Perfect recall is the common and natural assumption that an agent never forgets. As a consequence, the agent can always condition its choice of action on any prior observations. In this paper, we explore relaxing this assumption. We observe the negative impact this relaxation has on algorithms: some algorithms are no longer well-defined, while others lose their theoretical guarantees on the quality of a solution. Despite these disadvantages, we show that removing this restriction can provide considerable empirical advantages when modeling extremely large extensive games. In particular, it allows fine granularity of the most relevant observations without requiring decisions to be contingent on all past observations. In the domain of poker, this improvement enables new types of information to be used in the abstraction. By making use of imperfect recall and new types of information, our poker program was able to win the limit equilibrium event as well as the no-limit event at the 2008 AAAI Computer Poker Competition. We show experimental results to verify that our pro- grams using imperfect recall are indeed stronger than their perfect recall counterparts.

Generating minimal hitting sets of a collection of sets is known to be NP-hard, necessitating heuristic approaches to handle large problems. In this paper a low-cost, approximate minimal hitting set (MHS) algorithm, coined Staccato, is presented. Staccato uses a heuristic function, borrowed from a lightweight, statistics-based software fault localization approach, to guide the MHS search. Given the nature of the heuristic function, Staccato is specially tailored to model-based diagnosis problems (where each MHS solution is a diagnosis to the problem), although well-suited for other application domains as well. We apply Staccato in the context of model-based diagnosis and show that even for small problems our approach is orders of magnitude faster than the brute-force approach, while still capturing all important solutions. Furthermore, due to its low cost complexity, we also show that Staccato is amenable to large problems including millions of variables.

State abstraction has been widely used for state aggregation in approaches to AI search and planning. In this paper we use a powerful abstraction technique from software model checking for representing collections of states with different object quantities and properties. We exploit this method to develop precise abstractions and action operators for use in AI. This enables us to find scalable, algorithm-like plans with branches and loops which can solve problems of unbounded sizes. We describe how this method of abstraction can be effectively used in AI, with compelling results from implementations of two planning algorithms.

MINLP problems are hard constrained optimization problems, with nonlinear constraints and mixed discrete continuous variables. They can be solved using a Branch-and-Bound scheme combining several methods, such as linear programming, interval analysis, and cutting methods. Our goal is to integrate constraint programming techniques in this framework. Firstly, global constraints can be introduced to reformulate MINLP problems thus leading to clean models and more precise computations. Secondly, interval-based approximation techniques for nonlinear constraints can be improved by taking into account the integrality of variables early. These methods have been implemented in an interval solver and we present experimental results from a set of MINLP instances.

Pattern Databases (PDBs) are the most common form of memory-based heuristics, and they have been widely used in a variety of permutation puzzles and other domains. We explore the true-distance heuristics (TDHs) (also appeared in  (Sturtevant et al. 2009)) which are a different form of memory-based heuristics, designed to work in problem states where there isn't a fixed goal state. Unlike PDBs, which build a heuristic based on distances in an abstract state space, TDHs store distances which are computed in the actual state space. We look in detail at how TDHs work, providing both theoretical and experimental motivation for their use.

Abstraction, reformulation, and approximation including some copresented at the Symposium (ARA) techniques are deemed crucial in the on Combinatorial Search (SoCS), which was ability of humans to reason about complex and collocated with SARA this year.

Arc consistency algorithms are widely used to prune the search space of Constraint Satisfaction Problems (CSPs). Since many researchers associate arc consistency with binary normalized CSPs, there is a confusion between the notion of arc consistency and 2-consistency. 2-consistency guarantees that any instantiation of a value to a variable can be consistently extended to any second variable. Thus, 2-consistency can be stronger than arc-consistency in binary CSPs. In this paper, we present a new algorithm, called 2-C3, which achieves 2-consistency in binary and non-normalized CSPs. This algorithm is a reformulation of the well-known AC3 algorithm. The evaluation section shows that 2-C3 is able to prune more search space than AC3 and AC4.

In the satisfiability domain, it is well-known that a SAT algorithm may solve a problem instance easily and another instance hardly, whilst these two instances are equivalent CNF encodings of the original problem. Moreover, different algorithms may disagree on which encoding makes the problem easier to solve. In this paper, we focus on the CNF encoding of cardinality constraints, which states that exactly k propositional variables in a given set are assigned to true. We demonstrate the importance of the semantics of the SAT variables in the encoding of this constraint. We implement several variants of the CNF encoding in which the close semantic variables are grouped. We then examine these new encodings on problems generated from diagnosis of discrete-event system. Our results demonstrate that both stochastic and systematic SAT algorithms can now solve most of the problem instances, which were unreachable before. These results also indicate that, on average cases, there is an encoding that suits well both SLS and DPLL algorithms.

In a constraint satisfaction problem, the tightness of an individual constraint only describes the influence that the variables within its scope have on one another. Clusters provide a broader view; they are dense, tight subproblems within a problem. A set of clusters for a problem and the links between them provide an abstraction of it. That abstraction can be used to guide search, to curtail inference, and to provide explanations to the user. This work is a hybrid of global and local search, where local search creates an abstraction and then global search exploits it. Heuristics reference clusters to order variables and to propagate more thoughtfully with respect to them. Results are provided on a variety of challenging benchmark problems.

A problem that often arises in using abstraction is the generation of abstract states, called spurious states, that are—in the abstract space—reachable from some abstract image of a state s, but which have no corresponding state in the original space reachable from s. Spurious states can have a negative effect on pattern database sizes and heuristic quality. We formally define a property—the downward path preserving property (DPP)—that guarantees an abstraction has no spurious states. Analyzing the computational complexity of (i) testing the DPP property for a given state space and abstraction and of (ii) determining whether this property is achievable at all for a given state space, results in strong hardness theorems. On the positive side, we identify formal conditions under which finding DPP abstractions is tractable.