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.

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.

The exploration of complex interaction networks has attracted considerable interest in various fields, ranging from fundamental biology and medicine to statistical physics and information technology.  In -omics disciplines, significant progresses have been made in understanding the large-scale properties and the biological relevance of these interactions. Some properties such as scale-free distribution of nodes connectivity or centrality are aspects commonly described in such complex interaction systems. In many of these studies the analysis of network topology is complemented by a semantic analysis that may rely on  different labels associated to the interacting entities.   One of the bottleneck of these semantic analysis is that they  are computationally costly. In this paper we present a framework to explore abstraction of networks useful to speedup the computation  of ground network measures. Such abstraction mechanisms may be used to efficiently provide accurate approximations of ground network measures.

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.

This article presents two new algorithms whose purpose is to maintain the Max-RPC domain filtering consistency during search with a minimal memory footprint and implementation effort. Both are sub-optimal algorithms that make use of support residues, a backtrack-stable and highly efficient data structure which was successfully used to develop the state-of-the-art AC-3rm algorithm. The two proposed algorithms, Max-RPCrm and L-Max-RPCrm are competitive with best, optimal Max-RPC algorithms, while being considerably simpler to implement. L-Max-RPCrm computes an approximation of the Max-RPC consistency, which is guaranteed to be strictly stronger than AC with the same space complexity and better worst-case time complexity than Max-RPCrm. In practice, the difference in filtering power between L-Max-RPCrm and standard Max-RPC is nearly indistinguishable on random problems. Max-RPCrm and L-Max-RPCrm are implemented into the Choco Constraint Solver through a strong consistency global constraint. This work opens new perspectives upon the development of strong consistency algorithms into constraint solvers.

We study novel approaches for solving of hard combinatorial problems by translation to Boolean Satisfiability (SAT). Our focus is on combinatorial problems that can be represented as a permutation of n objects, subject to additional constraints. In the case of the Hamiltonian Cycle Problem (HCP), these constraints are that two adjacent nodes in a permutation should also be neighbors in the original graph for which we search for a Hamiltonian cycle. We use the absolute SAT encoding of permutations, where for each of the n objects and each of its pos- sible positions in a permutation, a predicate is defined to indicate whether the object is placed in that position. For implementation of this predicate, we compare the direct and logarithmic encodings that have been used previously, against 16 hierarchical parameterizable encodings of which we explore 416 instantiations. We propose the use of enumerative adjacency constraints—that enumerate the possible neighbors of a node in a permutation — instead of, or in addition to the exclusivity adjacency constraints — that exclude impossible neighbors, and that have been applied previously. We study 11 heuristics for efficiently choosing the first node in the Hamiltonian cycle, as well as 8 heuristics for static CNF variable ordering. We achieve at least 4 orders of magnitude average speedup on HCP benchmarks from the phase transition region, relative to the previously used encodings for solving of HCPs via SAT, such that the speedup is increasing with the size of the graphs.

Several explanation and interpretation tasks, such as diagnosis, plan recognition and image interpretation, can be formalized as abductive and consistency reasoning. The interpretation task is usually executed for the purpose of performing actions, e.g., in diagnosis, repair actions or therapy. In some cases actions are the only or the main way for discriminating among alternative explanations. Some proposals address the problem based on a task-independent representation of a domain which includes an ontology or taxonomy of hypotheses and actions. In this paper we rely on the same type of representation, and we point out the role of abstractions in an iterative process where, like in model-based diagnosis and troubleshooting, further observations or actions are proposed to achieve the overall goal of discriminating among candidate hypotheses and, more importantly, performing the appropriate actions for the case at hand. Discrimination is performed up to an appropriate level which depends on the cost of actions (e.g. repair actions or therapy) to be taken based on the results of abduction, and on the cost of additional observations, which should be balanced with the benefits, in terms of more suitable actions, of better discrimination. Abstractions have a significant impact on this trade-off, given that the cost of observing the same phenomenon at different levels of abstraction may be quite different, and choosing a generic action, without information on which specific instance is most appropriate, is, in general, suboptimal.

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.

We present algorithms for testing the satisfiability and finding the tightened transitive closure of conjunctions of addition constraints of the form ± x ± y ≤ d and bound constraints of the form ± x ≤ d where x and y are integer variables and d is an integer constrant. The running time of these algorithms is a cubic polynomial in the number of input constraints. We also describe an efficient matrix representation of addition and bound constraints. The matrix representation provides a easy, algebraic implementation of the satisfiability and tightened transitive closure algorithms. We also outline the use of these algorithms for the improved implementation of abstract interpretation methods based on the octagonal abstract domain.

Tailoring solver-independent constraint instances to target solvers is an important component of automated constraint modelling. We augment the tailoring process by a set of enhancement techniques of which many are successfully established in related fields, such as common subexpression elimination. Our aim is to apply these techniques in an efficient fashion,  since we tailor instance-wise, and not whole problem classes. We integrate automated enhancement into the tailoring procedure, which creates a novel setup with great potential, as our empirical analysis confirms: impressive speedups, additional propagation and instance  reduction, all for investing little computational effort.