Conjunctive Normal Form

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Sinisa Todorovic - One of the best experts on this subject based on the ideXlab platform.

  • pel cnf probabilistic event logic Conjunctive Normal Form for video interpretation
    International Conference on Computer Vision, 2011
    Co-Authors: Joe Selman, Mohamed R Amer, Alan Fern, Sinisa Todorovic
    Abstract:

    This is a theoretical paper that proves that probabilistic event logic (PEL) is MAP-equivalent to its Conjunctive Normal Form (PEL-CNF). This allows us to address the NP-hard MAP inference for PEL in a principled manner. We first map the confidence-weighted Formulas from a PEL knowledge base to PEL-CNF, and then conduct MAP inference for PEL-CNF using stochastic local search. Our MAP inference leverages the spanning-interval data structure for compactly representing and manipulating entire sets of time intervals without enumerating them. For experimental evaluation, we use the specific domain of volleyball videos. Our experiments demonstrate that the MAP inference for PEL-CNF successfully detects and localizes volleyball events in the face of different types of synthetic noise introduced in the ground-truth video annotations.

  • ICCV Workshops - PEL-CNF: Probabilistic event logic Conjunctive Normal Form for video interpretation
    2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops), 2011
    Co-Authors: Joe Selman, Mohamed R Amer, Alan Fern, Sinisa Todorovic
    Abstract:

    This is a theoretical paper that proves that probabilistic event logic (PEL) is MAP-equivalent to its Conjunctive Normal Form (PEL-CNF). This allows us to address the NP-hard MAP inference for PEL in a principled manner. We first map the confidence-weighted Formulas from a PEL knowledge base to PEL-CNF, and then conduct MAP inference for PEL-CNF using stochastic local search. Our MAP inference leverages the spanning-interval data structure for compactly representing and manipulating entire sets of time intervals without enumerating them. For experimental evaluation, we use the specific domain of volleyball videos. Our experiments demonstrate that the MAP inference for PEL-CNF successfully detects and localizes volleyball events in the face of different types of synthetic noise introduced in the ground-truth video annotations.

Peter Steinke - One of the best experts on this subject based on the ideXlab platform.

  • KI - A compact encoding of pseudo-boolean constraints into SAT
    Lecture Notes in Computer Science, 2012
    Co-Authors: Steffen Hölldobler, Norbert Manthey, Peter Steinke
    Abstract:

    Many different encodings for pseudo-Boolean constraints into the Boolean satisfiability problem have been proposed in the past. In this work we present a novel small sized and simple to implement encoding. The encoding maintains generalized arc consistency by unit propagation and results in a Formula in Conjunctive Normal Form that is linear in size with respect to the number of input variables. Experimental data confirms the advantages of the encoding over existing ones for most of the relevant pseudo-Boolean instances.

T Castell - One of the best experts on this subject based on the ideXlab platform.

  • computation of prime implicates and prime implicants by a variant of the davis and putnam procedure
    International Conference on Tools with Artificial Intelligence, 1996
    Co-Authors: T Castell
    Abstract:

    The problem is the transFormation of a Conjunctive Normal Form (CNF) into a minimized (for the inclusion operator) disjunctive Normal Form (DNF) and vice versa. This operation is called the unionist product. For a CNF (resp. DNF), one pass of the unionist product provides the prime implicants (resp. implicates); two passes provide the prime implicates (resp. implicants). An algorithm built upon the classical Davis and Putnam procedure is presented for calculating, without the explicit minimization for the inclusion, this unionist product.

  • ICTAI - Computation of prime implicates and prime implicants by a variant of the Davis and Putnam procedure
    Proceedings Eighth IEEE International Conference on Tools with Artificial Intelligence, 1996
    Co-Authors: T Castell
    Abstract:

    The problem is the transFormation of a Conjunctive Normal Form (CNF) into a minimized (for the inclusion operator) disjunctive Normal Form (DNF) and vice versa. This operation is called the unionist product. For a CNF (resp. DNF), one pass of the unionist product provides the prime implicants (resp. implicates); two passes provide the prime implicates (resp. implicants). An algorithm built upon the classical Davis and Putnam procedure is presented for calculating, without the explicit minimization for the inclusion, this unionist product.

Joe Selman - One of the best experts on this subject based on the ideXlab platform.

  • pel cnf probabilistic event logic Conjunctive Normal Form for video interpretation
    International Conference on Computer Vision, 2011
    Co-Authors: Joe Selman, Mohamed R Amer, Alan Fern, Sinisa Todorovic
    Abstract:

    This is a theoretical paper that proves that probabilistic event logic (PEL) is MAP-equivalent to its Conjunctive Normal Form (PEL-CNF). This allows us to address the NP-hard MAP inference for PEL in a principled manner. We first map the confidence-weighted Formulas from a PEL knowledge base to PEL-CNF, and then conduct MAP inference for PEL-CNF using stochastic local search. Our MAP inference leverages the spanning-interval data structure for compactly representing and manipulating entire sets of time intervals without enumerating them. For experimental evaluation, we use the specific domain of volleyball videos. Our experiments demonstrate that the MAP inference for PEL-CNF successfully detects and localizes volleyball events in the face of different types of synthetic noise introduced in the ground-truth video annotations.

  • ICCV Workshops - PEL-CNF: Probabilistic event logic Conjunctive Normal Form for video interpretation
    2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops), 2011
    Co-Authors: Joe Selman, Mohamed R Amer, Alan Fern, Sinisa Todorovic
    Abstract:

    This is a theoretical paper that proves that probabilistic event logic (PEL) is MAP-equivalent to its Conjunctive Normal Form (PEL-CNF). This allows us to address the NP-hard MAP inference for PEL in a principled manner. We first map the confidence-weighted Formulas from a PEL knowledge base to PEL-CNF, and then conduct MAP inference for PEL-CNF using stochastic local search. Our MAP inference leverages the spanning-interval data structure for compactly representing and manipulating entire sets of time intervals without enumerating them. For experimental evaluation, we use the specific domain of volleyball videos. Our experiments demonstrate that the MAP inference for PEL-CNF successfully detects and localizes volleyball events in the face of different types of synthetic noise introduced in the ground-truth video annotations.

Steffen Hölldobler - One of the best experts on this subject based on the ideXlab platform.

  • KI - A compact encoding of pseudo-boolean constraints into SAT
    Lecture Notes in Computer Science, 2012
    Co-Authors: Steffen Hölldobler, Norbert Manthey, Peter Steinke
    Abstract:

    Many different encodings for pseudo-Boolean constraints into the Boolean satisfiability problem have been proposed in the past. In this work we present a novel small sized and simple to implement encoding. The encoding maintains generalized arc consistency by unit propagation and results in a Formula in Conjunctive Normal Form that is linear in size with respect to the number of input variables. Experimental data confirms the advantages of the encoding over existing ones for most of the relevant pseudo-Boolean instances.