32998379
Learning languages from positive data and negative counterexamples
In this paper we introduce a paradigm for learning in the limit of potentially infinite languages from all positive data and negative counterexamples provided in response to the conjectures made by the learner. Several variants of this paradigm are considered that reflect different conditions/constraints on the type and size of negative counterexamples and on the time for obtaining them. In particular, we consider the models where (1) a learner gets the least negative counterexample; (2) the size of a negative counterexample must be bounded by the size of the positive data seen so far; (3) a counterexample can be delayed. Learning power, limitations of these models, relationships between them, as well as their relationships with classical paradigms for learning languages in the limit (without negative counterexamples) are explored. Several surprising results are obtained. In particular, for Gold's model of learning requiring a learner to syntactically stabilize on correct conjectures, learners getting negative counterexamples immediately turn out to be as powerful as the ones that do not get them for indefinitely (but finitely) long time (or are only told that their latest conjecture is not a subset of the target language, without any specific negative counterexample). Another result shows that for behaviorally correct learning (where semantic convergence is required from a learner) with negative counterexamples, a learner making just one error in almost all its conjectures has the ''ultimate power'': it can learn the class of all recursively enumerable languages. Yet another result demonstrates that sometimes positive data and negative counterexamples provided by a teacher are not enough to compensate for full positive and negative data.
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.
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".
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.
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.

47220301
Expert simulation for on-line scheduling
The state-of-the-art in manufacturing has moved toward flexibility, automation and integration. The efforts spent on bringing computer-integrated manufacturing (CIM) to plant floors have been motivated by the overall thrust to increase the speed of new products to market. One of the links in CIM is plant floor scheduling, which is concerned with efficiently orchestrating the plant floor to meet the customer demand and responding quickly to changes on the plant floor and changes in customer demand. The Expert System Scheduler (ESS) has been developed to address this link in CIM. The scheduler utilizes real-time plant information to generate plant floor schedules which honor the factory resource constraints while taking advantage of the flexibility of its components.
The scheduler uses heuristics developed by an experienced human factory scheduler for most of the decisions involved in scheduling. The expertise of the human scheduler has been built into the computerized version using the expert system approach of the discipline of artificial intelligence (AI). Deterministic simulation concepts have been used to develop the schedule and determine the decision points. As such, simulation modeling and AI techniques share many concepts, and the two disciplines can be used synergistically. Examples of some common concepts are the ability of entities to carry attributes and change dynamically (simulation—entities/attributes or transaction/parameters versus AI—frames/slots); the ability to control the flow of entities through a model of the system (simulation—conditional probabilities versus AI—production rules); and the ability to change the model based upon state variables (simulation—language constructs based on variables versus AI—pattern-invoked programs). Shannon [6] highlights similarities and differences between conventional simulation and an AI approach. Kusiak and Chen [3] report increasing use of simulation in development of expert systems.
ESS uses the synergy between AI techniques and simulation modeling to generate schedules for plant floors. Advanced concepts from each of the two areas are used in this endeavor. The expert system has been developed using frames and object-oriented coding which provides knowledge representation flexibility. The concept of “backward” simulation, similar to the AI concept of backward chaining, is used to construct the events in the schedule. Some portions of the schedule are constructed using forward or conventional simulation.
The implementation of expert systems and simulation concepts is intertwined in ESS. However, the application of the concepts from these two areas will be treated separately for ease of presentation. We will first discuss the expert system approach and provide a flavor of the heuristics. The concept of backward simulation and the motive behind it will then be explored along with some details of the implementation and the plant floor where the scheduler is currently being used. We will then highlight some advantages and disadvantages of using the expert simulation approach for scheduling, and, finally, the synergetic relationship between expert systems and simulation.
120386960
Evolutionary games with two timescales
We consider a two timescale model of learning by economic agents wherein active or 'ontogenetic' learning by individuals takes place on a fast scale and passive or 'phylogenetic' learning by society as a whole on a slow scale, each affecting the evolution of the other. The former is modelled by the Monte Carlo dynamics of physics, while the latter is modelled by the replicator dynamics of evolutionary biology. Various qualitative aspects of the dynamics are studied in some simple cases, both analytically and numerically, and its role as a useful modelling device is emphasized.
14852497
Towards standards for integrated gaming and simulation for incident management
Simulation and gaming can support decision making through all phases of incident management including prevention, preparedness, response, recovery and mitigation. A number of gaming and simulation tools have been developed for the purpose but they generally utilize proprietary or unique data interfaces and their own view of partitioning the application and solution space. This creates a large obstacle for wide use, and in particular, prevents the use of these tools in an integrated manner to address the application space. This paper explores the groundwork needed to build standards for integrated gaming and simulation tools for incident management. 
 
An architecture has been proposed to identify the required groups of simulation and gaming modules for incident management and define their scope in the solution space. A conceptual model is proposed for the data required for such simulations. Available data exchange standards are mapped to the conceptual data model. A concept prototype has been developed based on the architecture to demonstrate the value of integrated modeling and simulation and the architecture itself. A number of simulation and gaming modules have been utilized to model the major aspects of a hypothetical scenario. The exercise is used to identify the issues due to lack of data exchange standards.
10615305
Manufacturing sypply chain management: distributed supply chain simulation across enterprise boundaries
The effective practice of supply chain management (SCM) is crucial to improve corporations' competitive advantage. Many corporations have built simulation models to facilitate the application of simulation in designing, evaluating, and optimizing their supply chain. Traditionally, a supply chain involves only a single enterprise with multiple facilities and distribution centers. Hence, sharing of detailed simulation models is not a problem in this scenario. But in recent years, the scope of SCM has evolved to cross the enterprise boundaries. Applying simulation in designing, evaluating, and optimizing the supply chain becomes more difficult since the participating corporations might not be willing to share their simulation models with partners. In this paper, distributed simulation techniques are presented as an enabling technology that allows corporations to construct a cross enterprise simulation while hiding model details within the enterprise. This can be realized by either building the simulation on top of the Runtime Infrastructure of the High Level Architecture or building the simulation on top of a customized distributed discrete event simulation protocol. These alternative approaches are compared in terms of their performance and interoperability. The comparison of the performance is done through a benchmarking test of a semiconductor supply chain model.