percolation threshold is not a decreasing function of the average coordination number it is commonly believed that the percolation critical probability is a monotonically decreasing function of the average coordination number for periodic lattice graphs in the same dimension this paper provides counterexamples a pair of planar lattices for which the bond percolation critical probabilities and average coordination numbers are in the same order and a pair for which the site percolation critical probabilities and average coordination numbers are in the same order these counterexamples confirm the existence of this counterintuitive phenomenon which was observed in one case in numerical estimates by van der marck

grasp a search algorithm for propositional satisfiability this paper introduces grasp generic search algorithm for the satisfiability problem a new search algorithm for propositional satisfiability sat grasp incorporates several search pruning techniques that proved to be quite powerful on a wide variety of sat problems some of these techniques are specific to sat whereas others are similar in spirit to approaches in other fields of artificial intelligence grasp is premised on the inevitability of conflicts during the search and its most distinguishing feature is the augmentation of basic backtracking search with a powerful conflict analysis procedure analyzing conflicts to determine their causes enables grasp to backtrack nonchronologically to earlier levels in the search tree potentially pruning large portions of the search space in addition by recording the causes of conflicts grasp can recognize and preempt the occurrence of similar conflicts later on in the search finally straightforward bookkeeping of the causality chains leading up to conflicts allows grasp to identify assignments that are necessary for a solution to be found experimental results obtained from a large number of benchmarks indicate that application of the proposed conflict analysis techniques to sat algorithms can be extremely effective for a large number of representative classes of sat instances

site percolation thresholds for archimedean lattices precise thresholds for site percolation on eight archimedean lattices are determined by the hull walk gradient percolation simulation method with the results p c 0 697 043 honeycomb or 6 3 0 807 904 3 12 2 0 747 806 4 6 12 0 729 724 4 8 2 0 579 498 3 4 6 0 621 819 3 4 6 4 0 550 213 3 3 4 2 and 0 550 806 3 2 4 3 4 with errors of about 3 x 10 6 the remaining archimedean lattices are the square 4 4 triangular 3 6 and kagome 3 6 3 6 for which p c is already known exactly or to a high degree of accuracy the numerical result for the 3 12 2 lattice is consistent with the exact value 1 2 sin pi 18 1 2 the values of p c for all 11 archimedean lattices as well as a number of nonuniform lattices are found to be well correlated by a nearly linear function of a generalized scher zallen filling factor this correlation is much more accurate than recently proposed correlations based solely upon coordination number

red black planning to date delete relaxation underlies some of the most effective heuristics for deterministic planning despite its success however delete relaxation has significant pitfalls in many important classes of planning domains and it has been a challenge from the outset to devise heuristics that take some deletes into account we herein devise an elegant and simple method for doing just that in the context of finite domain state variables we define red variables to take the relaxed semantics in which they accumulate their values rather than switching between them as opposed to black variables that take the regular semantics red black planning then interpolates between relaxed planning and regular planning simply by allowing a subset of variables to be painted red we investigate the tractability region of red black planning extending chen and gimenez characterization theorems for regular planning to the more general red black setting in particular we identify significant islands of tractable red black planning use them to design practical heuristic functions and experiment with a range of painting strategies for automatically choosing the red variables our experiments show that these new heuristic functions can improve significantly on the state of the art in satisficing planning 1

discovering hidden structure in factored mdps markov decision processes mdps describe a wide variety of planning scenarios ranging from military operations planning to controlling a mars rover however email protected s solution techniques scale poorly limiting email protected practical applicability in this work we propose algorithms that automatically discover and exploit the hidden structure of factored mdps doing so helps solve mdps faster and with less memory than state of the art techniques our algorithms discover two complementary state abstractions basis functions and nogoods a basis function is a conjunction of literals if the conjunction holds true in a state this guarantees the existence of at least one trajectory to the goal conversely a nogood is a conjunction whose presence implies the non existence of any such trajectory meaning the state is a dead end we compute basis functions by regressing goal descriptions through a determinized version of the mdp nogoods are constructed with a novel machine learning algorithm that uses basis functions as training data our state abstractions can be leveraged in several ways we describe three diverse approaches goth a heuristic function for use in heuristic search algorithms such as rtdp retrase an mdp solver that performs modified bellman backups on basis functions instead of states and sixthsense a method to quickly detect dead end states in essence our work integrates ideas from deterministic planning and basis function based approximation leading to methods that outperform existing approaches by a wide margin

on polya random walks lattice green functions and the bond percolation threshold based on numerical evidence the authors conjecture a connection between the bond percolation threshold of bravais lattices in three or more dimensions and the value at the origin of a lattice green function related to the probability of return to the origin for a polya random walk

real time heuristic search abstract we apply the two player game assumptions of limited search horizon and commitment to moves in constant time to single agent heuristic search problems we present a variation of minimax lookahead search and an analog to alpha beta pruning that significantly improves the efficiency of the algorithm paradoxically the search horizon reachable with this algorithm increases with increasing branching factor in addition we present a new algorithm called real time a for interleaving planning and execution we prove that the algorithm makes locally optimal decisions and is guaranteed to find a solution we also present a learning version of this algorithm that improves its performance over successive problem solving trials by learning more accurate heuristic values and prove that the learned values converge to their exact values along every optimal path these algorithms effectively solve significantly larger problems than have previously been solvable using heuristic evaluation functions

on the relations between intelligent backtracking and failure driven explanation based learning in constraint satisfaction and planning abstract 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

percolation thresholds on planar euclidean relative neighborhood graphs in the present article statistical properties regarding the topology and standard percolation on relative neighborhood graphs rngs for planar sets of points considering the euclidean metric are put under scrutiny rngs belong to the family of proximity graphs i e their edgeset encodes proximity information regarding the close neighbors for the terminal nodes of a given edge therefore they are e g discussed in the context of the construction of backbones for wireless ad hoc networks that guarantee connectedness of all underlying nodes here by means of numerical simulations we determine the asymptotic degree and diameter of rngs and we estimate their bond and site percolation thresholds which were previously conjectured to be nontrivial we compare the results to regular 2d graphs for which the degree is close to that of the rng finally we deduce the common percolation critical exponents from the rng data to verify that the associated universality class is that of standard 2d percolation

random walks and percolation on trees there is a way to define an average number of branches per vertex for an arbitrary infinite locally finite tree it equals the exponential of the hausdorff dimension of the boundary in an appropriate metric its importance for probabilistic processes on a tree is shown in several ways including random walk and percolation where it provides points of phase transition

bond percolation critical probability bounds derived by edge contraction a contraction principle is valid for bond percolation models if gc is obtained from g by contraction of a set of edges then the bond percolation critical probabilities satisfy pc gc or pc g the contraction principle provides relationships between graphs which do not follow from the inclusion principle application of the principle provides the following bounds 0 5000 or pc pentagon lattice or 0 6527 pc kagome lattice or 0 6180 0 3820 or pc dice lattice

the computational complexity of propositional strips planning abstract i present several computational complexity results for propositional strips planning i e strips planning restricted to ground formulas different planning problems can be defined by restricting the type of formulas placing limits on the number of pre and postconditions by restricting negation in pre and postconditions and by requiring optimal plans for these types of restrictions i show when planning is tractable polynomial and intractable np hard in general it is pspace complete to determine if a given planning instance has any solutions extremely severe restrictions on both the operators and the formulas are required to guarantee polynomial time or even np completeness for example when only ground literals are permitted determining plan existence is pspace complete even if operators are limited to two preconditions and two postconditions when definite horn ground formulas are permitted determining plan existence is pspace complete even if operators are limited to zero preconditions and one postcondition one of the interesting tractable problems is if each operator is restricted to positive preconditions and one postcondition only ground literals the blocks world problem slightly modified is a subproblem of this restricted planning problem these results in combination with previous analyses are not encouraging for domain independent planning

universal formulas for percolation thresholds a power law is postulated for both site and bond percolation thresholds the formula is mathit p mathit c mathit p 0 d 1 q 1 mathrm ensuremath mathit a mathit d mathit b where d is the space dimension and q the coordination number all thresholds up to d ensuremath rightarrow ensuremath infty are found to belong to only three universality classes for two classes b 0 for site dilution while b a for bond dilution the remaining class associated with high dimensions is characterized by b 2a 1 for both sites and bonds classes are defined by a set of value for mathit p 0 a deviations from available numerical estimates at d ensuremath le 7 are within ifmmode pm else textpm fi 0 008 and ifmmode pm else textpm fi 0 0004 for high dimensional hypercubic expansions at d ensuremath ge 8 the formula is found to be also valid for ising critical temperatures textcopyright 1996 the american physical society

some exact results on bond percolation we present some exact results on bond percolation we derive a relation that specifies the consequences for bond percolation quantities of replacing each bond of a lattice by l bonds connecting the same adjacent vertices thereby yielding the lattice l this relation is used to calculate the bond percolation threshold on l we show that this bond inflation leaves the universality class of the percolation transition invariant on a lattice of dimensionality d 2 but changes it on a one dimensional lattice and quasi one dimensional infinite length strips we also present analytic expressions for the average cluster number per vertex and correlation length for the bond percolation problem on the n limits of several families of n vertex graphs finally we explore the effect of bond vacancies on families of graphs with the property of bounded diameter as n

site percolation thresholds in all dimensions abstract site percolation thresholds are reproduced in all dimensions for all lattices using a linear combination of two analytic terms one is the well known cayley tree percolation threshold which is believed to be exact at infinite dimension the other one is obtained from a new approach to two dimensional site dilution using a ferromagnetic ising system these two formulas are then combined with weighting factors a and 1 a respectively where a is a fitting parameter which depends only on space dimension it is equal to 0 047 at d 2 to 0 924 at d 6 and 1 at d our results agree with exact numerical estimates for any lattice in any dimension within few percent

enhancement schemes for constraint processing backjumping learning and cutset decomposition abstract researchers in the areas of constraint satisfaction problems logic programming and truth maintenance systems have suggested various schemes for enhancing the performance of the backtracking algorithm this paper defines and compares the performance of three such schemes backjumping learning and cycle cutset the backjumping and the cycle cutset methods work best when the constraint graph is sparse while the learning scheme mostly benefits problem instances with dense constraint graphs an integrated strategy is described which utilizes the distinct advantages of each scheme experiments show that in hard problems the average improvement realized by the integrated scheme is 20 25 higher than any of the individual schemes

universal formulas for percolation thresholds ii extension to anisotropic and aperiodic lattices in a recent paper we reported a universal power law for both site and bond percolation thresholds in any bravais lattice with q equivalent nearest neighbors in dimension d we now extend it to three different classes of lattices which are respectively anisotropic lattices without equivalent nearest neighbors non bravais lattices with two atom unit cells and quasicrystals the investigation is focused on d 2 and 3 due to the lack of experimental data at higher dimensions the extension to these lattices requires the substitution of q by an effective non integer value q mathrm eff in the universal law for each of the 17 lattices which constitute our sample we argue for the existence of one q mathrm eff which reproduces both the site and the percolation threshold with a deviation with respect to numerical estimates which does not exceed ensuremath mp 0 01

backjump based backtracking for constraint satisfaction problems the performance of backtracking algorithms for solving finite domain constraint satisfaction problems can be improved substantially by look back and look ahead methods look back techniques extract information by analyzing failing search paths that are terminated by dead ends look ahead techniques use constraint propagation algorithms to avoid such dead ends altogether this paper describes a number of look back variants including backjumping and constraint recording which recognize and avoid some unnecessary explorations of the search space the last portion of the paper gives an overview of look ahead methods such as forward checking and dynamic variable ordering and discusses their combination with backjumping

failure driven dynamic search control for partial order planners an explanation based approach abstract given the intractability of domain independent planning the ability to control the search of a planner is vitally important one way of doing this involves learning from search failures this paper describes snlp ebl the first implementation of an explanation based search control rule learning framework for a partial order plan space planner we will start by describing the basic learning framework of snlp ebl we will then concentrate on snlp ebl s ability to learn from failures and describe the results of empirical studies which demonstrate the effectiveness of the search control rules snlp ebl learns using our method we then demonstrate the generality of our learning methodology by extending it to ucpop penberthy and weld 1992 a descendant of snlp that allows for more expressive domain theories the resulting system ucpop ebl is used to analyze and understand the factors influencing the effectiveness of ebl specifically we analyze the effect of i expressive action representations ii domain specific failure theories and iii sophisticated backtracking strategies on the utility of ebl through empirical studies we demonstrate that expressive action representations allow for more explicit domain representations which in turn increase the ability of ebl to learn from analytical failures and obviate the need for domain specific failure theories we also explore the strong affinity between dependency directed backtracking and ebl in planning

percolation thresholds and universal formulas a calculation of percolation thresholds of 11 two dimensional and 18 three dimensional lattices is presented among the three dimensional ones are a random lattice and its dual plus a number of aniso tropic regular lattices the results are used to test universal formulas that relate the percolation thresholds of lattices to their dimension and coordination number the evidence suggests that dimension and coordination number are not sufficient to predict percolation thresholds

determinantal quintics and mirror symmetry of reye congruences we study a certain family of determinantal quintic hypersurfaces in mathbb p 4 whose singularities are similar to the well studied barth nieto quintic smooth calabi yau threefolds with hodge numbers h1 1 h2 1 52 2 are obtained by taking crepant resolutions of the singularities it turns out that these smooth calabi yau threefolds are in a two dimensional mirror family to the complete intersection calabi yau threefolds in mathbb p 4 times mathbb p 4 which have appeared in our previous study of reye congruences in dimension three we compactify the two dimensional family over mathbb p 2 and reproduce the mirror family to the reye congruences we also determine the monodromy of the family over mathbb p 2 completely our calculation shows an example of the orbifold mirror construction with a trivial orbifold group

an efficient algorithm for searching implicit and or graphs with cycles abstract we present an efficient ao like algorithm that handles cyclic graphs without neither unfolding the cycles nor looping through them its top down search strategy is based on mahanti and bagchi s cf j acm 32 1985 28 whereas its bottom up revision process is inspired in chakrabarti s rev artificial intelligence 65 1994 329 however important modifications have been introduced in both algorithms to attain a true integration and gain efficiency proofs of correctness and completeness are included up to our knowledge the resulting algorithm called cfc rev is the most efficient one available for this problem

critical probability bounds for two dimensional site percolation models the authors present three techniques for determining rigorous bounds for site percolation critical probabilities of two dimensional lattices a technique for finding lower bounds for critical probabilities of bipartite graphs is used to show that pc d or 0 5020 for the dice lattice d combining this method with kesten s duality result simplifies toth s derivation of the lower bound pc s or 0 5034 for the square lattice s the authors also present a technique for deriving upper bounds for bipartite graphs a technique of grouping sites is used to derive upper bounds for the critical probability of the hexagonal lattice h pc h or 0 8079 and pc h or pc s the grouping technique is applied to the dice lattice to find the upper bound pc d or 0 7937

a bond percolation critical probability determination based on the star triangle transformation the bond percolation critical probability of a planar graph with square and triangular faces obtained by inserting a diagonal in every other face of the square lattice is the root of 1 p 6p2 6p3 p5 0 in 0 1 which is approximately 0 404 518 the proof uses the star triangle transformation to determine the parameter value for which the percolative behaviour of the lattice and its dual lattice are identical

state space search nogood learning online refinement of critical path dead end detectors in planning abstract conflict directed learning is ubiquitous in constraint satisfaction problems like sat but has been elusive for state space search on reachability problems like classical planning almost all existing approaches learn nogoods relative to a fixed solution length bound in which case planning reachability reduces to a constraint satisfaction problem here we introduce an approach to learning more powerful nogoods that are sound regardless of solution length i e that identify dead end states for which no solution exists the key technique we build on are critical path heuristics h c relative to a set c of conjunctions these recognize a dead end state s returning h c s if s has no solution even when allowing to break up conjunctive subgoals into the elements of c our key idea is to learn c during search whenever forward search has identified an unrecognized dead end s where h c s we analyze the situation at s and add new conjunctions into c in a way guaranteeing to obtain h c s thus we learn to recognize s as well as similar dead ends search may encounter in the future we furthermore learn clauses where s implies h c s to avoid the overhead of computing h c on every search state arranging these techniques in a depth first search we obtain an algorithm approaching the elegance of nogood learning in constraint satisfaction learning to refute search subtrees we run comprehensive experiments on solvable and unsolvable planning benchmarks in cases where forward search can identify dead ends and where h c dead end detection is effective our techniques reduce the depth first search space size by several orders of magnitude and often result in state of the art performance

planning as satisfiability parallel plans and algorithms for plan search we address two aspects of constructing plans efficiently by means of satisfiability testing efficient encoding of the problem of existence of plans of a given number t of time points in the propositional logic and strategies for finding plans given these formulae for different values of t for the first problem we consider three semantics for plans with parallel operator application in order to make the search for plans more efficient the standard semantics requires that parallel operators are independent and can therefore be executed in any order we consider a more relaxed definition of parallel plans which was first proposed by dimopoulos et al as well as a normal form for parallel plans that requires every operator to be executed as early as possible we formalize the semantics of parallel plans emerging in this setting and present translations of these semantics into the propositional logic the sizes of the translations are asymptotically optimal each of the semantics is constructed in such a way that there is a plan following the semantics exactly when there is a sequential plan and moreover the existence of a parallel plan implies the existence of a sequential plan with as many operators as in the parallel one for the second problem we consider strategies based on testing the satisfiability of several formulae representing plans of n time steps for several values of n concurrently by several processes we show that big efficiency gains can be obtained in comparison to the standard strategy of sequentially testing the satisfiability of formulae for an increasing number of time steps