification by a single probabilistic machine. The present paper introduces, motivates, and studies the more difficult subject of team identification of grammars for languages from positive data. It is shown that an analog of Pitt's result about equivalence of team function identification and probabilistic function identification does not hold for language identification, and the results in the present paper reveal a very complex structure for team language identification. It is also shown that for certain cases probabilistic language identification is strictly more powerful than team language identification. Proofs of many results in the present paper involve very sophisticated diagonalization arguments. Two very general tools are presented that yield proofs of new results from simple arithmetic manipulation of the parameters of known ones.
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.
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.
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.
644359
Anomalous Learning Helps Succinctness
Abstract It is shown that allowing a bounded number of anomalies (mistakes) in the final programs learned by an algorithmic procedure can considerably “succinctify” those final programs. Naturally, only those contexts are investigated in which the presence of anomalies is not actually required for successful inference (learning). The contexts considered are certain infinite subclasses of the class of characteristic functions of finite sets. For each finite set D , these subclasses have a finite set containing D . This latter prevents the anomalies from wiping out all the information in the sets featured in these subclasses and shows the context to be fairly robust. Some of the results in the present paper are shown to be provably more constructive than others. The results of this paper can also be interpreted as facts about succinctness of coding finite sets, which facts have interesting consequences for learnability of decision procedures for finite sets.
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.
17470610
Load balancing for conservative simulation on shared memory multiprocessor systems
Load balancing is a crucial factor in achieving good performance for parallel discrete event simulations. We present a load balancing scheme that combines both static partitioning and dynamic load balancing. The static partitioning scheme maps simulation objects to logical processes before simulation starts while the dynamic load balancing scheme attempts to balance the load during runtime. The static scheme involves two steps. First, the simulation objects that contribute to small lookahead are merged together by using a merging algorithm. Then a partitioning algorithm is applied. The merging is needed to ensure a consistent performance for our dynamic scheme. Our dynamic scheme is tailor-made for an asynchronous simulation protocol that does not rely on null messages. The performance study on a supply chain simulation shows that the partitioning algorithm and dynamic load balancing are important in achieving good performance.
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.
44990266
Topology Independent Models for Parallel Computation
In a continuous or cyclic steam foam drive, recovery of an acidic reservoir oil (1) is improved by injecting steam accompanied by (a) enough dissolved alkaline monovalent salt to ion-exchange multivalent cations from the reservoir rocks and precipitate those ions in compounds which are insoluble in an alkaline aqueous liquid as well as forming soaps of the reservoir oil acids and (b) surfactants for foaming the steam and increasing the salt tolerance of an aqueous surfactant system containing the soaps of the reservoir oil acids, and (2) is further improved by using trona or an equivalent mixture of alkali metal carbonates and bicarbonates as the alkaline monovalent salt.
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.

9214465
Performance prediction tools for parallel discrete-event simulation
We have developed a set of performance prediction tools which help to estimate the achievable speedups from parallelizing a sequential simulation. The tools focus on two important factors in the actual speedup of a parallel simulation program: the simulation protocol used; and the inherent parallelism in the simulation model. The first two tools are a performance/parallelism analyzer for a conservative, asynchronous simulation protocol, and a similar analyzer for a conservative, synchronous (super-step) protocol. Each analyzer allows us to study how the speedup of a model changes with increasing number of processors, when a specific protocol is used. The third tool-a critical path analyzer-gives on ideal upper bound to the model's speedup. This paper gives an overview of the prediction tools, and reports the predictions from applying the tools to a discrete-event wafer fabrication simulation model. The predictions are close to speedups from actual parallel implementations. These tools help us to set realistic expectations of the speedup from a parallel simulation program, and to focus our work on issues which are more likely to yield performance improvement.