92 research outputs found

    Symmetries in planning problems

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    Symmetries arise in planning in a variety of ways. This paper describes the ways that symmetry aises most naturally in planning problems and reviews the approaches that have been applied to exploitation of symmetry in order to reduce search for plans. It then introduces some extensions to the use of symmetry in planning before moving on to consider how the exploitation of symmetry in planning might be generalised to offer new approaches to exploitation of symmetry in other combinatorial search problems

    Plan permutation symmetries as a source of inefficiency in planning

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    This paper briefly reviews sources of symmetry in planning and highlights one source that has not previously been tackled: plan permutation symmetry. Symmetries can be a significant problem for efficiency of planning systems, as has been previously observed in the treatment of other forms of symmetry in planning problems. We examine how plan permutation symmetries can be eliminated and present evidence to support the claim that these symmetries are an important problem for planning systems

    Abstraction-based action ordering in planning

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    Many planning problems contain collections of symmetric objects, actions and structures which render them difficult to solve efficiently. It has been shown that the detection and exploitation of symmetric structure in planning problems can dramatically reduce the size of the search space and the time taken to find a solution. We present the idea of using an abstraction of the problem domain to reveal symmetric structure and guide the navigation of the search space. We show that this is effective even in domains in which there is little accessible symmetric structure available for pruning. Proactive exploitation represents a flexible and powerfulalternative to the symmetry-breaking strategies exploited in earlier work in planning and CSPs. The notion of almost symmetry is defined and results are presented showing that proactive exploitation of almost symmetry can improve the performance of a heuristic forward search planner

    The identification and exploitation of almost symmetry in planning problems

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    Previous work in symmetry detection for planning has identified symmetries between domain objects and shown how the exploitation of this information can help reduce search at plan time. However these methods are unable to detect symmetries between objects that are almost symmetrical: where the objects must start (or end) in slightly different configurations but for much of the plan their behaviour is equivalent. In the paper we outline a method for identifying such symmetries and discuss how this symmetry information can be positively exploited to help direct search during planning we have implemented this method and integrated it with the FF-v2.3 planner and in the paper we present results of experiments with this approach that demonstrate its potential

    Multireference Alignment using Semidefinite Programming

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    The multireference alignment problem consists of estimating a signal from multiple noisy shifted observations. Inspired by existing Unique-Games approximation algorithms, we provide a semidefinite program (SDP) based relaxation which approximates the maximum likelihood estimator (MLE) for the multireference alignment problem. Although we show that the MLE problem is Unique-Games hard to approximate within any constant, we observe that our poly-time approximation algorithm for the MLE appears to perform quite well in typical instances, outperforming existing methods. In an attempt to explain this behavior we provide stability guarantees for our SDP under a random noise model on the observations. This case is more challenging to analyze than traditional semi-random instances of Unique-Games: the noise model is on vertices of a graph and translates into dependent noise on the edges. Interestingly, we show that if certain positivity constraints in the SDP are dropped, its solution becomes equivalent to performing phase correlation, a popular method used for pairwise alignment in imaging applications. Finally, we show how symmetry reduction techniques from matrix representation theory can simplify the analysis and computation of the SDP, greatly decreasing its computational cost

    Generalizing Boolean Satisfiability I: Background and Survey of Existing Work

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    This is the first of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper is a survey of the work underlying ZAP, and discusses previous attempts to improve the performance of the Davis-Putnam-Logemann-Loveland algorithm by exploiting the structure of the problem being solved. We examine existing ideas including extensions of the Boolean language to allow cardinality constraints, pseudo-Boolean representations, symmetry, and a limited form of quantification. While this paper is intended as a survey, our research results are contained in the two subsequent articles, with the theoretical structure of ZAP described in the second paper in this series, and ZAP's implementation described in the third

    Formally Verified Compositional Algorithms for Factored Transition Systems

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    Artificial Intelligence (AI) planning and model checking are two disciplines that found wide practical applications. It is often the case that a problem in those two fields concerns a transition system whose behaviour can be encoded in a digraph that models the system's state space. However, due to the very large size of state spaces of realistic systems, they are compactly represented as propositionally factored transition systems. These representations have the advantage of being exponentially smaller than the state space of the represented system. Many problems in AI~planning and model checking involve questions about state spaces, which correspond to graph theoretic questions on digraphs modelling the state spaces. However, existing techniques to answer those graph theoretic questions effectively require, in the worst case, constructing the digraph that models the state space, by expanding the propositionally factored representation of the syste\ m. This is not practical, if not impossible, in many cases because of the state space size compared to the factored representation. One common approach that is used to avoid constructing the state space is the compositional approach, where only smaller abstractions of the system at hand are processed and the given problem (e.g. reachability) is solved for them. Then, a solution for the problem on the concrete system is derived from the solutions of the problem on the abstract systems. The motivation of this approach is that, in the worst case, one need only construct the state spaces of the abstractions which can be exponentially smaller than the state space of the concrete system. We study the application of the compositional approach to two fundamental problems on transition systems: upper-bounding the topological properties (e.g. the largest distance between any two states, i.e. the diameter) of the state spa\ ce, and computing reachability between states. We provide new compositional algorithms to solve both problems by exploiting different structures of the given system. In addition to the use of an existing abstraction (usually referred to as projection) based on removing state space variables, we develop two new abstractions for use within our compositional algorithms. One of the new abstractions is also based on state variables, while the other is based on assignments to state variables. We theoretically and experimentally show that our new compositional algorithms improve the state-of-the-art in solving both problems, upper-bounding state space topological parameters and reachability. We designed the algorithms as well as formally verified them with the aid of an interactive theorem prover. This is the first application that we are aware of, for such a theorem prover based methodology to the design of new algorithms in either AI~planning or model checking
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