It has been observed previously that Random 3SAT exhibits a phase transition at a critical ratio of constraints to variables, where the average frequency of satisfiability falls abruptly from near 1 to near 0. In this paper we look beyond satisfiability to implicates and prime implicates of non-zero length and show experimentally that, for any given length, these exhibit their own phase transitions. All of these phase transitions appear to share the same critical point as the well-known satisfiability phase transition. We also find a rich, regular Some of this work was done while the first author was in the Qualitative Reasoning Group at the Artificial Intelligence Laboratory, the University of Texas at Austin, at a time when the Qualitative Reasoning Group was supported in part by NSF grants IRI-8904454, IRI-9017047, and IRI-9216584, and by NASA contracts NCC 2-760 and NAG 9-665. Some of this work also was done while the first author was at AT&T Bell Laboratories. y The second au...

Description Logics are a family of class based knowledge representation formalisms characterised by the use of various constructors to build complex classes from simpler ones, and by an emphasis on the provision of sound, complete and (empirically) tractable reasoning services.

Multiagent solutions to the distributed constraint satisfaction problem (DCSP) require new types of techniques which accommodate the local autonomy of agents and the difficulties of computing in a network environment. Recently a technique called asynchronous backtracking has been developed to solve the DCSP. The algorithm works by sending nogood messages among agents to effect intelligent backtracking. One important issue is developing nogood caching schemes which are appropriate to asynchronous backtracking. There has also been recent progress in a sequential algorithm called dynamic backtracking which exhibits a polynomial bound on nogood cache size. In this paper, we show by example that the existing caching scheme used by dynamic backtracking is not appropriate for the multiagent context. We suggest two alternate nogood caching schemes and two caching algorithms based on these schemes. Experimental comparisons of these caching algorithms are forthcoming. Introducti...

We show that problems at the uncolorability phase transition are well out of reach of intelligent algorithms. Since there are not small and easily checkable subgraphs which can be used to confirm uncolorability quickly, we cannot hope to build more intelligent algorithms to avoid hard problems at the phase transition. Also, our results suggest that a conjectured double phase transition in graph coloring occurs only in small graphs. Similar results are likely in other NP-complete problems where instances from phase transitions are hard for all known algorithms, and will help to explain the phenomenon. Furthermore, our results help to elucidate the distinction between polynomial and non-polynomial search behavior.

Abstract. Most CSP algorithms are based on refinements and extensions of backtracking, and employ one of two simple “branching schemes”: 2-way branching or d-way branching, for domain size d. The schemes are not equivalent, but little is known about their relative power. Here we compare them in terms of how efficiently they can refute an unsatisfiable instance with optimal branching choices, by studying two variants of the resolution proof system, denoted C-RES and NG-RES, which model the reasoning of CSP algorithms. The tree-like restrictions, tree-C-RES and tree-NG-RES, exactly capture the power of backtracking with 2-way branching and d-way branching, respectively. We give a family instances which require exponential sized search trees for backtracking with d-way branching, but have size O(d 2 n) search trees for backtracking with 2way branching. We also give a natural branching strategy with which backtracking with 2-way branching finds refutations of these instances in time O(d 2 n 2). The unrestricted variants of C-RES and NG-RES can simulate the reasoning of algorithms which incorporate learning and k-consistency enforcement. We show exponential separations between C-RES and NG-RES, as well as between the tree-like and unrestricted versions of each system. All separations given are nearly optimal. 1

Abstract. Description Logics (DLs) are a family of class based knowledge representation formalisms characterised by the use of various constructors to build complex classes from simpler ones, and by an emphasis on the provision of sound, complete and (empirically) tractable reasoning services. They have a range of applications, but are mostly widely known as the basis for ontology languages such as OWL. The increasing use of DL based ontologies in areas such as e-Science and the Semantic Web is, however, already stretching the capabilities of existing DL systems, and brings with it a range of challenges for future research. 1

Abstract. We study two resolution-like refutation systems for finitedomain constraint satisfaction problems, and the efficiency of these and of common CSP algorithms. By comparing the relative strength of these systems, we show that for instances with domain size d, backtracking with 2-way branching is super-polynomially more powerful than backtracking with d-way branching. We compare these systems with propositional resolution, and show that every family of CNF formulas which are hard for propositional resolution induces families of CSP instances that are hard for most of the standard CSP algorithms in the literature.

to A, true to B, false to C and false to D, is a satisfying truth value assignment. The structure of a constraintnetwork is depicted by a constraint graph whose nodes represents the variables and anytwo nodes are connected if the corresponding variables participate in the same constraint. In the k- colorability formulation, the graph to be colored is the constraint graph. In our SAT example the constraint graph has A connected to D and A; B and C are connected to each other. Constraintnetworks haveproven successful in modeling mundane cognitive tasks such as vision, language comprehension, default reasoning, and abduction, as well as in applications suchasscheduling, design, diagnosis, and temporal and spatial reasoning. In general, constraint satisfaction tasks are computationally intractable #NP-hard# #see COMPUTATIONAL COMPLEXITY #. Techniques for pr

There are several powerful solvers for satisfiability (SAT), such as wsat, Davis-Putnam, and relsat. However, in practice, the SAT encodings often have so many clauses that we exceed physical memory resources on attempting to solve them. This excessive size often arises because conversion to SAT, from a more natural encoding using quantifications over domains, requires expanding quantifiers. This suggests that we should "lift" successful SAT solvers. That is, adapt the solvers to use quantified clauses instead of ground clauses. However, it was generally believed that such lifted solvers would be impractical: Partially, because of the overhead of handling the predicates and quantifiers, and partially because lifting would not allow essential indexing and caching schemes. Here we show that, to the contrary, it is not only practical to handle quantified clauses directly, but that lifting can give exponential savings. We do this by identifying certain tasks that are central to...

The ideas of intelligent backtracking (IB) and explanation-based learning (EBL) have developed independently in the constraint satisfaction, planning, machine learning and problem solving communities. The variety of approaches developed for IB and EBL in the various communities have hither-to been incomparable. In this paper, I formalize and unify these ideas under the task-independent framework of refinement search, which can model the search strategies used in both planning and constraint satisfaction problems (CSPs). I show that both IB and EBL depend upon the common theory of explanation analysis--which involves explaining search failures, and regressing them to higher levels of the search tree. My comprehensive analysis shows that most of the differences between the CSP and planning approaches to EBL and IB revolve around different solutions to: (a) how the failure explanations are computed; (b) how they are contextualized (contextualization involves deciding whether or not to keep the flaw description and the description of the violated problem constraints); and (c) how the storage of explanations is managed. The differences themselves can be understood in terms of the differences between planning and CSP problems as instantiations of refinement search. This unified understanding is expected to support a greater cross-fertilization of ideas among CSP, planning and EBL communities.