This paper introduces the Seqbin meta-constraint with a polytime algorithm achieving generalized arc-consistency. Seqbin can be used for encoding counting constraints such as Change, Smooth, or InncreasingNValue. For all of them the time and space complexity is linear in the sum of domain sizes, which improves or equals the best known results of the literature.

Many systems use Markov models to generate finite-length sequences that imitate a given style. These systems often need to enforce specific control constraints on the sequences to generate. Unfortunately, control constraints are not compatible with Markov models, as they induce long-range dependencies that violate the Markov hypothesis of limited memory. Attempts to solve this issue using heuristic search do not give any guarantee on the nature and probability of the sequences generated. We propose a novel and efficient approach to controlled Markov generation for a specific class of control constraints that 1) guarantees that generated sequences satisfy control constraints and 2) follow the statistical distribution of the initial Markov model. Revisiting Markov generation in the framework of constraint satisfaction, we show how constraints can be compiled into a non-homogeneous Markov model, using arc-consistency techniques and renormalization. We illustrate the approach on a melody generation problem and sketch some realtime applications in which control constraints are given by gesture controllers.

Special-purpose constraint propagation algorithms (such as those for the element constraint) frequently make implicit use of short supports — by examining a subset of the variables, they can infer support for all other variables and values and save substantial work. However, to date general purpose propagation algorithms (such as GAC-Schema) rely upon supports involving all variables. We demonstrate how to employ short supports in a new general purpose propagation algorithm called ShortGAC. This works when provided with either an explicit list of allowed short tuples, or a function to calculate the next supporting short tuple. Empirical analyses demonstrate the efficiency of ShortGAC compared to other general-purpose propagation algorithms. In some cases ShortGAC even exhibits similar performance to special-purpose propagators.

As adversarial environments become more complex, it is increasingly crucial for agents to exploit the mistakes of weaker opponents, particularly in the context of winning tournaments and competitions.In this work, we present a simple post processing technique, which wecall Perfect Information Post-Mortem Analysis (PIPMA), that can quickly assess the playing strength of an opponent in certain classes of game environments. We apply this technique to skat, a popular German card game, and show that we can achieve substantial performance gains against not only players weaker than our program, but against stronger players as well. Most importantly, PIPMA can model the opponent after only a handful of games. To our knowledge, this makes our work the first successful example of an opponent modelling technique that can adapt its play to a particular opponent in real time in a complex game setting.

We define solving techniques for the Minimum Satisfiability Problem (MinSAT), propose an efficient branch-and-bound algorithm to solve the Weighted Partial MinSAT problem, and report on an empirical evaluation of the algorithm on Min-3SAT, MaxClique, and combinatorial auction problems. Techniques solving MinSAT are substantially different from those for the Maximum Satisfiability Problem (MaxSAT). Our results provide empirical evidence that solving combinatorial optimization problems by reducing them to MinSAT may be substantially faster than reducing them to MaxSAT, and even competitive with specific algorithms. We also use MinSAT to study an interesting correlation between the minimum number and the maximum number of satisfied clauses of a SAT instance.

Classical constraint satisfaction problems (CSPs) are commonly defined on finite domains. In real life, constrained variables can evolve over time. A variable can actually take an infinite sequence of values over discrete time points. In this paper, we propose constraint programming on infinite data streams, which provides a natural way to model constrained time-varying problems. In our framework, variable domains are specified by ω-regular languages. We introduce special stream operators as basis to form stream expressions and constraints. Stream CSPs have infinite search space. We propose a search procedure that can recognize and avoid infinite search over duplicate search space. The solution set of a stream CSP can be represented by a Büchi automaton allowing stream values to be non-periodic. Consistency notions are defined to reduce the search space early. We illustrate the feasibility of the framework by examples and experiments.

This paper proposes the integration of the resolution rule for Max-SAT with unsatisfiability-based Max-SAT solvers. First, we show that the resolution rule for Max-SAT can be safely applied as dictated by the resolution proof associated with an unsatisfiable core when such proof is read-once, that is, each clause is used at most once in the resolution process. Second, we study how this property can be integrated in an unsatisfiability-based solver. In particular, the resolution rule for Max-SAT is applied to read-once proofs or to read-once subparts of a general proof. Finally, we perform an empirical investigation on structured instances from recent Max-SAT evaluations. Preliminary results show that the use of read-once resolution substantially improves the performance of the solver.

The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are tractable. We study the complexity of minimization for formulas in two established frameworks for restricted propositional logic: The Post framework allowing arbitrarily nested formulas over a set of Boolean connectors, and the constraint setting, allowing generalizations of CNF formulas. In the Post case, we obtain a dichotomy result: Minimization is solvable in polynomial time or coNP-hard. This result also applies to Boolean circuits. For CNF formulas, we obtain new minimization algorithms for a large class of formulas, and give strong evidence that we have covered all polynomial-time cases.

ADOPT and BnB-ADOPT are two optimal DCOP search algorithms that are similar except for their search strategies: the former uses best-first search and the latter uses depth-first branch-and-bound search. In this paper, we present a new algorithm, called ADOPT( k ), that generalizes them. Its behavior depends on the k parameter. It behaves like ADOPT when k = 1, like BnB-ADOPT when k = ∞ and like a hybrid of ADOPT and BnB-ADOPT when 1 < k < ∞. We prove that ADOPT( k ) is a correct and complete algorithm and experimentally show that ADOPT( k ) outperforms ADOPT and BnB-ADOPT on several benchmarks across several metrics.

Bessiere et al. (AAAI'08) showed that several intractable global constraints can be efficiently propagated when certain natural problem parameters are small. In particular, the complete propagation of a global constraint is fixed-parameter tractable in k — the number of holes in domains — whenever bound consistency can be enforced in polynomial time; this applies to the global constraints AtMost-NValue and Extended Global Cardinality (EGC). In this paper we extend this line of research and introduce the concept of reduction to a problem kernel, a key concept of parameterized complexity, to the field of global constraints. In particular, we show that the consistency problem for AtMost-NValue constraints admits a linear time reduction to an equivalent instance on O(k 2 ) variables and domain values. This small kernel can be used to speed up the complete propagation of NValue constraints. We contrast this result by showing that the consistency problem for EGC constraints does not admit a reduction to a polynomial problem kernel unless the polynomial hierarchy collapses.