We investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a strong Nash equilibrium is SigmaP2-complete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each player's payoff depends on moves of other players. We say that a game has small neighborhood if the utility function for each player depends only on (the actions of) a logarithmically small number of other players. The dependency structure of a game G can be expressed by a graph DG(G) or by a hypergraph H(G). By relating Nash equilibrium problems to constraint satisfaction problems (CSPs), we show that if G has small neighborhood and if H(G) has bounded hypertree width (or if DG(G) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFL-complete and thus in the class NC2 of highly parallelizable problems.

A fundamental requirement of any task-oriented dialogue system is the ability to generate object descriptions that refer to objects in the task domain. The subproblem of content selection for object descriptions in task-oriented dialogue has been the focus of much previous work and a large number of models have been proposed. In this paper, we use the annotated COCONUT corpus of task-oriented design dialogues to develop feature sets based on Dale and Reiter's (1995) incremental model, Brennan and Clark's (1996) conceptual pact model, and Jordan's (2000b) intentional influences model, and use these feature sets in a machine learning experiment to automatically learn a model of content selection for object descriptions. Since Dale and Reiter's model requires a representation of discourse structure, the corpus annotations are used to derive a representation based on Grosz and Sidner's (1986) theory of the intentional structure of discourse, as well as two very simple representations of discourse structure based purely on recency. We then apply the rule-induction program RIPPER to train and test the content selection component of an object description generator on a set of 393 object descriptions from the corpus. To our knowledge, this is the first reported experiment of a trainable content selection component for object description generation in dialogue. Three separate content selection models that are based on the three theoretical models, all independently achieve accuracies significantly above the majority class baseline (17%) on unseen test data, with the intentional influences model (42.4%) performing significantly better than either the incremental model (30.4%) or the conceptual pact model (28.9%). But the best performing models combine all the feature sets, achieving accuracies near 60%. Surprisingly, a simple recency-based representation of discourse structure does as well as one based on intentional structure. To our knowledge, this is also the first empirical comparison of a representation of Grosz and Sidner's model of discourse structure with a simpler model for any generation task.

In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show that it is possible to construct an efficient set domain propagator which compactly represents many set domains and set constraints using ROBDDs. We demonstrate that the ROBDD-based approach provides unprecedented flexibility in modeling constraint satisfaction problems, leading to performance improvements. We also show that the ROBDD-based modeling approach can be extended to the modeling of integer and multiset constraint problems in a straightforward manner. Since domain propagation is not always practical, we also show how to incorporate less strict consistency notions into the ROBDD framework, such as set bounds, cardinality bounds and lexicographic bounds consistency. Finally, we present experimental results that demonstrate the ROBDD-based solver performs better than various more conventional constraint solvers on several standard set constraint problems.

Today, approximately 10 percent of the world's population is over the age of 60; by 2050 this proportion will have more than doubled. Moreover, the greatest rate of increase is amongst the "oldest old," people aged 85 and over. While many older adults remain healthy and productive, overall this segment of the population is subject to physical and cognitive impairment at higher rates than younger people. This article surveys new technologies that incorporate artificial intelligence techniques to support older adults and help them cope with the changes of aging, in particular with cognitive decline.

Variable elimination is a general technique for constraint processing. It is often discarded because of its high space complexity. However, it can be extremely useful when combined with other techniques. In this paper we study the applicability of variable elimination to the challenging problem of finding still-lifes. We illustrate several alternatives: variable elimination as a stand-alone algorithm, interleaved with search, and as a source of good quality lower bounds. We show that these techniques are the best known option both theoretically and empirically. In our experiments we have been able to solve the n 20 instance, which is far beyond reach with alternative approaches.

We present a modified version of the perceptron learning algorithm (PLA) which solves semidefinite programs (SDPs) in polynomial time. The algorithm is based on the following three observations: (i) Semidefinite programs are linear programs with infinitely many (linear) constraints; (ii) every linear program can be solved by a sequence of constraint satisfaction problems with linear constraints; (iii) in general, the perceptron learning algorithm solves a constraint satisfaction problem with linear constraints in finitely many updates. Combining the PLA with a probabilistic rescaling algorithm (which, on average, increases the size of the feasable region) results in a probabilistic algorithm for solving SDPs that runs in polynomial time. We present preliminary results which demonstrate that the algorithm works, but is not competitive with state-of-the-art interior point methods.

We present a modified version of the perceptron learning algorithm (PLA) which solves semidefinite programs (SDPs) in polynomial time. The algorithm is based on the following three observations: (i) Semidefinite programs are linear programs with infinitely many (linear) constraints; (ii) every linear program can be solved by a sequence of constraint satisfaction problems with linear constraints; (iii) in general, the perceptron learning algorithm solves a constraint satisfaction problem with linear constraints in finitely many updates. Combining the PLA with a probabilistic rescaling algorithm (which, on average, increases the size of the feasable region) results in a probabilistic algorithm for solving SDPs that runs in polynomial time. We present preliminary results which demonstrate that the algorithm works, but is not competitive with state-of-the-art interior point methods.

We present a modified version of the perceptron learning algorithm (PLA) which solves semidefinite programs (SDPs) in polynomial time. The algorithm is based on the following three observations: (i) Semidefinite programs are linear programs with infinitely many (linear) constraints; (ii) every linear program can be solved by a sequence of constraint satisfaction problems with linear constraints; (iii) in general, the perceptron learning algorithm solves a constraint satisfaction problem with linear constraints in finitely many updates. Combining the PLA with a probabilistic rescaling algorithm (which, on average, increases the size of the feasable region) results in a probabilistic algorithmfor solving SDPs that runs in polynomial time. We present preliminary results which demonstrate that the algorithm works,but is not competitive with state-of-the-art interior point methods.

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This article is a sequel to an article titled "A New Direction in AI -- Toward a Computational Theory of Perceptions," which appeared in the Spring 2001 issue of AI Magazine (volume 22, No. 1, 73-84). The concept of precisiated natural language (PNL) was briefly introduced in that article, and PNL was employed as a basis for computation with perceptions. In what follows, the conceptual structure of PNL is described in greater detail, and PNL's role in knowledge representation, deduction, and concept definition is outlined and illustrated by examples. What should be understood is that PNL is in its initial stages of development and that the exposition that follows is an outline of the basic ideas that underlie PNL rather than a definitive theory. A natural language is basically a system for describing perceptions. Perceptions, such as perceptions of distance, height, weight, color, temperature, similarity, likelihood, relevance, and most other attributes of physical and mental objects are intrinsically imprecise, reflecting the bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information. In this perspective, the imprecision of natural languages is a direct consequence of the imprecision of perceptions (Zadeh 1999, 2000). How can a natural language be precisiated -- precisiated in the sense of making it possible to treat propositions drawn from a natural language as objects of computation? This is what PNL attempts to do. In PNL, precisiation is accomplished through translation into what is termed a precisiation language. In the case of PNL, the precisiation language is the generalized-constraint language (GCL), a language whose elements are so-called generalized constraints and their combinations. What distinguishes GCL from languages such as Prolog, LISP, SQL, and, more generally, languages associated with various logical systems, for example, predicate logic, modal logic, and so on, is its much higher expressive power. The conceptual structure of PNL mirrors two fundamental facets of human cognition: (a) partiality and (b) granularity (Zadeh 1997). Partiality relates to the fact that most human concepts are not bivalent, that is, are a matter of degree. Thus, we have partial understanding, partial truth, partial possibility, partial certainty, partial similarity, and partial relevance, to cite a few examples. Similarly, granularity and granulation relate to clumping of values of attributes, forming granules with words as labels, for example, young, middle-aged, and old as labels of granules of age. Existing approaches to natural language processing are based on bivalent logic -- a logic in which shading of truth is not allowed. PNL abandons bivalence. By so doing, PNL frees itself from limitations imposed by bivalence and categoricity, and opens the door to new approaches for dealing with long-standing problems in AI and related fields (Novak 1991). At this juncture, PNL is in its initial stages of development. As it matures, PNL is likely to find a variety of applications, especially in the realms of world knowledge representation, concept definition, deduction, decision, search, and question answering.