The Proof-Search Problem between Bounded-Width Resolution and Bounded-Degree Semi-algebraic Proofs

  • Albert Atserias
Conference paper

DOI: 10.1007/978-3-642-39071-5_1

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7962)
Cite this paper as:
Atserias A. (2013) The Proof-Search Problem between Bounded-Width Resolution and Bounded-Degree Semi-algebraic Proofs. In: Järvisalo M., Van Gelder A. (eds) Theory and Applications of Satisfiability Testing – SAT 2013. SAT 2013. Lecture Notes in Computer Science, vol 7962. Springer, Berlin, Heidelberg

Abstract

In recent years there has been some progress in our understanding of the proof-search problem for very low-depth proof systems, e.g. proof systems that manipulate formulas of very low complexity such as clauses (i.e. resolution), DNF-formulas (i.e. R(k) systems), or polynomial inequalities (i.e. semi-algebraic proof systems). In this talk I will overview this progress. I will start with bounded-width resolution, whose specialized proof-search algorithm is as easy as uninteresting, but whose proof-search problem is unintentionally solved by certain versions of conflict-driven clause-learning algorithms with restarts. I will continue with R(k) systems, whose proof-search problem turned out to hide the complexity of certain two-player games of interest in the area of systems synthesis and verification. And I will close with bounded-degree semi-algebraic proof systems, whose proof-search problem turned out to hide the complexity of systems of linear equations over finite fields, among other problems.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Albert Atserias
    • 1
  1. 1.Universitat Politècnica de CatalunyaBarcelonaSpain

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