16032991
Not-So-Nearly-Minimal-Size Program Inference
Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and “nearly” minimal size, i.e, within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs severely limits learning power. Nonetheless, in, for example, scientific inference, parsimony is considered highly desirable. A limcomputable function is (by definition) one computable by a procedure allowed to change its mind finitely many times about its output. Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be “not-so-nearly” minimal size, e.g.; to be within a lim-computable function of actual minimal size. It is interestingly shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Also considered are lim-computable functions as above but for which notations for constructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal complexity bounded version of lim-computability, the power of the resultant learning criteria form strict infinite hierarchies intermediate between the computable and the lim-computable cases. Many open questions are also presented.
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.
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.
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.
122230605
On the intrinsic complexity of learning recursive functions
The intrinsic complexity of learning compares the difficulty of learning classes of objects by using some reducibility notion. For several types of learning recursive functions, both natural complete classes are exhibited and necessary and sufficient conditions for completeness are derived. Informally, a class is complete iff both its topological structure is highly complex while its algorithmic structure is easy. Some self-describing classes turn out to be complete. Furthermore, the structure of the intrinsic complexity is shown to be much richer than the structure of the mind change complexity, though in general, intrinsic complexity and mind change complexity can behave "orthogonally".
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.
5859647
Simulation in the next millennium
The paper looks into the future of simulation. The capabilities and features of simulation software of the future are hypothesized, focusing on the major aspects of their use. The features addressed include model building, visualization, output analysis and optimization, integration and the Internet. The discussion of simulation software in the future is closely related to the vision of future applications of simulation. Applications of simulation in the near term future are proposed using examples of advanced applications that are in conceptual stages at present. Applications of simulation in the long term future are also proposed, bordering on science fiction.
11952430
David vs. Goliath: An Analysis of Asymmetric Mixed-Strategy Games and Experimental Evidence
Mixed strategies are widely used to model strategic situations in diverse fields such as economics, marketing, political science, and biology. However, some of the implications of asymmetric mixed-strategy solutions are counterintuitive. We develop a stylized model of patent race to examine some of these implications. In our model two firms compete to develop a product and obtain a patent. However, one firm values the patent more because of its market advantages, such as brand reputation and distribution network. Contrary to some intuition, we find that the firm that values the patent less is likely to invest more aggressively in developing the product and will also win the patent more often. We argue that the reason for these counterintuitive results is inherent in the very concept of mixed strategy solution. In a laboratory test, we examine whether subjects' behavior conforms to the equilibrium predictions. We find that the aggregate behavior of our subjects is consistent with the game-theoretic predictions. With the help of the experience-weighted attraction (EWA) learning model proposed by Camerer and Ho (1999), we show that adaptive learning can account for the investment behavior of our subjects.We find that the EWA learning model tracks the investment decisions of our subjects well, whether we hold out trials or an entire group of subjects.
1408878
Distributed simulation for interoperability testing along the supply chain
The need for interoperability of information systems among supply chain partners has been recognized. A number of standards have been or are being developed to ensure interoperability of applications used along the supply chain. An associated need for interoperability testing has emerged. There is a need to evaluate compliance of applications to standards across specific platforms. The standards themselves need to be evaluated for a comprehensive coverage of the application scope (validation testing). This paper reports on a distributed simulation based approach for supply chain interoperability testing. Simulations are used to represent real life organizations to serve as sources and consumers of dynamic data. The data can be encapsulated per the standard under consideration and exchanged with other organizations directly or through selected applications for testing. Error free performance of the simulated systems over time will provide confidence in the interoperability of applications and in the standards themselves.
3133166
Tradeoffs in building a generic supply chain simulation capability
Building a simulation model for any large complex system requires high expertise and effort. These requirements can be reduced through building generic simulation capability that includes artifacts for facilitating the development of the simulation model. The artifacts can have a range of capabilities depending on the design goals for the simulation. This paper focuses on issues to be considered in building a generic simulation capability for supply chains. A number of approaches used in recent years for building generic supply chain simulation capability are discussed. Such approaches include data-driven simulators, interactive simulators, and sub-models for supply chain components. Tradeoffs are identified that should be considered in selecting an approach for building a generic supply chain simulation capability.
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