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Probabilistic Model Counting with Short XORs

  • Dimitris Achlioptas
  • Panos Theodoropoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10491)

Abstract

The idea of counting the number of satisfying truth assignments (models) of a formula by adding random parity constraints can be traced back to the seminal work of Valiant and Vazirani, showing that NP is as easy as detecting unique solutions. While theoretically sound, the random parity constraints in that construction have the following drawback: each constraint, on average, involves half of all variables. As a result, the branching factor associated with searching for models that also satisfy the parity constraints quickly gets out of hand. In this work we prove that one can work with much shorter parity constraints and still get rigorous mathematical guarantees, especially when the number of models is large so that many constraints need to be added. Our work is based on the realization that the essential feature for random systems of parity constraints to be useful in probabilistic model counting is that the geometry of their set of solutions resembles an error-correcting code.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of California Santa CruzSanta CruzUSA
  2. 2.Department of Informatics and TelecommunicationsUniversity of AthensAthensGreece

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