We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop formulas. Our results provide an abstract account of properties of some recent extensions of logic programming with aggregates, especially the formalism of lparse programs. They imply a method to compute stable models of lparse programs by means of off-the-shelf solvers of pseudo-boolean constraints, which is often much faster than the smodels system.

Multimodal conversational interfaces provide a natural means for users to communicate with computer systems through multiple modalities such as speech and gesture. To build effective multimodal interfaces, automated interpretation of user multimodal inputs is important. Inspired by the previous investigation on cognitive status in multimodal human machine interaction, we have developed a greedy algorithm for interpreting user referring expressions (i.e., multimodal reference resolution). This algorithm incorporates the cognitive principles of Conversational Implicature and Givenness Hierarchy and applies constraints from various sources (e.g., temporal, semantic, and contextual) to resolve references. Our empirical results have shown the advantage of this algorithm in efficiently resolving a variety of user references. Because of its simplicity and generality, this approach has the potential to improve the robustness of multimodal input interpretation.

In a field of research about general reasoning mechanisms, it is essential to have appropriate benchmarks. Ideally, the benchmarks should reflect possible applications of the developed technology. In AI Planning, researchers more and more tend to draw their testing examples from the benchmark collections used in the International Planning Competition (IPC). In the organization of (the deterministic part of) the fourth IPC, IPC-4, the authors therefore invested significant effort to create a useful set of benchmarks. They come from five different (potential) real-world applications of planning: airport ground traffic control, oil derivative transportation in pipeline networks, model-checking safety properties, power supply restoration, and UMTS call setup. Adapting and preparing such an application for use as a benchmark in the IPC involves, at the time, inevitable (often drastic) simplifications, as well as careful choice between, and engineering of, domain encodings. For the first time in the IPC, we used compilations to formulate complex domain features in simple languages such as STRIPS, rather than just dropping the more interesting problem constraints in the simpler language subsets. The article explains and discusses the five application domains and their adaptation to form the PDDL test suites used in IPC-4. We summarize known theoretical results on structural properties of the domains, regarding their computational complexity and provable properties of their topology under the h+ function (an idealized version of the relaxed plan heuristic). We present new (empirical) results illuminating properties such as the quality of the most wide-spread heuristic functions (planning graph, serial planning graph, and relaxed plan), the growth of propositional representations over instance size, and the number of actions available to achieve each fact; we discuss these data in conjunction with the best results achieved by the different kinds of planners participating in IPC-4.

This paper presents a new framework for anytime heuristic search where the task is to achieve as many goals as possible within the allocated resources. We show the inadequacy of traditional distance-estimation heuristics for tasks of this type and present alternative heuristics that are more appropriate for multiple-goal search. In particular, we introduce the marginal-utility heuristic, which estimates the cost and the benefit of exploring a subtree below a search node. We developed two methods for online learning of the marginal-utility heuristic. One is based on local similarity of the partial marginal utility of sibling nodes, and the other generalizes marginal-utility over the state feature space. We apply our adaptive and non-adaptive multiple-goal search algorithms to several problems, including focused crawling, and show their superiority over existing methods.

In this paper, we present the partitioning of mutual-exclusion (mutex) constraints in temporal planning problems and its implementation in the SGPlan4 planner. Based on the strong locality of mutex constraints observed in many benchmarks of the Fourth International Planning Competition (IPC4), we propose to partition the constraints of a planning problem into groups based on their subgoals. Constraint partitioning leads to significantly easier subproblems that are similar to the original problem and that can be efficiently solved by the same planner with some modifications to its objective function. We present a partition-and-resolve strategy that looks for locally optimal subplans in constraint-partitioned temporal planning subproblems and that resolves those inconsistent global constraints across the subproblems. We also discuss some implementation details of SGPlan4, which include the resolution of violated global constraints, techniques for handling producible resources, landmark analysis, path finding and optimization, search-space reduction, and modifications of Metric-FF when used as a basic planner in SGPlan4. Last, we show results on the sensitivity of each of these techniques in quality-time trade-offs and experimentally demonstrate that SGPlan4 is effective for solving the IPC3 and IPC4 benchmarks.

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature.

We characterize the search landscape of random instances of the job shop scheduling problem (JSP). Specifically, we investigate how the expected values of (1) backbone size, (2) distance between near-optimal schedules, and (3) makespan of random schedules vary as a function of the job to machine ratio (N/M). For the limiting cases N/M approaches 0 and N/M approaches infinity we provide analytical results, while for intermediate values of N/M we perform experiments. We prove that as N/M approaches 0, backbone size approaches 100%, while as N/M approaches infinity the backbone vanishes. In the process we show that as N/M approaches 0 (resp. N/M approaches infinity), simple priority rules almost surely generate an optimal schedule, providing theoretical evidence of an "easy-hard-easy" pattern of typical-case instance difficulty in job shop scheduling. We also draw connections between our theoretical results and the "big valley" picture of JSP landscapes.

Fast Downward is a classical planning system based on heuristic search. It can deal with general deterministic planning problems encoded in the propositional fragment of PDDL2.2, including advanced features like ADL conditions and effects and derived predicates (axioms). Like other well-known planners such as HSP and FF, Fast Downward is a progression planner, searching the space of world states of a planning task in the forward direction. However, unlike other PDDL planning systems, Fast Downward does not use the propositional PDDL representation of a planning task directly. Instead, the input is first translated into an alternative representation called multi-valued planning tasks, which makes many of the implicit constraints of a propositional planning task explicit. Exploiting this alternative representation, Fast Downward uses hierarchical decompositions of planning tasks for computing its heuristic function, called the causal graph heuristic, which is very different from traditional HSP-like heuristics based on ignoring negative interactions of operators. In this article, we give a full account of Fast Downward's approach to solving multi-valued planning tasks. We extend our earlier discussion of the causal graph heuristic to tasks involving axioms and conditional effects and present some novel techniques for search control that are used within Fast Downward's best-first search algorithm: preferred operators transfer the idea of helpful actions from local search to global best-first search, deferred evaluation of heuristic functions mitigates the negative effect of large branching factors on search performance, and multi-heuristic best-first search combines several heuristic evaluation functions within a single search algorithm in an orthogonal way. We also describe efficient data structures for fast state expansion (successor generators and axiom evaluators) and present a new non-heuristic search algorithm called focused iterative-broadening search, which utilizes the information encoded in causal graphs in a novel way. Fast Downward has proven remarkably successful: It won the "classical'' (i.e., propositional, non-optimising) track of the 4th International Planning Competition at ICAPS 2004, following in the footsteps of planners such as FF and LPG. Our experiments show that it also performs very well on the benchmarks of the earlier planning competitions and provide some insights about the usefulness of the new search enhancements.

Some recent works in conditional planning have proposed reachability heuristics to improve planner scalability, but many lack a formal description of the properties of their distance estimates. To place previous work in context and extend work on heuristics for conditional planning, we provide a formal basis for distance estimates between belief states. We give a definition for the distance between belief states that relies on aggregating underlying state distance measures. We give several techniques to aggregate state distances and their associated properties. Many existing heuristics exhibit a subset of the properties, but in order to provide a standardized comparison we present several generalizations of planning graph heuristics that are used in a single planner. We compliment our belief state distance estimate framework by also investigating efficient planning graph data structures that incorporate BDDs to compute the most effective heuristics. We developed two planners to serve as test-beds for our investigation. The first, CAltAlt, is a conformant regression planner that uses A* search. The second, POND, is a conditional progression planner that uses AO* search. We show the relative effectiveness of our heuristic techniques within these planners. We also compare the performance of these planners with several state of the art approaches in conditional planning.

MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation Pr, or the problem of computing the most probable explanation (MPE). This paper investigates the complexity of MAP in Bayesian networks. Specifically, we show that MAP is complete for NP^PP and provide further negative complexity results for algorithms based on variable elimination. We also show that MAP remains hard even when MPE and Pr become easy. For example, we show that MAP is NP-complete when the networks are restricted to polytrees, and even then can not be effectively approximated. Given the difficulty of computing MAP exactly, and the difficulty of approximating MAP while providing useful guarantees on the resulting approximation, we investigate best effort approximations. We introduce a generic MAP approximation framework. We provide two instantiations of the framework; one for networks which are amenable to exact inference Pr, and one for networks for which even exact inference is too hard. This allows MAP approximation on networks that are too complex to even exactly solve the easier problems, Pr and MPE. Experimental results indicate that using these approximation algorithms provides much better solutions than standard techniques, and provide accurate MAP estimates in many cases.