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The complexity of weighted and unweighted #CSP

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Andrei Bulatov, Martin Dyer, Leslie Ann Goldberg, Markus Jalsenius, Mark Jerrum, David Richerby

Computational Complexity · Submitted 15 May 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, we show that a recent dichotomy for unweighted #CSP can be extended to rational-weighted #CSP.

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arXiv ID1005.2678 (version 2)
Pith IDEXDZQ5LU, Pith's permanent record of this paper and its review
CitationAndrei Bulatov, David Richerby, Leslie Ann Goldberg, Mark Jerrum, Markus Jalsenius, Martin Dyer. "The complexity of weighted and unweighted #CSP." arXiv:1005.2678 (2010). https://pith.science/paper/EXDZQ5LU
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,880 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.75 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We give some reductions among problems in (nonnegative) weighted #CSP which restrict the class of functions that needs to be considered in computational complexity studies. Our reductions can be applied to both exact and approximate computation. In particular, we show that a recent dichotomy for unweighted #CSP can be extended to rational-weighted #CSP.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We give some reductions among problems in (nonnegative) weighted #CSP which restrict the class of functions that needs to be considered in computational complexity studies. contribution 0.99 0.94 0.23 asserted 1.00
s1 Our reductions can be applied to both exact and approximate computation. result 0.42 0.85 0.08 asserted 0.97
s2 In particular, we show that a recent dichotomy for unweighted #CSP can be extended to rational-weighted #CSP. result 0.90 0.92 0.69 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We give some reductions among problems in (nonnegative) weighted #CSP which restrict the class of functions that needs to be considered in computational complexity studies. Our reductions can be applied to both exact and approximate computation. In particular, we show that a recent dichotomy for unweighted #CSP can be extended to rational-weighted #CSP.

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1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as background 1 paper
  • The investigation of CSP includes at least the following major bran­ches: Decision Problems — whether a solution exists [ref] ; Optimization Problems — finding a solution that satisfies the most constraints (or in the weighted case achieving the highest total weight) [ref] ; and Counting Problems — to count the number of solutions, including its weighted version [ref] .

    Non-negative Weighted #CSPs: An Effective Complexity Dichotomy · Introduction · 1.00

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