Now showing items 1-3 of 3

    • Feasible interpolation for polynomial calculus and sums-of-squares 

      Hakoniemi, Tuomas Antero (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020)
      Conference report
      Open Access
      We prove that both Polynomial Calculus and Sums-of-Squares proof systems admit a strong form of feasible interpolation property for sets of polynomial equality constraints. Precisely, given two sets P(x, z) and Q(y, z) of ...
    • Size bounds for algebraic and semialgebraic proof systems 

      Hakoniemi, Tuomas Antero (Universitat Politècnica de Catalunya, 2022-03-25)
      Doctoral thesis
      Open Access
      This thesis concerns the proof complexity of algebraic and semialgebraic proof systems Polynomial Calculus, Sums-of-Squares and Sherali-Adams. The most studied complexity measure for these systems is the degree of the ...
    • Size-degree trade-offs for Sums-of-Squares and Positivstellensatz proofs 

      Atserias, Albert; Hakoniemi, Tuomas Antero (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019)
      Conference report
      Open Access
      We show that if a system of degree-k polynomial constraints on n Boolean variables has a Sums-of-Squares (SOS) proof of unsatisfiability with at most s many monomials, then it also has one whose degree is of the order of ...