5,337 research outputs found

    The complexity of conservative finite-valued CSPs

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    We study the complexity of valued constraint satisfaction problems (VCSP). A problem from VCSP is characterised by a \emph{constraint language}, a fixed set of cost functions over a finite domain. An instance of the problem is specified by a sum of cost functions from the language and the goal is to minimise the sum. We consider the case of so-called \emph{conservative} languages; that is, languages containing all unary cost functions, thus allowing arbitrary restrictions on the domains of the variables. This problem has been studied by Bulatov [LICS'03] for {0,}\{0,\infty\}-valued languages (i.e. CSP), by Cohen~\etal\ (AIJ'06) for Boolean domains, by Deineko et al. (JACM'08) for {0,1}\{0,1\}-valued cost functions (i.e. Max-CSP), and by Takhanov (STACS'10) for {0,}\{0,\infty\}-valued languages containing all finite-valued unary cost functions (i.e. Min-Cost-Hom). We give an elementary proof of a complete complexity classification of conservative finite-valued languages: we show that every conservative finite-valued language is either tractable or NP-hard. This is the \emph{first} dichotomy result for finite-valued VCSPs over non-Boolean domains.Comment: 15 page

    Using edit distance to analyse errors in a natural language to logic translation corpus

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    We have assembled a large corpus of student submissions to an automatic grading system, where the subject matter involves the translation of natural language sentences into propositional logic. Of the 2.3 million translation instances in the corpus, 286,000 (approximately 12%) are categorized as being in error. We want to understand the nature of the errors that students make, so that we can develop tools and supporting infrastructure that help students with the problems that these errors represent. With this aim in mind, this paper describes an analysis of a significant proportion of the data, using edit distance between incorrect answers and their corresponding correct solutions, and the associated edit sequences, as a means of organising the data and detecting categories of errors. We demonstrate that a large proportion of errors can be accounted for by means of a small number of relatively simple error types, and that the method draws attention to interesting phenomena in the data set

    Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

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    Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

    On SAT representations of XOR constraints

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    We study the representation of systems S of linear equations over the two-element field (aka xor- or parity-constraints) via conjunctive normal forms F (boolean clause-sets). First we consider the problem of finding an "arc-consistent" representation ("AC"), meaning that unit-clause propagation will fix all forced assignments for all possible instantiations of the xor-variables. Our main negative result is that there is no polysize AC-representation in general. On the positive side we show that finding such an AC-representation is fixed-parameter tractable (fpt) in the number of equations. Then we turn to a stronger criterion of representation, namely propagation completeness ("PC") --- while AC only covers the variables of S, now all the variables in F (the variables in S plus auxiliary variables) are considered for PC. We show that the standard translation actually yields a PC representation for one equation, but fails so for two equations (in fact arbitrarily badly). We show that with a more intelligent translation we can also easily compute a translation to PC for two equations. We conjecture that computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing proof of the transformation from AC-representations to monotone circuits, improved wording and literature review; 3rd v. updated literature, strengthened treatment of monotonisation, improved discussions; 4th v. update of literature, discussions and formulations, more details and examples; conference v. to appear LATA 201

    Fiscal Policy in a Tractable Liquidity-Constrained Economy

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    In this paper, we analyse the effects of transitory fiscal expansions when public debt is used as liquidity by the private sector. Aggregate shocks are introduced into a tractable flexible-price, incomplete-market economy where heterogenous, infinitely-lived agents face occasionally binding borrowing constraints and store wealth to smooth out idiosyncratic income fluctuations. Debt-financed increases in public spending facilitate self insurance by bond holders and may crowd in private consumption. The implied higher stock of liquidity also loosens the borrowing constraints faced by firms, thereby raising labour demand and possibly the real wage. Whether private consumption and wages actually rise or fall ultimately depends on the relative strengths of the liquidity and wealth effects that arise following the shock. The expansionary effects of tax cuts are also discussed. Classification-JEL: E21; E62.Borrowing constraints; Public Debt; Fiscal Policy Shocks.
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