The Blackbox planning system unifies the planning as satisfiability framework (Kautz and Selman 1992, 1996) with the plan graph approach to STRIPS planning (Blum and Furst 1995). We show that STRIPS problems can be directly translated into SAT and efficiently solved using new randomized systematic solvers. For certain computationally challenging benchmark problems this unified approach outperforms both SATPLAN and Graphplan alone. We also demonstrate that polynomialtime SAT simplification algorithms applied to the encoded problem instances are a powerful complement to the "mutex" propagation algorithm that works directly on the plan graph. 1 Introduction It has often been observed that the classical AI planning problem (that is, planning with complete and certain information) is a form of logical deduction. Because early attempts to use general theorem provers to solve planning problems proved impractical, research became focused on specialized planning algorithms. Sometimes the rela...

We describe some new preprocessing techniques that enable faster domain-independent planning. The first set of techniques is aimed at inferring state constraints from the structure of planning operators and the initial state. Our methods consist of generating hypothetical state constraints by inspection of operator effects and preconditions, and checking each hypothesis against all operators and the initial conditions. Another technique extracts (supersets of) predicate domains from sets of ground literals obtained by Graphplan-like forward propagation from the initial state. Our various techniques are implemented in a package called DISCOPLAN. We show preliminary results on the effectiveness of adding computed state constraints and predicate domains to the specification of problems for SAT-based planners such as SATPLAN or MEDIC. The results suggest that large speedups in planning can be obtained by such automated methods, potentially obviating the need for adding h...

Abstract. The increasingrole of quantified Boolean logic in many applications calls for practically efficient decision procedures. One of the most promisingparadigms is the semantic tree format implemented in the style of the DPLL procedure. In this paper, so-called learningtechniques like intelligent backtrackingand cachingof lemmas which proved useful in the pure propositional case are generalised to the quantified Boolean case and the occuringdifferences are discussed. Due to the strongrestriction of the variable selection in semantic tree procedures for quantified Boolean formulas, learningmethods are more important than in the propositional case, as we demonstrate. Furthermore, in addition to the cachingof lemmas, significant advances can be achieved by techniques based on the caching of models, too. The theoretical effect of these improvements is illustrated by a comparison of the search spaces on pathological examples. We also describe the basic features of the system Semprop, which is an efficient implementation of (some of) the developed techniques, and give the results of an experimental evaluation of the system on a number of practical examples. 1

The hybridisation of systematic and stochastic search is an active research area with potential bene ts for real-world combinatorial problems. This paper shows that randomising the backtracking component of a systematic backtracker can improve its scalability to equal that of stochastic local search. The hybrid may be viewed as stochastic local search in a constrained space, cleanly combining local search with constraint programming techniques. The approach is applied to two very dierent problems. Firstly a hybrid of local search and constraint propagation is applied to hard random 3-SAT problems, and is the rst constructive search algorithm to solve very large instances. Secondly a hybrid of local search and branch-and-bound is applied to low-autocorrelation binary sequences (a notoriously dicult communications engineering problem), and is the rst stochastic search algorithm to nd optimal solutions. These results show that the approach is a promising one for both constraint satisfaction and optimisation problems.

In recent years, many improvements to backtracking algorithms for solving constraint satisfaction problems have been proposed. The techniques for improving backtracking algorithms can be conveniently classified as look-ahead schemes and look-back schemes. Unfortunately, look-ahead and look-back schemes are not entirely orthogonal as it has been observed empirically that the enhancement of look-ahead techniques is sometimes counter-productive to the effects of look-back techniques. In this paper, we focus on the relationship between the two most important look-ahead techniques -- using a variable ordering heuristic and maintaining a level of local consistency during the backtracking search -- and the look-back technique of conflict-directed backjumping (CBJ). We show that there exists a "perfect" dynamic variable ordering such that CBJ becomes redundant. We also show theoretically that as the level of local consistency that is maintained in the backtracking search is increased, the less that backjumping will be an improvement. Our theoretical results partially explain why a backtracking algorithm doing more in the look-ahead phase cannot benefit more from the backjumping look-back scheme. Finally, we show empirically that adding CBJ to a backtracking algorithm that maintains generalized arc consistency (GAC), an algorithm that we refer to as GAC-CBJ, can still provide orders of magnitude speedups. Our empirical results contrast with Bessiere and Regin's conclusion (1996) that CBJ is useless to an algorithm that maintains arc consistency.

Planning as satisfiability is a very efficient technique for classical planning, i.e., for planning domains in which both the effects of actions and the initial state are completely specified. In this paper we present C-SAT, a SAT-based procedure capable of dealing with planning domains having incomplete information about the initial state, and whose underlying transition system is specified using the highly expressive action language C. Thus, C-SAT allows for planning in domains involving (i) actions which can be executed concurrently; (ii) (ramification and qualification) constraints affecting the effects of actions; and (iii) nondeterminism in the initial state and in the effects of actions. We first prove the correctness and the completeness of C-SAT, discuss some optimizations, and then we present C-PLAN, a system based on C-SAT. C-PLAN works on any C planning problem, but some optimizations have not been fully implemented yet. Nevertheless, the experimental analysis shows that SAT-based approaches to planning with incomplete information are viable, at least in the case of problems with a high degree of parallelism.

reasoning, reasoning about action and change This paper investigates the use of commonsense reasoning to understand texts involving stereotypical activities or scripts. We present a system that understands news stories involving four terrorism scripts. The system (1) builds a commonsense reasoning problem given an information extraction template representing a terrorist incident, and (2) uses commonsense reasoning and a commonsense knowledge base to build a model of the terrorist incident. The reasoning problem, commonsense knowledge base, and model are expressed in the classical logic event calculus. The system was developed using the MUC3 and MUC4 development data set. We present the results of running the system on the MUC3 and MUC4 test data sets, using manually generated answer key templates and templates generated automatically by two MUC4 information extraction systems. We present a detailed analysis of the models produced by the system given automatically generated templates. We present methods for answering questions based on the models produced by our system. We assess the portability of the system by extending it to handle 10 scripts frequent in Project Gutenberg American literature texts. 1

This paper addresses the following question: what is the essential difference between stochastic local search (LS) and systematic backtracking (BT) that gives LS superior scalability ? One possibility is LS's lack of firm commitment to any variable assignment. Three BT algorithms are modified to have this feature by introducing randomness into the choice of backtracking variable: a forward checker for n-queens, the DSATUR graph colouring algorithm, and a Davis-Logemann-Loveland procedure for satisfiability. In each case the modified algorithm scales like LS and sometimes gives better results. It is argued that randomised backtracking is a form of local search.

Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a path-finding problem in belief space where good belief representations and heuristics are critical for scaling up. In this work, a different formulation is introduced for conformant problems with deterministic actions where they are automatically converted into classical ones and solved by an off-the-shelf classical planner. The translation maps literals L and sets of assumptions t about the initial situation, into new literals KL/t that represent that L must be true if t is initially true. We lay out a general translation scheme that is sound and establish the conditions under which the translation is also complete. We show that the complexity of the complete translation is exponential in a parameter of the problem called the conformant width, which for most benchmarks is bounded. The planner based on this translation exhibits good performance in comparison with existing planners, and is the basis for T0, the best performing planner in the Conformant Track of the 2006 International Planning Competition. 1.

In the futile questioning problem, one must decide whether acquisition of additional information can possibly lead to the proof of a conclusion. Solution of that problem demands evaluation of a quantified Boolean formula at the second level of the polynomial hierarchy. The same evaluation problem, called Q-ALL SAT, arises in many other applications. In this paper, we introduce a special subclass of Q-ALL SAT that is at the first level of the polynomial hierarchy. We develop a solution algorithm for the general case that utilizes backtracking search and a new form of learning of clauses. Results are reported for two sets of instances involving a robot route problem and a game problem. For these instances, the algorithm is substantially faster than state-of-the-art solvers for quantified Boolean formulas. 1